linear_algebra.tensor_product ⟷ Mathlib.LinearAlgebra.TensorProduct.Basic

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

@@ -984,7 +984,7 @@ protected theorem map_pow (f : M →ₗ[R] M) (g : N →ₗ[R] N) (n : ℕ) :
   by
   induction' n with n ih
   · simp only [pow_zero, map_one]
-  · simp only [pow_succ', ih, map_mul]
+  · simp only [pow_succ, ih, map_mul]
 #align tensor_product.map_pow TensorProduct.map_pow
 -/
 

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

@@ -1446,14 +1446,14 @@ variable {M}
 #print LinearMap.rTensor_pow /-
 @[simp]
 theorem rTensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rTensor N ^ n = (f ^ n).rTensor N := by
-  have h := TensorProduct.map_pow f (id : N →ₗ[R] N) n; rwa [id_pow] at h 
+  have h := TensorProduct.map_pow f (id : N →ₗ[R] N) n; rwa [id_pow] at h
 #align linear_map.rtensor_pow LinearMap.rTensor_pow
 -/
 
 #print LinearMap.lTensor_pow /-
 @[simp]
 theorem lTensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.lTensor M ^ n = (f ^ n).lTensor M := by
-  have h := TensorProduct.map_pow (id : M →ₗ[R] M) f n; rwa [id_pow] at h 
+  have h := TensorProduct.map_pow (id : M →ₗ[R] M) f n; rwa [id_pow] at h
 #align linear_map.ltensor_pow LinearMap.lTensor_pow
 -/
 

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

@@ -468,13 +468,21 @@ open scoped BigOperators
 
 #print TensorProduct.sum_tmul /-
 theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
-    (∑ a in s, m a) ⊗ₜ[R] n = ∑ a in s, m a ⊗ₜ[R] n := by classical
+    (∑ a in s, m a) ⊗ₜ[R] n = ∑ a in s, m a ⊗ₜ[R] n := by
+  classical
+  induction' s using Finset.induction with a s has ih h
+  · simp
+  · simp [Finset.sum_insert has, add_tmul, ih]
 #align tensor_product.sum_tmul TensorProduct.sum_tmul
 -/
 
 #print TensorProduct.tmul_sum /-
 theorem tmul_sum (m : M) {α : Type _} (s : Finset α) (n : α → N) :
-    m ⊗ₜ[R] ∑ a in s, n a = ∑ a in s, m ⊗ₜ[R] n a := by classical
+    m ⊗ₜ[R] ∑ a in s, n a = ∑ a in s, m ⊗ₜ[R] n a := by
+  classical
+  induction' s using Finset.induction with a s has ih h
+  · simp
+  · simp [Finset.sum_insert has, tmul_add, ih]
 #align tensor_product.tmul_sum TensorProduct.tmul_sum
 -/
 

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

@@ -468,21 +468,13 @@ open scoped BigOperators
 
 #print TensorProduct.sum_tmul /-
 theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
-    (∑ a in s, m a) ⊗ₜ[R] n = ∑ a in s, m a ⊗ₜ[R] n := by
-  classical
-  induction' s using Finset.induction with a s has ih h
-  · simp
-  · simp [Finset.sum_insert has, add_tmul, ih]
+    (∑ a in s, m a) ⊗ₜ[R] n = ∑ a in s, m a ⊗ₜ[R] n := by classical
 #align tensor_product.sum_tmul TensorProduct.sum_tmul
 -/
 
 #print TensorProduct.tmul_sum /-
 theorem tmul_sum (m : M) {α : Type _} (s : Finset α) (n : α → N) :
-    m ⊗ₜ[R] ∑ a in s, n a = ∑ a in s, m ⊗ₜ[R] n a := by
-  classical
-  induction' s using Finset.induction with a s has ih h
-  · simp
-  · simp [Finset.sum_insert has, tmul_add, ih]
+    m ⊗ₜ[R] ∑ a in s, n a = ∑ a in s, m ⊗ₜ[R] n a := by classical
 #align tensor_product.tmul_sum TensorProduct.tmul_sum
 -/
 

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

@@ -1488,11 +1488,9 @@ def Neg.aux : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
 
 variable {R}
 
-#print TensorProduct.Neg.aux_of /-
 theorem Neg.aux_of (m : M) (n : N) : Neg.aux R (FreeAddMonoid.of (m, n)) = (-m) ⊗ₜ[R] n :=
   rfl
 #align tensor_product.neg.aux_of TensorProduct.Neg.aux_of
--/
 
 instance : Neg (M ⊗[R] N)
     where neg :=

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

@@ -3,8 +3,8 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro
 -/
-import Mathbin.GroupTheory.Congruence
-import Mathbin.Algebra.Module.Submodule.Bilinear
+import GroupTheory.Congruence
+import Algebra.Module.Submodule.Bilinear
 
 #align_import linear_algebra.tensor_product from "leanprover-community/mathlib"@"88fcdc3da43943f5b01925deddaa5bf0c0e85e4e"
 

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

@@ -328,7 +328,7 @@ instance leftDistribMulAction : DistribMulAction R' (M ⊗[R] N) :=
   have : ∀ (r : R') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   { smul := (· • ·)
     smul_add := fun r x y => TensorProduct.smul_add r x y
-    mul_smul := fun r s x =>
+    hMul_smul := fun r s x =>
       TensorProduct.induction_on x (by simp_rw [TensorProduct.smul_zero])
         (fun m n => by simp_rw [this, mul_smul]) fun x y ihx ihy => by
         simp_rw [TensorProduct.smul_add]; rw [ihx, ihy]

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -385,13 +385,15 @@ variable {R'₂ : Type _} [Monoid R'₂] [DistribMulAction R'₂ M]
 
 variable [SMulCommClass R R'₂ M]
 
+#print TensorProduct.smulCommClass_left /-
 /-- `smul_comm_class R' R'₂ M` implies `smul_comm_class R' R'₂ (M ⊗[R] N)` -/
-instance sMulCommClass_left [SMulCommClass R' R'₂ M] : SMulCommClass R' R'₂ (M ⊗[R] N)
+instance smulCommClass_left [SMulCommClass R' R'₂ M] : SMulCommClass R' R'₂ (M ⊗[R] N)
     where smul_comm r' r'₂ x :=
     TensorProduct.induction_on x (by simp_rw [TensorProduct.smul_zero])
       (fun m n => by simp_rw [smul_tmul', smul_comm]) fun x y ihx ihy => by
       simp_rw [TensorProduct.smul_add]; rw [ihx, ihy]
-#align tensor_product.smul_comm_class_left TensorProduct.sMulCommClass_left
+#align tensor_product.smul_comm_class_left TensorProduct.smulCommClass_left
+-/
 
 variable [SMul R'₂ R']
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/88fcdc3da43943f5b01925deddaa5bf0c0e85e4e

@@ -6,7 +6,7 @@ Authors: Kenny Lau, Mario Carneiro
 import Mathbin.GroupTheory.Congruence
 import Mathbin.Algebra.Module.Submodule.Bilinear
 
-#align_import linear_algebra.tensor_product from "leanprover-community/mathlib"@"832f7b9162039c28b9361289c8681f155cae758f"
+#align_import linear_algebra.tensor_product from "leanprover-community/mathlib"@"88fcdc3da43943f5b01925deddaa5bf0c0e85e4e"
 
 /-!
 # Tensor product of modules over commutative semirings.
@@ -383,7 +383,17 @@ section
 -- Like `R'`, `R'₂` provides a `distrib_mul_action R'₂ (M ⊗[R] N)`
 variable {R'₂ : Type _} [Monoid R'₂] [DistribMulAction R'₂ M]
 
-variable [SMulCommClass R R'₂ M] [SMul R'₂ R']
+variable [SMulCommClass R R'₂ M]
+
+/-- `smul_comm_class R' R'₂ M` implies `smul_comm_class R' R'₂ (M ⊗[R] N)` -/
+instance sMulCommClass_left [SMulCommClass R' R'₂ M] : SMulCommClass R' R'₂ (M ⊗[R] N)
+    where smul_comm r' r'₂ x :=
+    TensorProduct.induction_on x (by simp_rw [TensorProduct.smul_zero])
+      (fun m n => by simp_rw [smul_tmul', smul_comm]) fun x y ihx ihy => by
+      simp_rw [TensorProduct.smul_add]; rw [ihx, ihy]
+#align tensor_product.smul_comm_class_left TensorProduct.sMulCommClass_left
+
+variable [SMul R'₂ R']
 
 #print TensorProduct.isScalarTower_left /-
 /-- `is_scalar_tower R'₂ R' M` implies `is_scalar_tower R'₂ R' (M ⊗[R] N)` -/

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

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro
-
-! This file was ported from Lean 3 source module linear_algebra.tensor_product
-! leanprover-community/mathlib commit 832f7b9162039c28b9361289c8681f155cae758f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.GroupTheory.Congruence
 import Mathbin.Algebra.Module.Submodule.Bilinear
 
+#align_import linear_algebra.tensor_product from "leanprover-community/mathlib"@"832f7b9162039c28b9361289c8681f155cae758f"
+
 /-!
 # Tensor product of modules over commutative semirings.
 

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

@@ -722,7 +722,7 @@ theorem curry_injective : Function.Injective (curry : (M ⊗[R] N →ₗ[R] P) 
 theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
     (H : ∀ x y z, g (x ⊗ₜ y ⊗ₜ z) = h (x ⊗ₜ y ⊗ₜ z)) : g = h :=
   by
-  ext (x y z)
+  ext x y z
   exact H x y z
 #align tensor_product.ext_threefold TensorProduct.ext_threefold
 -/
@@ -732,7 +732,7 @@ theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
 theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
     (H : ∀ w x y z, g (w ⊗ₜ x ⊗ₜ y ⊗ₜ z) = h (w ⊗ₜ x ⊗ₜ y ⊗ₜ z)) : g = h :=
   by
-  ext (w x y z)
+  ext w x y z
   exact H w x y z
 #align tensor_product.ext_fourfold TensorProduct.ext_fourfold
 -/
@@ -743,7 +743,7 @@ form (m ⊗ₜ n) ⊗ₜ (p ⊗ₜ q) are equal. -/
 theorem ext_fourfold' {φ ψ : (M ⊗[R] N) ⊗[R] P ⊗[R] Q →ₗ[R] S}
     (H : ∀ w x y z, φ (w ⊗ₜ x ⊗ₜ (y ⊗ₜ z)) = ψ (w ⊗ₜ x ⊗ₜ (y ⊗ₜ z))) : φ = ψ :=
   by
-  ext (m n p q)
+  ext m n p q
   exact H m n p q
 #align tensor_product.ext_fourfold' TensorProduct.ext_fourfold'
 -/
@@ -1243,9 +1243,8 @@ attribute [local ext] TensorProduct.ext
 def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
     where
   toFun := lTensor M
-  map_add' f g := by ext (x y);
-    simp only [compr₂_apply, mk_apply, add_apply, ltensor_tmul, tmul_add]
-  map_smul' r f := by dsimp; ext (x y);
+  map_add' f g := by ext x y; simp only [compr₂_apply, mk_apply, add_apply, ltensor_tmul, tmul_add]
+  map_smul' r f := by dsimp; ext x y;
     simp only [compr₂_apply, mk_apply, tmul_smul, smul_apply, ltensor_tmul]
 #align linear_map.ltensor_hom LinearMap.lTensorHom
 -/
@@ -1255,9 +1254,8 @@ def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
 def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
     where
   toFun f := f.rTensor M
-  map_add' f g := by ext (x y);
-    simp only [compr₂_apply, mk_apply, add_apply, rtensor_tmul, add_tmul]
-  map_smul' r f := by dsimp; ext (x y);
+  map_add' f g := by ext x y; simp only [compr₂_apply, mk_apply, add_apply, rtensor_tmul, add_tmul]
+  map_smul' r f := by dsimp; ext x y;
     simp only [compr₂_apply, mk_apply, smul_tmul, tmul_smul, smul_apply, rtensor_tmul]
 #align linear_map.rtensor_hom LinearMap.rTensorHom
 -/
@@ -1319,7 +1317,7 @@ theorem rTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).rTensor M = r • f
 -/
 
 #print LinearMap.lTensor_comp /-
-theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) := by ext (m n);
+theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) := by ext m n;
   simp only [compr₂_apply, mk_apply, comp_apply, ltensor_tmul]
 #align linear_map.ltensor_comp LinearMap.lTensor_comp
 -/
@@ -1331,7 +1329,7 @@ theorem lTensor_comp_apply (x : M ⊗[R] N) :
 -/
 
 #print LinearMap.rTensor_comp /-
-theorem rTensor_comp : (g.comp f).rTensor M = (g.rTensor M).comp (f.rTensor M) := by ext (m n);
+theorem rTensor_comp : (g.comp f).rTensor M = (g.rTensor M).comp (f.rTensor M) := by ext m n;
   simp only [compr₂_apply, mk_apply, comp_apply, rtensor_tmul]
 #align linear_map.rtensor_comp LinearMap.rTensor_comp
 -/

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

@@ -58,8 +58,6 @@ variable [DistribMulAction R' M]
 
 variable [Module R'' M]
 
-include R
-
 variable (M N)
 
 namespace TensorProduct
@@ -106,10 +104,8 @@ def TensorProduct : Type _ :=
 
 variable {R}
 
--- mathport name: tensor_product.infer
 scoped[TensorProduct] infixl:100 " ⊗ " => TensorProduct hole!
 
--- mathport name: tensor_product
 scoped[TensorProduct] notation:100 M " ⊗[" R "] " N:100 => TensorProduct R M N
 
 namespace TensorProduct
@@ -140,44 +136,52 @@ def tmul (m : M) (n : N) : M ⊗[R] N :=
 
 variable {R}
 
--- mathport name: «expr ⊗ₜ »
 infixl:100 " ⊗ₜ " => tmul _
 
--- mathport name: «expr ⊗ₜ[ ] »
 notation:100 x " ⊗ₜ[" R "] " y:100 => tmul R x y
 
+#print TensorProduct.induction_on /-
 @[elab_as_elim]
 protected theorem induction_on {C : M ⊗[R] N → Prop} (z : M ⊗[R] N) (C0 : C 0)
     (C1 : ∀ {x y}, C <| x ⊗ₜ[R] y) (Cp : ∀ {x y}, C x → C y → C (x + y)) : C z :=
   AddCon.induction_on z fun x =>
     FreeAddMonoid.recOn x C0 fun ⟨m, n⟩ y ih => by rw [AddCon.coe_add]; exact Cp C1 ih
 #align tensor_product.induction_on TensorProduct.induction_on
+-/
 
 variable (M)
 
+#print TensorProduct.zero_tmul /-
 @[simp]
 theorem zero_tmul (n : N) : (0 : M) ⊗ₜ[R] n = 0 :=
   Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_zero_left _
 #align tensor_product.zero_tmul TensorProduct.zero_tmul
+-/
 
 variable {M}
 
+#print TensorProduct.add_tmul /-
 theorem add_tmul (m₁ m₂ : M) (n : N) : (m₁ + m₂) ⊗ₜ n = m₁ ⊗ₜ n + m₂ ⊗ₜ[R] n :=
   Eq.symm <| Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_add_left _ _ _
 #align tensor_product.add_tmul TensorProduct.add_tmul
+-/
 
 variable (N)
 
+#print TensorProduct.tmul_zero /-
 @[simp]
 theorem tmul_zero (m : M) : m ⊗ₜ[R] (0 : N) = 0 :=
   Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_zero_right _
 #align tensor_product.tmul_zero TensorProduct.tmul_zero
+-/
 
 variable {N}
 
+#print TensorProduct.tmul_add /-
 theorem tmul_add (m : M) (n₁ n₂ : N) : m ⊗ₜ (n₁ + n₂) = m ⊗ₜ n₁ + m ⊗ₜ[R] n₂ :=
   Eq.symm <| Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_add_right _ _ _
 #align tensor_product.tmul_add TensorProduct.tmul_add
+-/
 
 section
 
@@ -201,6 +205,7 @@ class CompatibleSMul [DistribMulAction R' N] where
 
 end
 
+#print TensorProduct.CompatibleSMul.isScalarTower /-
 /-- Note that this provides the default `compatible_smul R R M N` instance through
 `mul_action.is_scalar_tower.left`. -/
 instance (priority := 100) CompatibleSMul.isScalarTower [SMul R' R] [IsScalarTower R' R M]
@@ -211,27 +216,35 @@ instance (priority := 100) CompatibleSMul.isScalarTower [SMul R' R] [IsScalarTow
     rw [← smul_assoc, ← smul_assoc]
     exact Quotient.sound' <| AddConGen.Rel.of _ _ <| eqv.of_smul _ _ _⟩
 #align tensor_product.compatible_smul.is_scalar_tower TensorProduct.CompatibleSMul.isScalarTower
+-/
 
+#print TensorProduct.smul_tmul /-
 /-- `smul` can be moved from one side of the product to the other .-/
 theorem smul_tmul [DistribMulAction R' N] [CompatibleSMul R R' M N] (r : R') (m : M) (n : N) :
     (r • m) ⊗ₜ n = m ⊗ₜ[R] (r • n) :=
   CompatibleSMul.smul_tmul _ _ _
 #align tensor_product.smul_tmul TensorProduct.smul_tmul
+-/
 
+#print TensorProduct.SMul.aux /-
 /-- Auxiliary function to defining scalar multiplication on tensor product. -/
 def SMul.aux {R' : Type _} [SMul R' M] (r : R') : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
   FreeAddMonoid.lift fun p : M × N => (r • p.1) ⊗ₜ p.2
 #align tensor_product.smul.aux TensorProduct.SMul.aux
+-/
 
+#print TensorProduct.SMul.aux_of /-
 theorem SMul.aux_of {R' : Type _} [SMul R' M] (r : R') (m : M) (n : N) :
     SMul.aux r (FreeAddMonoid.of (m, n)) = (r • m) ⊗ₜ[R] n :=
   rfl
 #align tensor_product.smul.aux_of TensorProduct.SMul.aux_of
+-/
 
 variable [SMulCommClass R R' M]
 
 variable [SMulCommClass R R'' M]
 
+#print TensorProduct.leftHasSMul /-
 /-- Given two modules over a commutative semiring `R`, if one of the factors carries a
 (distributive) action of a second type of scalars `R'`, which commutes with the action of `R`, then
 the tensor product (over `R`) carries an action of `R'`.
@@ -263,37 +276,48 @@ instance leftHasSMul : SMul R' (M ⊗[R] N) :=
         | _, _, eqv.add_comm x y =>
           (AddCon.ker_rel _).2 <| by simp_rw [AddMonoidHom.map_add, add_comm]⟩
 #align tensor_product.left_has_smul TensorProduct.leftHasSMul
+-/
 
 instance : SMul R (M ⊗[R] N) :=
   TensorProduct.leftHasSMul
 
+#print TensorProduct.smul_zero /-
 protected theorem smul_zero (r : R') : (r • 0 : M ⊗[R] N) = 0 :=
   AddMonoidHom.map_zero _
 #align tensor_product.smul_zero TensorProduct.smul_zero
+-/
 
+#print TensorProduct.smul_add /-
 protected theorem smul_add (r : R') (x y : M ⊗[R] N) : r • (x + y) = r • x + r • y :=
   AddMonoidHom.map_add _ _ _
 #align tensor_product.smul_add TensorProduct.smul_add
+-/
 
+#print TensorProduct.zero_smul /-
 protected theorem zero_smul (x : M ⊗[R] N) : (0 : R'') • x = 0 :=
   have : ∀ (r : R'') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   TensorProduct.induction_on x (by rw [TensorProduct.smul_zero])
     (fun m n => by rw [this, zero_smul, zero_tmul]) fun x y ihx ihy => by
     rw [TensorProduct.smul_add, ihx, ihy, add_zero]
 #align tensor_product.zero_smul TensorProduct.zero_smul
+-/
 
+#print TensorProduct.one_smul /-
 protected theorem one_smul (x : M ⊗[R] N) : (1 : R') • x = x :=
   have : ∀ (r : R') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   TensorProduct.induction_on x (by rw [TensorProduct.smul_zero]) (fun m n => by rw [this, one_smul])
     fun x y ihx ihy => by rw [TensorProduct.smul_add, ihx, ihy]
 #align tensor_product.one_smul TensorProduct.one_smul
+-/
 
+#print TensorProduct.add_smul /-
 protected theorem add_smul (r s : R'') (x : M ⊗[R] N) : (r + s) • x = r • x + s • x :=
   have : ∀ (r : R'') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   TensorProduct.induction_on x (by simp_rw [TensorProduct.smul_zero, add_zero])
     (fun m n => by simp_rw [this, add_smul, add_tmul]) fun x y ihx ihy => by
     simp_rw [TensorProduct.smul_add]; rw [ihx, ihy, add_add_add_comm]
 #align tensor_product.add_smul TensorProduct.add_smul
+-/
 
 instance : AddCommMonoid (M ⊗[R] N) :=
   { TensorProduct.addCommSemigroup _ _,
@@ -302,6 +326,7 @@ instance : AddCommMonoid (M ⊗[R] N) :=
     nsmul_zero := by simp [TensorProduct.zero_smul]
     nsmul_succ := by simp [Nat.succ_eq_one_add, TensorProduct.one_smul, TensorProduct.add_smul] }
 
+#print TensorProduct.leftDistribMulAction /-
 instance leftDistribMulAction : DistribMulAction R' (M ⊗[R] N) :=
   have : ∀ (r : R') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   { smul := (· • ·)
@@ -313,23 +338,30 @@ instance leftDistribMulAction : DistribMulAction R' (M ⊗[R] N) :=
     one_smul := TensorProduct.one_smul
     smul_zero := TensorProduct.smul_zero }
 #align tensor_product.left_distrib_mul_action TensorProduct.leftDistribMulAction
+-/
 
 instance : DistribMulAction R (M ⊗[R] N) :=
   TensorProduct.leftDistribMulAction
 
+#print TensorProduct.smul_tmul' /-
 theorem smul_tmul' (r : R') (m : M) (n : N) : r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n :=
   rfl
 #align tensor_product.smul_tmul' TensorProduct.smul_tmul'
+-/
 
+#print TensorProduct.tmul_smul /-
 @[simp]
 theorem tmul_smul [DistribMulAction R' N] [CompatibleSMul R R' M N] (r : R') (x : M) (y : N) :
     x ⊗ₜ (r • y) = r • x ⊗ₜ[R] y :=
   (smul_tmul _ _ _).symm
 #align tensor_product.tmul_smul TensorProduct.tmul_smul
+-/
 
+#print TensorProduct.smul_tmul_smul /-
 theorem smul_tmul_smul (r s : R) (m : M) (n : N) : (r • m) ⊗ₜ[R] (s • n) = (r * s) • m ⊗ₜ[R] n := by
   simp only [tmul_smul, smul_tmul, mul_smul]
 #align tensor_product.smul_tmul_smul TensorProduct.smul_tmul_smul
+-/
 
 #print TensorProduct.leftModule /-
 instance leftModule : Module R'' (M ⊗[R] N) :=
@@ -356,6 +388,7 @@ variable {R'₂ : Type _} [Monoid R'₂] [DistribMulAction R'₂ M]
 
 variable [SMulCommClass R R'₂ M] [SMul R'₂ R']
 
+#print TensorProduct.isScalarTower_left /-
 /-- `is_scalar_tower R'₂ R' M` implies `is_scalar_tower R'₂ R' (M ⊗[R] N)` -/
 instance isScalarTower_left [IsScalarTower R'₂ R' M] : IsScalarTower R'₂ R' (M ⊗[R] N) :=
   ⟨fun s r x =>
@@ -363,11 +396,13 @@ instance isScalarTower_left [IsScalarTower R'₂ R' M] : IsScalarTower R'₂ R'
       (fun m n => by rw [smul_tmul', smul_tmul', smul_tmul', smul_assoc]) fun x y ihx ihy => by
       rw [smul_add, smul_add, smul_add, ihx, ihy]⟩
 #align tensor_product.is_scalar_tower_left TensorProduct.isScalarTower_left
+-/
 
 variable [DistribMulAction R'₂ N] [DistribMulAction R' N]
 
 variable [CompatibleSMul R R'₂ M N] [CompatibleSMul R R' M N]
 
+#print TensorProduct.isScalarTower_right /-
 /-- `is_scalar_tower R'₂ R' N` implies `is_scalar_tower R'₂ R' (M ⊗[R] N)` -/
 instance isScalarTower_right [IsScalarTower R'₂ R' N] : IsScalarTower R'₂ R' (M ⊗[R] N) :=
   ⟨fun s r x =>
@@ -375,42 +410,54 @@ instance isScalarTower_right [IsScalarTower R'₂ R' N] : IsScalarTower R'₂ R'
       (fun m n => by rw [← tmul_smul, ← tmul_smul, ← tmul_smul, smul_assoc]) fun x y ihx ihy => by
       rw [smul_add, smul_add, smul_add, ihx, ihy]⟩
 #align tensor_product.is_scalar_tower_right TensorProduct.isScalarTower_right
+-/
 
 end
 
+#print TensorProduct.isScalarTower /-
 /-- A short-cut instance for the common case, where the requirements for the `compatible_smul`
 instances are sufficient. -/
 instance isScalarTower [SMul R' R] [IsScalarTower R' R M] : IsScalarTower R' R (M ⊗[R] N) :=
   TensorProduct.isScalarTower_left
 #align tensor_product.is_scalar_tower TensorProduct.isScalarTower
+-/
 
 -- or right
 variable (R M N)
 
+#print TensorProduct.mk /-
 /-- The canonical bilinear map `M → N → M ⊗[R] N`. -/
 def mk : M →ₗ[R] N →ₗ[R] M ⊗[R] N :=
   LinearMap.mk₂ R (· ⊗ₜ ·) add_tmul (fun c m n => by rw [smul_tmul, tmul_smul]) tmul_add tmul_smul
 #align tensor_product.mk TensorProduct.mk
+-/
 
 variable {R M N}
 
+#print TensorProduct.mk_apply /-
 @[simp]
 theorem mk_apply (m : M) (n : N) : mk R M N m n = m ⊗ₜ n :=
   rfl
 #align tensor_product.mk_apply TensorProduct.mk_apply
+-/
 
+#print TensorProduct.ite_tmul /-
 theorem ite_tmul (x₁ : M) (x₂ : N) (P : Prop) [Decidable P] :
     (if P then x₁ else 0) ⊗ₜ[R] x₂ = if P then x₁ ⊗ₜ x₂ else 0 := by split_ifs <;> simp
 #align tensor_product.ite_tmul TensorProduct.ite_tmul
+-/
 
+#print TensorProduct.tmul_ite /-
 theorem tmul_ite (x₁ : M) (x₂ : N) (P : Prop) [Decidable P] :
     (x₁ ⊗ₜ[R] if P then x₂ else 0) = if P then x₁ ⊗ₜ x₂ else 0 := by split_ifs <;> simp
 #align tensor_product.tmul_ite TensorProduct.tmul_ite
+-/
 
 section
 
 open scoped BigOperators
 
+#print TensorProduct.sum_tmul /-
 theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
     (∑ a in s, m a) ⊗ₜ[R] n = ∑ a in s, m a ⊗ₜ[R] n := by
   classical
@@ -418,7 +465,9 @@ theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
   · simp
   · simp [Finset.sum_insert has, add_tmul, ih]
 #align tensor_product.sum_tmul TensorProduct.sum_tmul
+-/
 
+#print TensorProduct.tmul_sum /-
 theorem tmul_sum (m : M) {α : Type _} (s : Finset α) (n : α → N) :
     m ⊗ₜ[R] ∑ a in s, n a = ∑ a in s, m ⊗ₜ[R] n a := by
   classical
@@ -426,11 +475,13 @@ theorem tmul_sum (m : M) {α : Type _} (s : Finset α) (n : α → N) :
   · simp
   · simp [Finset.sum_insert has, tmul_add, ih]
 #align tensor_product.tmul_sum TensorProduct.tmul_sum
+-/
 
 end
 
 variable (R M N)
 
+#print TensorProduct.span_tmul_eq_top /-
 /-- The simple (aka pure) elements span the tensor product. -/
 theorem span_tmul_eq_top : Submodule.span R {t : M ⊗[R] N | ∃ m n, m ⊗ₜ n = t} = ⊤ :=
   by
@@ -440,13 +491,16 @@ theorem span_tmul_eq_top : Submodule.span R {t : M ⊗[R] N | ∃ m n, m ⊗ₜ
   · intro m n; apply Submodule.subset_span; use m, n
   · intro t₁ t₂ ht₁ ht₂; exact Submodule.add_mem _ ht₁ ht₂
 #align tensor_product.span_tmul_eq_top TensorProduct.span_tmul_eq_top
+-/
 
+#print TensorProduct.map₂_mk_top_top_eq_top /-
 @[simp]
 theorem map₂_mk_top_top_eq_top : Submodule.map₂ (mk R M N) ⊤ ⊤ = ⊤ :=
   by
   rw [← top_le_iff, ← span_tmul_eq_top, Submodule.map₂_eq_span_image2]
   exact Submodule.span_mono fun _ ⟨m, n, h⟩ => ⟨m, n, trivial, trivial, h⟩
 #align tensor_product.map₂_mk_top_top_eq_top TensorProduct.map₂_mk_top_top_eq_top
+-/
 
 end Module
 
@@ -483,12 +537,15 @@ def liftAux : M ⊗[R] N →+ P :=
 #align tensor_product.lift_aux TensorProduct.liftAux
 -/
 
+#print TensorProduct.liftAux_tmul /-
 theorem liftAux_tmul (m n) : liftAux f (m ⊗ₜ n) = f m n :=
   rfl
 #align tensor_product.lift_aux_tmul TensorProduct.liftAux_tmul
+-/
 
 variable {f}
 
+#print TensorProduct.liftAux.smul /-
 @[simp]
 theorem liftAux.smul (r : R) (x) : liftAux f (r • x) = r • liftAux f x :=
   TensorProduct.induction_on x (smul_zero _).symm
@@ -496,6 +553,7 @@ theorem liftAux.smul (r : R) (x) : liftAux f (r • x) = r • liftAux f x :=
     fun p q ih1 ih2 => by
     rw [smul_add, (lift_aux f).map_add, ih1, ih2, (lift_aux f).map_add, smul_add]
 #align tensor_product.lift_aux.smul TensorProduct.liftAux.smul
+-/
 
 variable (f)
 
@@ -510,38 +568,53 @@ def lift : M ⊗ N →ₗ[R] P :=
 
 variable {f}
 
+#print TensorProduct.lift.tmul /-
 @[simp]
 theorem lift.tmul (x y) : lift f (x ⊗ₜ y) = f x y :=
   rfl
 #align tensor_product.lift.tmul TensorProduct.lift.tmul
+-/
 
+#print TensorProduct.lift.tmul' /-
 @[simp]
 theorem lift.tmul' (x y) : (lift f).1 (x ⊗ₜ y) = f x y :=
   rfl
 #align tensor_product.lift.tmul' TensorProduct.lift.tmul'
+-/
 
+#print TensorProduct.ext' /-
 theorem ext' {g h : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x ⊗ₜ y)) : g = h :=
   LinearMap.ext fun z =>
     TensorProduct.induction_on z (by simp_rw [LinearMap.map_zero]) H fun x y ihx ihy => by
       rw [g.map_add, h.map_add, ihx, ihy]
 #align tensor_product.ext' TensorProduct.ext'
+-/
 
+#print TensorProduct.lift.unique /-
 theorem lift.unique {g : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = f x y) : g = lift f :=
   ext' fun m n => by rw [H, lift.tmul]
 #align tensor_product.lift.unique TensorProduct.lift.unique
+-/
 
+#print TensorProduct.lift_mk /-
 theorem lift_mk : lift (mk R M N) = LinearMap.id :=
   Eq.symm <| lift.unique fun x y => rfl
 #align tensor_product.lift_mk TensorProduct.lift_mk
+-/
 
+#print TensorProduct.lift_compr₂ /-
 theorem lift_compr₂ (g : P →ₗ[R] Q) : lift (f.compr₂ g) = g.comp (lift f) :=
   Eq.symm <| lift.unique fun x y => by simp
 #align tensor_product.lift_compr₂ TensorProduct.lift_compr₂
+-/
 
+#print TensorProduct.lift_mk_compr₂ /-
 theorem lift_mk_compr₂ (f : M ⊗ N →ₗ[R] P) : lift ((mk R M N).compr₂ f) = f := by
   rw [lift_compr₂ f, lift_mk, LinearMap.comp_id]
 #align tensor_product.lift_mk_compr₂ TensorProduct.lift_mk_compr₂
+-/
 
+#print TensorProduct.ext /-
 /-- This used to be an `@[ext]` lemma, but it fails very slowly when the `ext` tactic tries to apply
 it in some cases, notably when one wants to show equality of two linear maps. The `@[ext]`
 attribute is now added locally where it is needed. Using this as the `@[ext]` lemma instead of
@@ -551,6 +624,7 @@ See note [partially-applied ext lemmas]. -/
 theorem ext {g h : M ⊗ N →ₗ[R] P} (H : (mk R M N).compr₂ g = (mk R M N).compr₂ h) : g = h := by
   rw [← lift_mk_compr₂ g, H, lift_mk_compr₂]
 #align tensor_product.ext TensorProduct.ext
+-/
 
 attribute [local ext] ext
 
@@ -569,10 +643,12 @@ def uncurry : (M →ₗ[R] N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] P :=
 
 variable {R M N P}
 
+#print TensorProduct.uncurry_apply /-
 @[simp]
 theorem uncurry_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
     uncurry R M N P f (m ⊗ₜ n) = f m n := by rw [uncurry, LinearMap.flip_apply, lift.tmul] <;> rfl
 #align tensor_product.uncurry_apply TensorProduct.uncurry_apply
+-/
 
 variable (R M N P)
 
@@ -588,53 +664,70 @@ def lift.equiv : (M →ₗ[R] N →ₗ[R] P) ≃ₗ[R] M ⊗ N →ₗ[R] P :=
 #align tensor_product.lift.equiv TensorProduct.lift.equiv
 -/
 
+#print TensorProduct.lift.equiv_apply /-
 @[simp]
 theorem lift.equiv_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
     lift.equiv R M N P f (m ⊗ₜ n) = f m n :=
   uncurry_apply f m n
 #align tensor_product.lift.equiv_apply TensorProduct.lift.equiv_apply
+-/
 
+#print TensorProduct.lift.equiv_symm_apply /-
 @[simp]
 theorem lift.equiv_symm_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) :
     (lift.equiv R M N P).symm f m n = f (m ⊗ₜ n) :=
   rfl
 #align tensor_product.lift.equiv_symm_apply TensorProduct.lift.equiv_symm_apply
+-/
 
+#print TensorProduct.lcurry /-
 /-- Given a linear map `M ⊗ N → P`, compose it with the canonical bilinear map `M → N → M ⊗ N` to
 form a bilinear map `M → N → P`. -/
 def lcurry : (M ⊗[R] N →ₗ[R] P) →ₗ[R] M →ₗ[R] N →ₗ[R] P :=
   (lift.equiv R M N P).symm
 #align tensor_product.lcurry TensorProduct.lcurry
+-/
 
 variable {R M N P}
 
+#print TensorProduct.lcurry_apply /-
 @[simp]
 theorem lcurry_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) : lcurry R M N P f m n = f (m ⊗ₜ n) :=
   rfl
 #align tensor_product.lcurry_apply TensorProduct.lcurry_apply
+-/
 
+#print TensorProduct.curry /-
 /-- Given a linear map `M ⊗ N → P`, compose it with the canonical bilinear map `M → N → M ⊗ N` to
 form a bilinear map `M → N → P`. -/
 def curry (f : M ⊗ N →ₗ[R] P) : M →ₗ[R] N →ₗ[R] P :=
   lcurry R M N P f
 #align tensor_product.curry TensorProduct.curry
+-/
 
+#print TensorProduct.curry_apply /-
 @[simp]
 theorem curry_apply (f : M ⊗ N →ₗ[R] P) (m : M) (n : N) : curry f m n = f (m ⊗ₜ n) :=
   rfl
 #align tensor_product.curry_apply TensorProduct.curry_apply
+-/
 
+#print TensorProduct.curry_injective /-
 theorem curry_injective : Function.Injective (curry : (M ⊗[R] N →ₗ[R] P) → M →ₗ[R] N →ₗ[R] P) :=
   fun g h H => ext H
 #align tensor_product.curry_injective TensorProduct.curry_injective
+-/
 
+#print TensorProduct.ext_threefold /-
 theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
     (H : ∀ x y z, g (x ⊗ₜ y ⊗ₜ z) = h (x ⊗ₜ y ⊗ₜ z)) : g = h :=
   by
   ext (x y z)
   exact H x y z
 #align tensor_product.ext_threefold TensorProduct.ext_threefold
+-/
 
+#print TensorProduct.ext_fourfold /-
 -- We'll need this one for checking the pentagon identity!
 theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
     (H : ∀ w x y z, g (w ⊗ₜ x ⊗ₜ y ⊗ₜ z) = h (w ⊗ₜ x ⊗ₜ y ⊗ₜ z)) : g = h :=
@@ -642,7 +735,9 @@ theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
   ext (w x y z)
   exact H w x y z
 #align tensor_product.ext_fourfold TensorProduct.ext_fourfold
+-/
 
+#print TensorProduct.ext_fourfold' /-
 /-- Two linear maps (M ⊗ N) ⊗ (P ⊗ Q) → S which agree on all elements of the
 form (m ⊗ₜ n) ⊗ₜ (p ⊗ₜ q) are equal. -/
 theorem ext_fourfold' {φ ψ : (M ⊗[R] N) ⊗[R] P ⊗[R] Q →ₗ[R] S}
@@ -651,6 +746,7 @@ theorem ext_fourfold' {φ ψ : (M ⊗[R] N) ⊗[R] P ⊗[R] Q →ₗ[R] S}
   ext (m n p q)
   exact H m n p q
 #align tensor_product.ext_fourfold' TensorProduct.ext_fourfold'
+-/
 
 end UMP
 
@@ -660,47 +756,59 @@ section
 
 variable (R M)
 
+#print TensorProduct.lid /-
 /-- The base ring is a left identity for the tensor product of modules, up to linear equivalence.
 -/
 protected def lid : R ⊗ M ≃ₗ[R] M :=
   LinearEquiv.ofLinear (lift <| LinearMap.lsmul R M) (mk R R M 1) (LinearMap.ext fun _ => by simp)
     (ext' fun r m => by simp <;> rw [← tmul_smul, ← smul_tmul, smul_eq_mul, mul_one])
 #align tensor_product.lid TensorProduct.lid
+-/
 
 end
 
+#print TensorProduct.lid_tmul /-
 @[simp]
 theorem lid_tmul (m : M) (r : R) : (TensorProduct.lid R M : R ⊗ M → M) (r ⊗ₜ m) = r • m :=
   by
   dsimp [TensorProduct.lid]
   simp
 #align tensor_product.lid_tmul TensorProduct.lid_tmul
+-/
 
+#print TensorProduct.lid_symm_apply /-
 @[simp]
 theorem lid_symm_apply (m : M) : (TensorProduct.lid R M).symm m = 1 ⊗ₜ m :=
   rfl
 #align tensor_product.lid_symm_apply TensorProduct.lid_symm_apply
+-/
 
 section
 
 variable (R M N)
 
+#print TensorProduct.comm /-
 /-- The tensor product of modules is commutative, up to linear equivalence.
 -/
 protected def comm : M ⊗ N ≃ₗ[R] N ⊗ M :=
   LinearEquiv.ofLinear (lift (mk R N M).flip) (lift (mk R M N).flip) (ext' fun m n => rfl)
     (ext' fun m n => rfl)
 #align tensor_product.comm TensorProduct.comm
+-/
 
+#print TensorProduct.comm_tmul /-
 @[simp]
 theorem comm_tmul (m : M) (n : N) : (TensorProduct.comm R M N) (m ⊗ₜ n) = n ⊗ₜ m :=
   rfl
 #align tensor_product.comm_tmul TensorProduct.comm_tmul
+-/
 
+#print TensorProduct.comm_symm_tmul /-
 @[simp]
 theorem comm_symm_tmul (m : M) (n : N) : (TensorProduct.comm R M N).symm (n ⊗ₜ m) = m ⊗ₜ n :=
   rfl
 #align tensor_product.comm_symm_tmul TensorProduct.comm_symm_tmul
+-/
 
 end
 
@@ -708,25 +816,31 @@ section
 
 variable (R M)
 
+#print TensorProduct.rid /-
 /-- The base ring is a right identity for the tensor product of modules, up to linear equivalence.
 -/
 protected def rid : M ⊗[R] R ≃ₗ[R] M :=
   LinearEquiv.trans (TensorProduct.comm R M R) (TensorProduct.lid R M)
 #align tensor_product.rid TensorProduct.rid
+-/
 
 end
 
+#print TensorProduct.rid_tmul /-
 @[simp]
 theorem rid_tmul (m : M) (r : R) : (TensorProduct.rid R M) (m ⊗ₜ r) = r • m :=
   by
   dsimp [TensorProduct.rid, TensorProduct.comm, TensorProduct.lid]
   simp
 #align tensor_product.rid_tmul TensorProduct.rid_tmul
+-/
 
+#print TensorProduct.rid_symm_apply /-
 @[simp]
 theorem rid_symm_apply (m : M) : (TensorProduct.rid R M).symm m = m ⊗ₜ 1 :=
   rfl
 #align tensor_product.rid_symm_apply TensorProduct.rid_symm_apply
+-/
 
 open LinearMap
 
@@ -734,6 +848,7 @@ section
 
 variable (R M N P)
 
+#print TensorProduct.assoc /-
 /-- The associator for tensor product of R-modules, as a linear equivalence. -/
 protected def assoc : (M ⊗[R] N) ⊗[R] P ≃ₗ[R] M ⊗[R] N ⊗[R] P := by
   refine'
@@ -753,31 +868,41 @@ protected def assoc : (M ⊗[R] N) ⊗[R] P ≃ₗ[R] M ⊗[R] N ⊗[R] P := by
       | rw [curry_apply]
       | rw [id_apply]
 #align tensor_product.assoc TensorProduct.assoc
+-/
 
 end
 
+#print TensorProduct.assoc_tmul /-
 @[simp]
 theorem assoc_tmul (m : M) (n : N) (p : P) :
     (TensorProduct.assoc R M N P) (m ⊗ₜ n ⊗ₜ p) = m ⊗ₜ (n ⊗ₜ p) :=
   rfl
 #align tensor_product.assoc_tmul TensorProduct.assoc_tmul
+-/
 
+#print TensorProduct.assoc_symm_tmul /-
 @[simp]
 theorem assoc_symm_tmul (m : M) (n : N) (p : P) :
     (TensorProduct.assoc R M N P).symm (m ⊗ₜ (n ⊗ₜ p)) = m ⊗ₜ n ⊗ₜ p :=
   rfl
 #align tensor_product.assoc_symm_tmul TensorProduct.assoc_symm_tmul
+-/
 
+#print TensorProduct.map /-
 /-- The tensor product of a pair of linear maps between modules. -/
 def map (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : M ⊗ N →ₗ[R] P ⊗ Q :=
   lift <| comp (compl₂ (mk _ _ _) g) f
 #align tensor_product.map TensorProduct.map
+-/
 
+#print TensorProduct.map_tmul /-
 @[simp]
 theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f g (m ⊗ₜ n) = f m ⊗ₜ g n :=
   rfl
 #align tensor_product.map_tmul TensorProduct.map_tmul
+-/
 
+#print TensorProduct.map_range_eq_span_tmul /-
 theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (map f g).range = Submodule.span R {t | ∃ m n, f m ⊗ₜ g n = t} :=
   by
@@ -788,12 +913,15 @@ theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
   · rintro ⟨_, ⟨⟨m, n, rfl⟩, rfl⟩⟩; use m, n; simp only [map_tmul]
   · rintro ⟨m, n, rfl⟩; use m ⊗ₜ n, m, n; simp only [map_tmul]
 #align tensor_product.map_range_eq_span_tmul TensorProduct.map_range_eq_span_tmul
+-/
 
+#print TensorProduct.mapIncl /-
 /-- Given submodules `p ⊆ P` and `q ⊆ Q`, this is the natural map: `p ⊗ q → P ⊗ Q`. -/
 @[simp]
 def mapIncl (p : Submodule R P) (q : Submodule R Q) : p ⊗[R] q →ₗ[R] P ⊗[R] Q :=
   map p.Subtype q.Subtype
 #align tensor_product.map_incl TensorProduct.mapIncl
+-/
 
 section
 
@@ -803,33 +931,44 @@ variable [AddCommMonoid P'] [Module R P']
 
 variable [AddCommMonoid Q'] [Module R Q']
 
+#print TensorProduct.map_comp /-
 theorem map_comp (f₂ : P →ₗ[R] P') (f₁ : M →ₗ[R] P) (g₂ : Q →ₗ[R] Q') (g₁ : N →ₗ[R] Q) :
     map (f₂.comp f₁) (g₂.comp g₁) = (map f₂ g₂).comp (map f₁ g₁) :=
   ext' fun _ _ => rfl
 #align tensor_product.map_comp TensorProduct.map_comp
+-/
 
+#print TensorProduct.lift_comp_map /-
 theorem lift_comp_map (i : P →ₗ[R] Q →ₗ[R] Q') (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (lift i).comp (map f g) = lift ((i.comp f).compl₂ g) :=
   ext' fun _ _ => rfl
 #align tensor_product.lift_comp_map TensorProduct.lift_comp_map
+-/
 
 attribute [local ext] ext
 
+#print TensorProduct.map_id /-
 @[simp]
 theorem map_id : map (id : M →ₗ[R] M) (id : N →ₗ[R] N) = id := by ext;
   simp only [mk_apply, id_coe, compr₂_apply, id.def, map_tmul]
 #align tensor_product.map_id TensorProduct.map_id
+-/
 
+#print TensorProduct.map_one /-
 @[simp]
 theorem map_one : map (1 : M →ₗ[R] M) (1 : N →ₗ[R] N) = 1 :=
   map_id
 #align tensor_product.map_one TensorProduct.map_one
+-/
 
+#print TensorProduct.map_mul /-
 theorem map_mul (f₁ f₂ : M →ₗ[R] M) (g₁ g₂ : N →ₗ[R] N) :
     map (f₁ * f₂) (g₁ * g₂) = map f₁ g₁ * map f₂ g₂ :=
   map_comp f₁ f₂ g₁ g₂
 #align tensor_product.map_mul TensorProduct.map_mul
+-/
 
+#print TensorProduct.map_pow /-
 @[simp]
 protected theorem map_pow (f : M →ₗ[R] M) (g : N →ₗ[R] N) (n : ℕ) :
     map f g ^ n = map (f ^ n) (g ^ n) :=
@@ -838,29 +977,40 @@ protected theorem map_pow (f : M →ₗ[R] M) (g : N →ₗ[R] N) (n : ℕ) :
   · simp only [pow_zero, map_one]
   · simp only [pow_succ', ih, map_mul]
 #align tensor_product.map_pow TensorProduct.map_pow
+-/
 
+#print TensorProduct.map_add_left /-
 theorem map_add_left (f₁ f₂ : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (f₁ + f₂) g = map f₁ g + map f₂ g :=
   by ext; simp only [add_tmul, compr₂_apply, mk_apply, map_tmul, add_apply]
 #align tensor_product.map_add_left TensorProduct.map_add_left
+-/
 
+#print TensorProduct.map_add_right /-
 theorem map_add_right (f : M →ₗ[R] P) (g₁ g₂ : N →ₗ[R] Q) : map f (g₁ + g₂) = map f g₁ + map f g₂ :=
   by ext; simp only [tmul_add, compr₂_apply, mk_apply, map_tmul, add_apply]
 #align tensor_product.map_add_right TensorProduct.map_add_right
+-/
 
+#print TensorProduct.map_smul_left /-
 theorem map_smul_left (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (r • f) g = r • map f g := by
   ext; simp only [smul_tmul, compr₂_apply, mk_apply, map_tmul, smul_apply, tmul_smul]
 #align tensor_product.map_smul_left TensorProduct.map_smul_left
+-/
 
+#print TensorProduct.map_smul_right /-
 theorem map_smul_right (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map f (r • g) = r • map f g := by
   ext; simp only [smul_tmul, compr₂_apply, mk_apply, map_tmul, smul_apply, tmul_smul]
 #align tensor_product.map_smul_right TensorProduct.map_smul_right
+-/
 
 variable (R M N P Q)
 
+#print TensorProduct.mapBilinear /-
 /-- The tensor product of a pair of linear maps between modules, bilinear in both maps. -/
 def mapBilinear : (M →ₗ[R] P) →ₗ[R] (N →ₗ[R] Q) →ₗ[R] M ⊗[R] N →ₗ[R] P ⊗[R] Q :=
   LinearMap.mk₂ R map map_add_left map_smul_left map_add_right map_smul_right
 #align tensor_product.map_bilinear TensorProduct.mapBilinear
+-/
 
 #print TensorProduct.lTensorHomToHomLTensor /-
 /-- The canonical linear map from `P ⊗[R] (M →ₗ[R] Q)` to `(M →ₗ[R] P ⊗[R] Q)` -/
@@ -886,31 +1036,40 @@ def homTensorHomMap : (M →ₗ[R] P) ⊗[R] (N →ₗ[R] Q) →ₗ[R] M ⊗[R]
 
 variable {R M N P Q}
 
+#print TensorProduct.mapBilinear_apply /-
 @[simp]
 theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear R M N P Q f g = map f g :=
   rfl
 #align tensor_product.map_bilinear_apply TensorProduct.mapBilinear_apply
+-/
 
+#print TensorProduct.lTensorHomToHomLTensor_apply /-
 @[simp]
 theorem lTensorHomToHomLTensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
     lTensorHomToHomLTensor R M P Q (p ⊗ₜ f) m = p ⊗ₜ f m :=
   rfl
 #align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.lTensorHomToHomLTensor_apply
+-/
 
+#print TensorProduct.rTensorHomToHomRTensor_apply /-
 @[simp]
 theorem rTensorHomToHomRTensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
     rTensorHomToHomRTensor R M P Q (f ⊗ₜ q) m = f m ⊗ₜ q :=
   rfl
 #align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rTensorHomToHomRTensor_apply
+-/
 
+#print TensorProduct.homTensorHomMap_apply /-
 @[simp]
 theorem homTensorHomMap_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     homTensorHomMap R M N P Q (f ⊗ₜ g) = map f g :=
   rfl
 #align tensor_product.hom_tensor_hom_map_apply TensorProduct.homTensorHomMap_apply
+-/
 
 end
 
+#print TensorProduct.congr /-
 /-- If `M` and `P` are linearly equivalent and `N` and `Q` are linearly equivalent
 then `M ⊗ N` and `P ⊗ Q` are linearly equivalent. -/
 def congr (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) : M ⊗ N ≃ₗ[R] P ⊗ Q :=
@@ -918,21 +1077,27 @@ def congr (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) : M ⊗ N ≃ₗ[R] P ⊗ Q :=
     (ext' fun m n => by simp <;> simp only [LinearEquiv.apply_symm_apply])
     (ext' fun m n => by simp <;> simp only [LinearEquiv.symm_apply_apply])
 #align tensor_product.congr TensorProduct.congr
+-/
 
+#print TensorProduct.congr_tmul /-
 @[simp]
 theorem congr_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (m : M) (n : N) :
     congr f g (m ⊗ₜ n) = f m ⊗ₜ g n :=
   rfl
 #align tensor_product.congr_tmul TensorProduct.congr_tmul
+-/
 
+#print TensorProduct.congr_symm_tmul /-
 @[simp]
 theorem congr_symm_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (p : P) (q : Q) :
     (congr f g).symm (p ⊗ₜ q) = f.symm p ⊗ₜ g.symm q :=
   rfl
 #align tensor_product.congr_symm_tmul TensorProduct.congr_symm_tmul
+-/
 
 variable (R M N P Q)
 
+#print TensorProduct.leftComm /-
 /-- A tensor product analogue of `mul_left_comm`. -/
 def leftComm : M ⊗[R] N ⊗[R] P ≃ₗ[R] N ⊗[R] M ⊗[R] P :=
   let e₁ := (TensorProduct.assoc R M N P).symm
@@ -940,22 +1105,28 @@ def leftComm : M ⊗[R] N ⊗[R] P ≃ₗ[R] N ⊗[R] M ⊗[R] P :=
   let e₃ := TensorProduct.assoc R N M P
   e₁ ≪≫ₗ (e₂ ≪≫ₗ e₃)
 #align tensor_product.left_comm TensorProduct.leftComm
+-/
 
 variable {M N P Q}
 
+#print TensorProduct.leftComm_tmul /-
 @[simp]
 theorem leftComm_tmul (m : M) (n : N) (p : P) : leftComm R M N P (m ⊗ₜ (n ⊗ₜ p)) = n ⊗ₜ (m ⊗ₜ p) :=
   rfl
 #align tensor_product.left_comm_tmul TensorProduct.leftComm_tmul
+-/
 
+#print TensorProduct.leftComm_symm_tmul /-
 @[simp]
 theorem leftComm_symm_tmul (m : M) (n : N) (p : P) :
     (leftComm R M N P).symm (n ⊗ₜ (m ⊗ₜ p)) = m ⊗ₜ (n ⊗ₜ p) :=
   rfl
 #align tensor_product.left_comm_symm_tmul TensorProduct.leftComm_symm_tmul
+-/
 
 variable (M N P Q)
 
+#print TensorProduct.tensorTensorTensorComm /-
 /-- This special case is worth defining explicitly since it is useful for defining multiplication
 on tensor products of modules carrying multiplications (e.g., associative rings, Lie rings, ...).
 
@@ -972,23 +1143,29 @@ def tensorTensorTensorComm : (M ⊗[R] N) ⊗[R] P ⊗[R] Q ≃ₗ[R] (M ⊗[R]
   let e₃ := (TensorProduct.assoc R M P (N ⊗[R] Q)).symm
   e₁ ≪≫ₗ (e₂ ≪≫ₗ e₃)
 #align tensor_product.tensor_tensor_tensor_comm TensorProduct.tensorTensorTensorComm
+-/
 
 variable {M N P Q}
 
+#print TensorProduct.tensorTensorTensorComm_tmul /-
 @[simp]
 theorem tensorTensorTensorComm_tmul (m : M) (n : N) (p : P) (q : Q) :
     tensorTensorTensorComm R M N P Q (m ⊗ₜ n ⊗ₜ (p ⊗ₜ q)) = m ⊗ₜ p ⊗ₜ (n ⊗ₜ q) :=
   rfl
 #align tensor_product.tensor_tensor_tensor_comm_tmul TensorProduct.tensorTensorTensorComm_tmul
+-/
 
+#print TensorProduct.tensorTensorTensorComm_symm /-
 @[simp]
 theorem tensorTensorTensorComm_symm :
     (tensorTensorTensorComm R M N P Q).symm = tensorTensorTensorComm R M P N Q :=
   rfl
 #align tensor_product.tensor_tensor_tensor_comm_symm TensorProduct.tensorTensorTensorComm_symm
+-/
 
 variable (M N P Q)
 
+#print TensorProduct.tensorTensorTensorAssoc /-
 /-- This special case is useful for describing the interplay between `dual_tensor_hom_equiv` and
 composition of linear maps.
 
@@ -1001,20 +1178,25 @@ def tensorTensorTensorAssoc : (M ⊗[R] N) ⊗[R] P ⊗[R] Q ≃ₗ[R] (M ⊗[R]
   (TensorProduct.assoc R (M ⊗[R] N) P Q).symm ≪≫ₗ
     congr (TensorProduct.assoc R M N P) (1 : Q ≃ₗ[R] Q)
 #align tensor_product.tensor_tensor_tensor_assoc TensorProduct.tensorTensorTensorAssoc
+-/
 
 variable {M N P Q}
 
+#print TensorProduct.tensorTensorTensorAssoc_tmul /-
 @[simp]
 theorem tensorTensorTensorAssoc_tmul (m : M) (n : N) (p : P) (q : Q) :
     tensorTensorTensorAssoc R M N P Q (m ⊗ₜ n ⊗ₜ (p ⊗ₜ q)) = m ⊗ₜ (n ⊗ₜ p) ⊗ₜ q :=
   rfl
 #align tensor_product.tensor_tensor_tensor_assoc_tmul TensorProduct.tensorTensorTensorAssoc_tmul
+-/
 
+#print TensorProduct.tensorTensorTensorAssoc_symm_tmul /-
 @[simp]
 theorem tensorTensorTensorAssoc_symm_tmul (m : M) (n : N) (p : P) (q : Q) :
     (tensorTensorTensorAssoc R M N P Q).symm (m ⊗ₜ (n ⊗ₜ p) ⊗ₜ q) = m ⊗ₜ n ⊗ₜ (p ⊗ₜ q) :=
   rfl
 #align tensor_product.tensor_tensor_tensor_assoc_symm_tmul TensorProduct.tensorTensorTensorAssoc_symm_tmul
+-/
 
 end TensorProduct
 
@@ -1022,32 +1204,41 @@ namespace LinearMap
 
 variable {R} (M) {N P Q}
 
+#print LinearMap.lTensor /-
 /-- `ltensor M f : M ⊗ N →ₗ M ⊗ P` is the natural linear map induced by `f : N →ₗ P`. -/
 def lTensor (f : N →ₗ[R] P) : M ⊗ N →ₗ[R] M ⊗ P :=
   TensorProduct.map id f
 #align linear_map.ltensor LinearMap.lTensor
+-/
 
+#print LinearMap.rTensor /-
 /-- `rtensor f M : N₁ ⊗ M →ₗ N₂ ⊗ M` is the natural linear map induced by `f : N₁ →ₗ N₂`. -/
 def rTensor (f : N →ₗ[R] P) : N ⊗ M →ₗ[R] P ⊗ M :=
   TensorProduct.map f id
 #align linear_map.rtensor LinearMap.rTensor
+-/
 
 variable (g : P →ₗ[R] Q) (f : N →ₗ[R] P)
 
+#print LinearMap.lTensor_tmul /-
 @[simp]
 theorem lTensor_tmul (m : M) (n : N) : f.lTensor M (m ⊗ₜ n) = m ⊗ₜ f n :=
   rfl
 #align linear_map.ltensor_tmul LinearMap.lTensor_tmul
+-/
 
+#print LinearMap.rTensor_tmul /-
 @[simp]
 theorem rTensor_tmul (m : M) (n : N) : f.rTensor M (n ⊗ₜ m) = f n ⊗ₜ m :=
   rfl
 #align linear_map.rtensor_tmul LinearMap.rTensor_tmul
+-/
 
 open TensorProduct
 
 attribute [local ext] TensorProduct.ext
 
+#print LinearMap.lTensorHom /-
 /-- `ltensor_hom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
 def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
     where
@@ -1057,7 +1248,9 @@ def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
   map_smul' r f := by dsimp; ext (x y);
     simp only [compr₂_apply, mk_apply, tmul_smul, smul_apply, ltensor_tmul]
 #align linear_map.ltensor_hom LinearMap.lTensorHom
+-/
 
+#print LinearMap.rTensorHom /-
 /-- `rtensor_hom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
 def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
     where
@@ -1067,142 +1260,195 @@ def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
   map_smul' r f := by dsimp; ext (x y);
     simp only [compr₂_apply, mk_apply, smul_tmul, tmul_smul, smul_apply, rtensor_tmul]
 #align linear_map.rtensor_hom LinearMap.rTensorHom
+-/
 
+#print LinearMap.coe_lTensorHom /-
 @[simp]
 theorem coe_lTensorHom : (lTensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R] M ⊗[R] P) = lTensor M :=
   rfl
 #align linear_map.coe_ltensor_hom LinearMap.coe_lTensorHom
+-/
 
+#print LinearMap.coe_rTensorHom /-
 @[simp]
 theorem coe_rTensorHom : (rTensorHom M : (N →ₗ[R] P) → N ⊗[R] M →ₗ[R] P ⊗[R] M) = rTensor M :=
   rfl
 #align linear_map.coe_rtensor_hom LinearMap.coe_rTensorHom
+-/
 
+#print LinearMap.lTensor_add /-
 @[simp]
 theorem lTensor_add (f g : N →ₗ[R] P) : (f + g).lTensor M = f.lTensor M + g.lTensor M :=
   (lTensorHom M).map_add f g
 #align linear_map.ltensor_add LinearMap.lTensor_add
+-/
 
+#print LinearMap.rTensor_add /-
 @[simp]
 theorem rTensor_add (f g : N →ₗ[R] P) : (f + g).rTensor M = f.rTensor M + g.rTensor M :=
   (rTensorHom M).map_add f g
 #align linear_map.rtensor_add LinearMap.rTensor_add
+-/
 
+#print LinearMap.lTensor_zero /-
 @[simp]
 theorem lTensor_zero : lTensor M (0 : N →ₗ[R] P) = 0 :=
   (lTensorHom M).map_zero
 #align linear_map.ltensor_zero LinearMap.lTensor_zero
+-/
 
+#print LinearMap.rTensor_zero /-
 @[simp]
 theorem rTensor_zero : rTensor M (0 : N →ₗ[R] P) = 0 :=
   (rTensorHom M).map_zero
 #align linear_map.rtensor_zero LinearMap.rTensor_zero
+-/
 
+#print LinearMap.lTensor_smul /-
 @[simp]
 theorem lTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).lTensor M = r • f.lTensor M :=
   (lTensorHom M).map_smul r f
 #align linear_map.ltensor_smul LinearMap.lTensor_smul
+-/
 
+#print LinearMap.rTensor_smul /-
 @[simp]
 theorem rTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).rTensor M = r • f.rTensor M :=
   (rTensorHom M).map_smul r f
 #align linear_map.rtensor_smul LinearMap.rTensor_smul
+-/
 
+#print LinearMap.lTensor_comp /-
 theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) := by ext (m n);
   simp only [compr₂_apply, mk_apply, comp_apply, ltensor_tmul]
 #align linear_map.ltensor_comp LinearMap.lTensor_comp
+-/
 
+#print LinearMap.lTensor_comp_apply /-
 theorem lTensor_comp_apply (x : M ⊗[R] N) :
     (g.comp f).lTensor M x = (g.lTensor M) ((f.lTensor M) x) := by rw [ltensor_comp, coe_comp]
 #align linear_map.ltensor_comp_apply LinearMap.lTensor_comp_apply
+-/
 
+#print LinearMap.rTensor_comp /-
 theorem rTensor_comp : (g.comp f).rTensor M = (g.rTensor M).comp (f.rTensor M) := by ext (m n);
   simp only [compr₂_apply, mk_apply, comp_apply, rtensor_tmul]
 #align linear_map.rtensor_comp LinearMap.rTensor_comp
+-/
 
+#print LinearMap.rTensor_comp_apply /-
 theorem rTensor_comp_apply (x : N ⊗[R] M) :
     (g.comp f).rTensor M x = (g.rTensor M) ((f.rTensor M) x) := by rw [rtensor_comp, coe_comp]
 #align linear_map.rtensor_comp_apply LinearMap.rTensor_comp_apply
+-/
 
+#print LinearMap.lTensor_mul /-
 theorem lTensor_mul (f g : Module.End R N) : (f * g).lTensor M = f.lTensor M * g.lTensor M :=
   lTensor_comp M f g
 #align linear_map.ltensor_mul LinearMap.lTensor_mul
+-/
 
+#print LinearMap.rTensor_mul /-
 theorem rTensor_mul (f g : Module.End R N) : (f * g).rTensor M = f.rTensor M * g.rTensor M :=
   rTensor_comp M f g
 #align linear_map.rtensor_mul LinearMap.rTensor_mul
+-/
 
 variable (N)
 
+#print LinearMap.lTensor_id /-
 @[simp]
 theorem lTensor_id : (id : N →ₗ[R] N).lTensor M = id :=
   map_id
 #align linear_map.ltensor_id LinearMap.lTensor_id
+-/
 
+#print LinearMap.lTensor_id_apply /-
 -- `simp` can prove this.
 theorem lTensor_id_apply (x : M ⊗[R] N) : (LinearMap.id : N →ₗ[R] N).lTensor M x = x := by
   rw [ltensor_id, id_coe, id.def]
 #align linear_map.ltensor_id_apply LinearMap.lTensor_id_apply
+-/
 
+#print LinearMap.rTensor_id /-
 @[simp]
 theorem rTensor_id : (id : N →ₗ[R] N).rTensor M = id :=
   map_id
 #align linear_map.rtensor_id LinearMap.rTensor_id
+-/
 
+#print LinearMap.rTensor_id_apply /-
 -- `simp` can prove this.
 theorem rTensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rTensor M x = x := by
   rw [rtensor_id, id_coe, id.def]
 #align linear_map.rtensor_id_apply LinearMap.rTensor_id_apply
+-/
 
 variable {N}
 
+#print LinearMap.lTensor_comp_rTensor /-
 @[simp]
 theorem lTensor_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (g.lTensor P).comp (f.rTensor N) = map f g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.ltensor_comp_rtensor LinearMap.lTensor_comp_rTensor
+-/
 
+#print LinearMap.rTensor_comp_lTensor /-
 @[simp]
 theorem rTensor_comp_lTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (f.rTensor Q).comp (g.lTensor M) = map f g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.rtensor_comp_ltensor LinearMap.rTensor_comp_lTensor
+-/
 
+#print LinearMap.map_comp_rTensor /-
 @[simp]
 theorem map_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (f' : S →ₗ[R] M) :
     (map f g).comp (f'.rTensor _) = map (f.comp f') g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.map_comp_rtensor LinearMap.map_comp_rTensor
+-/
 
+#print LinearMap.map_comp_lTensor /-
 @[simp]
 theorem map_comp_lTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (g' : S →ₗ[R] N) :
     (map f g).comp (g'.lTensor _) = map f (g.comp g') := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.map_comp_ltensor LinearMap.map_comp_lTensor
+-/
 
+#print LinearMap.rTensor_comp_map /-
 @[simp]
 theorem rTensor_comp_map (f' : P →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (f'.rTensor _).comp (map f g) = map (f'.comp f) g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.rtensor_comp_map LinearMap.rTensor_comp_map
+-/
 
+#print LinearMap.lTensor_comp_map /-
 @[simp]
 theorem lTensor_comp_map (g' : Q →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (g'.lTensor _).comp (map f g) = map f (g'.comp g) := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.ltensor_comp_map LinearMap.lTensor_comp_map
+-/
 
 variable {M}
 
+#print LinearMap.rTensor_pow /-
 @[simp]
 theorem rTensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rTensor N ^ n = (f ^ n).rTensor N := by
   have h := TensorProduct.map_pow f (id : N →ₗ[R] N) n; rwa [id_pow] at h 
 #align linear_map.rtensor_pow LinearMap.rTensor_pow
+-/
 
+#print LinearMap.lTensor_pow /-
 @[simp]
 theorem lTensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.lTensor M ^ n = (f ^ n).lTensor M := by
   have h := TensorProduct.map_pow (id : M →ₗ[R] M) f n; rwa [id_pow] at h 
 #align linear_map.ltensor_pow LinearMap.lTensor_pow
+-/
 
 end LinearMap
 
@@ -1226,16 +1472,20 @@ open LinearMap
 
 variable (R)
 
+#print TensorProduct.Neg.aux /-
 /-- Auxiliary function to defining negation multiplication on tensor product. -/
 def Neg.aux : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
   FreeAddMonoid.lift fun p : M × N => (-p.1) ⊗ₜ p.2
 #align tensor_product.neg.aux TensorProduct.Neg.aux
+-/
 
 variable {R}
 
+#print TensorProduct.Neg.aux_of /-
 theorem Neg.aux_of (m : M) (n : N) : Neg.aux R (FreeAddMonoid.of (m, n)) = (-m) ⊗ₜ[R] n :=
   rfl
 #align tensor_product.neg.aux_of TensorProduct.Neg.aux_of
+-/
 
 instance : Neg (M ⊗[R] N)
     where neg :=
@@ -1256,6 +1506,7 @@ instance : Neg (M ⊗[R] N)
         | _, _, eqv.add_comm x y =>
           (AddCon.ker_rel _).2 <| by simp_rw [AddMonoidHom.map_add, add_comm]
 
+#print TensorProduct.add_left_neg /-
 protected theorem add_left_neg (x : M ⊗[R] N) : -x + x = 0 :=
   TensorProduct.induction_on x (by rw [add_zero]; apply (neg.aux R).map_zero)
     (fun x y => by convert (add_tmul (-x) x y).symm; rw [add_left_neg, zero_tmul]) fun x y hx hy =>
@@ -1265,6 +1516,7 @@ protected theorem add_left_neg (x : M ⊗[R] N) : -x + x = 0 :=
     ac_change -x + x + (-y + y) = 0
     rw [hx, hy, add_zero]
 #align tensor_product.add_left_neg TensorProduct.add_left_neg
+-/
 
 instance : AddCommGroup (M ⊗[R] N) :=
   { TensorProduct.addCommMonoid with
@@ -1282,22 +1534,31 @@ instance : AddCommGroup (M ⊗[R] N) :=
         add_smul, ← sub_eq_add_neg, sub_self, zero_smul, add_zero]
       rfl }
 
+#print TensorProduct.neg_tmul /-
 theorem neg_tmul (m : M) (n : N) : (-m) ⊗ₜ n = -m ⊗ₜ[R] n :=
   rfl
 #align tensor_product.neg_tmul TensorProduct.neg_tmul
+-/
 
+#print TensorProduct.tmul_neg /-
 theorem tmul_neg (m : M) (n : N) : m ⊗ₜ (-n) = -m ⊗ₜ[R] n :=
   (mk R M N _).map_neg _
 #align tensor_product.tmul_neg TensorProduct.tmul_neg
+-/
 
+#print TensorProduct.tmul_sub /-
 theorem tmul_sub (m : M) (n₁ n₂ : N) : m ⊗ₜ (n₁ - n₂) = m ⊗ₜ[R] n₁ - m ⊗ₜ[R] n₂ :=
   (mk R M N _).map_sub _ _
 #align tensor_product.tmul_sub TensorProduct.tmul_sub
+-/
 
+#print TensorProduct.sub_tmul /-
 theorem sub_tmul (m₁ m₂ : M) (n : N) : (m₁ - m₂) ⊗ₜ n = m₁ ⊗ₜ[R] n - m₂ ⊗ₜ[R] n :=
   (mk R M N).map_sub₂ _ _ _
 #align tensor_product.sub_tmul TensorProduct.sub_tmul
+-/
 
+#print TensorProduct.CompatibleSMul.int /-
 /-- While the tensor product will automatically inherit a ℤ-module structure from
 `add_comm_group.int_module`, that structure won't be compatible with lemmas like `tmul_smul` unless
 we use a `ℤ-module` instance provided by `tensor_product.left_module`.
@@ -1311,35 +1572,46 @@ instance CompatibleSMul.int : CompatibleSMul R ℤ M N :=
     Int.induction_on r (by simp) (fun r ih => by simpa [add_smul, tmul_add, add_tmul] using ih)
       fun r ih => by simpa [sub_smul, tmul_sub, sub_tmul] using ih⟩
 #align tensor_product.compatible_smul.int TensorProduct.CompatibleSMul.int
+-/
 
+#print TensorProduct.CompatibleSMul.unit /-
 instance CompatibleSMul.unit {S} [Monoid S] [DistribMulAction S M] [DistribMulAction S N]
     [CompatibleSMul R S M N] : CompatibleSMul R Sˣ M N :=
   ⟨fun s m n => (CompatibleSMul.smul_tmul (s : S) m n : _)⟩
 #align tensor_product.compatible_smul.unit TensorProduct.CompatibleSMul.unit
+-/
 
 end TensorProduct
 
 namespace LinearMap
 
+#print LinearMap.lTensor_sub /-
 @[simp]
 theorem lTensor_sub (f g : N →ₗ[R] P) : (f - g).lTensor M = f.lTensor M - g.lTensor M := by
   simp only [← coe_ltensor_hom, map_sub]
 #align linear_map.ltensor_sub LinearMap.lTensor_sub
+-/
 
+#print LinearMap.rTensor_sub /-
 @[simp]
 theorem rTensor_sub (f g : N →ₗ[R] P) : (f - g).rTensor M = f.rTensor M - g.rTensor M := by
   simp only [← coe_rtensor_hom, map_sub]
 #align linear_map.rtensor_sub LinearMap.rTensor_sub
+-/
 
+#print LinearMap.lTensor_neg /-
 @[simp]
 theorem lTensor_neg (f : N →ₗ[R] P) : (-f).lTensor M = -f.lTensor M := by
   simp only [← coe_ltensor_hom, map_neg]
 #align linear_map.ltensor_neg LinearMap.lTensor_neg
+-/
 
+#print LinearMap.rTensor_neg /-
 @[simp]
 theorem rTensor_neg (f : N →ₗ[R] P) : (-f).rTensor M = -f.rTensor M := by
   simp only [← coe_rtensor_hom, map_neg]
 #align linear_map.rtensor_neg LinearMap.rTensor_neg
+-/
 
 end LinearMap
 

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

@@ -420,7 +420,7 @@ theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
 #align tensor_product.sum_tmul TensorProduct.sum_tmul
 
 theorem tmul_sum (m : M) {α : Type _} (s : Finset α) (n : α → N) :
-    (m ⊗ₜ[R] ∑ a in s, n a) = ∑ a in s, m ⊗ₜ[R] n a := by
+    m ⊗ₜ[R] ∑ a in s, n a = ∑ a in s, m ⊗ₜ[R] n a := by
   classical
   induction' s using Finset.induction with a s has ih h
   · simp

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

@@ -414,17 +414,17 @@ open scoped BigOperators
 theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
     (∑ a in s, m a) ⊗ₜ[R] n = ∑ a in s, m a ⊗ₜ[R] n := by
   classical
-    induction' s using Finset.induction with a s has ih h
-    · simp
-    · simp [Finset.sum_insert has, add_tmul, ih]
+  induction' s using Finset.induction with a s has ih h
+  · simp
+  · simp [Finset.sum_insert has, add_tmul, ih]
 #align tensor_product.sum_tmul TensorProduct.sum_tmul
 
 theorem tmul_sum (m : M) {α : Type _} (s : Finset α) (n : α → N) :
     (m ⊗ₜ[R] ∑ a in s, n a) = ∑ a in s, m ⊗ₜ[R] n a := by
   classical
-    induction' s using Finset.induction with a s has ih h
-    · simp
-    · simp [Finset.sum_insert has, tmul_add, ih]
+  induction' s using Finset.induction with a s has ih h
+  · simp
+  · simp [Finset.sum_insert has, tmul_add, ih]
 #align tensor_product.tmul_sum TensorProduct.tmul_sum
 
 end
@@ -432,7 +432,7 @@ end
 variable (R M N)
 
 /-- The simple (aka pure) elements span the tensor product. -/
-theorem span_tmul_eq_top : Submodule.span R { t : M ⊗[R] N | ∃ m n, m ⊗ₜ n = t } = ⊤ :=
+theorem span_tmul_eq_top : Submodule.span R {t : M ⊗[R] N | ∃ m n, m ⊗ₜ n = t} = ⊤ :=
   by
   ext t; simp only [Submodule.mem_top, iff_true_iff]
   apply t.induction_on
@@ -779,7 +779,7 @@ theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f
 #align tensor_product.map_tmul TensorProduct.map_tmul
 
 theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
-    (map f g).range = Submodule.span R { t | ∃ m n, f m ⊗ₜ g n = t } :=
+    (map f g).range = Submodule.span R {t | ∃ m n, f m ⊗ₜ g n = t} :=
   by
   simp only [← Submodule.map_top, ← span_tmul_eq_top, Submodule.map_span, Set.mem_image,
     Set.mem_setOf_eq]
@@ -1258,7 +1258,7 @@ instance : Neg (M ⊗[R] N)
 
 protected theorem add_left_neg (x : M ⊗[R] N) : -x + x = 0 :=
   TensorProduct.induction_on x (by rw [add_zero]; apply (neg.aux R).map_zero)
-    (fun x y => by convert(add_tmul (-x) x y).symm; rw [add_left_neg, zero_tmul]) fun x y hx hy =>
+    (fun x y => by convert (add_tmul (-x) x y).symm; rw [add_left_neg, zero_tmul]) fun x y hx hy =>
     by
     unfold Neg.neg SubNegMonoid.neg
     rw [AddMonoidHom.map_add]

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

@@ -743,7 +743,15 @@ protected def assoc : (M ⊗[R] N) ⊗[R] P ≃ₗ[R] M ⊗[R] N ⊗[R] P := by
         (ext <| flip_inj <| LinearMap.ext fun p => ext' fun m n => _) <;>
     repeat'
       first
-        |rw [lift.tmul]|rw [compr₂_apply]|rw [comp_apply]|rw [mk_apply]|rw [flip_apply]|rw [lcurry_apply]|rw [uncurry_apply]|rw [curry_apply]|rw [id_apply]
+      | rw [lift.tmul]
+      | rw [compr₂_apply]
+      | rw [comp_apply]
+      | rw [mk_apply]
+      | rw [flip_apply]
+      | rw [lcurry_apply]
+      | rw [uncurry_apply]
+      | rw [curry_apply]
+      | rw [id_apply]
 #align tensor_product.assoc TensorProduct.assoc
 
 end
@@ -775,7 +783,7 @@ theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
   by
   simp only [← Submodule.map_top, ← span_tmul_eq_top, Submodule.map_span, Set.mem_image,
     Set.mem_setOf_eq]
-  congr ; ext t
+  congr; ext t
   constructor
   · rintro ⟨_, ⟨⟨m, n, rfl⟩, rfl⟩⟩; use m, n; simp only [map_tmul]
   · rintro ⟨m, n, rfl⟩; use m ⊗ₜ n, m, n; simp only [map_tmul]
@@ -1188,12 +1196,12 @@ variable {M}
 
 @[simp]
 theorem rTensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rTensor N ^ n = (f ^ n).rTensor N := by
-  have h := TensorProduct.map_pow f (id : N →ₗ[R] N) n; rwa [id_pow] at h
+  have h := TensorProduct.map_pow f (id : N →ₗ[R] N) n; rwa [id_pow] at h 
 #align linear_map.rtensor_pow LinearMap.rTensor_pow
 
 @[simp]
 theorem lTensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.lTensor M ^ n = (f ^ n).lTensor M := by
-  have h := TensorProduct.map_pow (id : M →ₗ[R] M) f n; rwa [id_pow] at h
+  have h := TensorProduct.map_pow (id : M →ₗ[R] M) f n; rwa [id_pow] at h 
 #align linear_map.ltensor_pow LinearMap.lTensor_pow
 
 end LinearMap

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

@@ -409,7 +409,7 @@ theorem tmul_ite (x₁ : M) (x₂ : N) (P : Prop) [Decidable P] :
 
 section
 
-open BigOperators
+open scoped BigOperators
 
 theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
     (∑ a in s, m a) ⊗ₜ[R] n = ∑ a in s, m a ⊗ₜ[R] n := by
@@ -1212,7 +1212,7 @@ variable [Module R M] [Module R N] [Module R P] [Module R Q] [Module R S]
 
 namespace TensorProduct
 
-open TensorProduct
+open scoped TensorProduct
 
 open LinearMap
 

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

@@ -146,9 +146,6 @@ infixl:100 " ⊗ₜ " => tmul _
 -- mathport name: «expr ⊗ₜ[ ] »
 notation:100 x " ⊗ₜ[" R "] " y:100 => tmul R x y
 
-/- warning: tensor_product.induction_on -> TensorProduct.induction_on is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.induction_on TensorProduct.induction_onₓ'. -/
 @[elab_as_elim]
 protected theorem induction_on {C : M ⊗[R] N → Prop} (z : M ⊗[R] N) (C0 : C 0)
     (C1 : ∀ {x y}, C <| x ⊗ₜ[R] y) (Cp : ∀ {x y}, C x → C y → C (x + y)) : C z :=
@@ -158,12 +155,6 @@ protected theorem induction_on {C : M ⊗[R] N → Prop} (z : M ⊗[R] N) (C0 :
 
 variable (M)
 
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 @[simp]
 theorem zero_tmul (n : N) : (0 : M) ⊗ₜ[R] n = 0 :=
   Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_zero_left _
@@ -171,24 +162,12 @@ theorem zero_tmul (n : N) : (0 : M) ⊗ₜ[R] n = 0 :=
 
 variable {M}
 
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 theorem add_tmul (m₁ m₂ : M) (n : N) : (m₁ + m₂) ⊗ₜ n = m₁ ⊗ₜ n + m₂ ⊗ₜ[R] n :=
   Eq.symm <| Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_add_left _ _ _
 #align tensor_product.add_tmul TensorProduct.add_tmul
 
 variable (N)
 
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 @[simp]
 theorem tmul_zero (m : M) : m ⊗ₜ[R] (0 : N) = 0 :=
   Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_zero_right _
@@ -196,12 +175,6 @@ theorem tmul_zero (m : M) : m ⊗ₜ[R] (0 : N) = 0 :=
 
 variable {N}
 
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 theorem tmul_add (m : M) (n₁ n₂ : N) : m ⊗ₜ (n₁ + n₂) = m ⊗ₜ n₁ + m ⊗ₜ[R] n₂ :=
   Eq.symm <| Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_add_right _ _ _
 #align tensor_product.tmul_add TensorProduct.tmul_add
@@ -228,12 +201,6 @@ class CompatibleSMul [DistribMulAction R' N] where
 
 end
 
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 /-- Note that this provides the default `compatible_smul R R M N` instance through
 `mul_action.is_scalar_tower.left`. -/
 instance (priority := 100) CompatibleSMul.isScalarTower [SMul R' R] [IsScalarTower R' R M]
@@ -245,29 +212,17 @@ instance (priority := 100) CompatibleSMul.isScalarTower [SMul R' R] [IsScalarTow
     exact Quotient.sound' <| AddConGen.Rel.of _ _ <| eqv.of_smul _ _ _⟩
 #align tensor_product.compatible_smul.is_scalar_tower TensorProduct.CompatibleSMul.isScalarTower
 
-/- warning: tensor_product.smul_tmul -> TensorProduct.smul_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.smul_tmul TensorProduct.smul_tmulₓ'. -/
 /-- `smul` can be moved from one side of the product to the other .-/
 theorem smul_tmul [DistribMulAction R' N] [CompatibleSMul R R' M N] (r : R') (m : M) (n : N) :
     (r • m) ⊗ₜ n = m ⊗ₜ[R] (r • n) :=
   CompatibleSMul.smul_tmul _ _ _
 #align tensor_product.smul_tmul TensorProduct.smul_tmul
 
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 /-- Auxiliary function to defining scalar multiplication on tensor product. -/
 def SMul.aux {R' : Type _} [SMul R' M] (r : R') : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
   FreeAddMonoid.lift fun p : M × N => (r • p.1) ⊗ₜ p.2
 #align tensor_product.smul.aux TensorProduct.SMul.aux
 
-/- warning: tensor_product.smul.aux_of -> TensorProduct.SMul.aux_of is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.smul.aux_of TensorProduct.SMul.aux_ofₓ'. -/
 theorem SMul.aux_of {R' : Type _} [SMul R' M] (r : R') (m : M) (n : N) :
     SMul.aux r (FreeAddMonoid.of (m, n)) = (r • m) ⊗ₜ[R] n :=
   rfl
@@ -277,12 +232,6 @@ variable [SMulCommClass R R' M]
 
 variable [SMulCommClass R R'' M]
 
-/- warning: tensor_product.left_has_smul -> TensorProduct.leftHasSMul is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tensor_product.left_has_smul TensorProduct.leftHasSMulₓ'. -/
 /-- Given two modules over a commutative semiring `R`, if one of the factors carries a
 (distributive) action of a second type of scalars `R'`, which commutes with the action of `R`, then
 the tensor product (over `R`) carries an action of `R'`.
@@ -318,23 +267,14 @@ instance leftHasSMul : SMul R' (M ⊗[R] N) :=
 instance : SMul R (M ⊗[R] N) :=
   TensorProduct.leftHasSMul
 
-/- warning: tensor_product.smul_zero -> TensorProduct.smul_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.smul_zero TensorProduct.smul_zeroₓ'. -/
 protected theorem smul_zero (r : R') : (r • 0 : M ⊗[R] N) = 0 :=
   AddMonoidHom.map_zero _
 #align tensor_product.smul_zero TensorProduct.smul_zero
 
-/- warning: tensor_product.smul_add -> TensorProduct.smul_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.smul_add TensorProduct.smul_addₓ'. -/
 protected theorem smul_add (r : R') (x y : M ⊗[R] N) : r • (x + y) = r • x + r • y :=
   AddMonoidHom.map_add _ _ _
 #align tensor_product.smul_add TensorProduct.smul_add
 
-/- warning: tensor_product.zero_smul -> TensorProduct.zero_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.zero_smul TensorProduct.zero_smulₓ'. -/
 protected theorem zero_smul (x : M ⊗[R] N) : (0 : R'') • x = 0 :=
   have : ∀ (r : R'') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   TensorProduct.induction_on x (by rw [TensorProduct.smul_zero])
@@ -342,18 +282,12 @@ protected theorem zero_smul (x : M ⊗[R] N) : (0 : R'') • x = 0 :=
     rw [TensorProduct.smul_add, ihx, ihy, add_zero]
 #align tensor_product.zero_smul TensorProduct.zero_smul
 
-/- warning: tensor_product.one_smul -> TensorProduct.one_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.one_smul TensorProduct.one_smulₓ'. -/
 protected theorem one_smul (x : M ⊗[R] N) : (1 : R') • x = x :=
   have : ∀ (r : R') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   TensorProduct.induction_on x (by rw [TensorProduct.smul_zero]) (fun m n => by rw [this, one_smul])
     fun x y ihx ihy => by rw [TensorProduct.smul_add, ihx, ihy]
 #align tensor_product.one_smul TensorProduct.one_smul
 
-/- warning: tensor_product.add_smul -> TensorProduct.add_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.add_smul TensorProduct.add_smulₓ'. -/
 protected theorem add_smul (r s : R'') (x : M ⊗[R] N) : (r + s) • x = r • x + s • x :=
   have : ∀ (r : R'') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   TensorProduct.induction_on x (by simp_rw [TensorProduct.smul_zero, add_zero])
@@ -368,12 +302,6 @@ instance : AddCommMonoid (M ⊗[R] N) :=
     nsmul_zero := by simp [TensorProduct.zero_smul]
     nsmul_succ := by simp [Nat.succ_eq_one_add, TensorProduct.one_smul, TensorProduct.add_smul] }
 
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-Case conversion may be inaccurate. Consider using '#align tensor_product.left_distrib_mul_action TensorProduct.leftDistribMulActionₓ'. -/
 instance leftDistribMulAction : DistribMulAction R' (M ⊗[R] N) :=
   have : ∀ (r : R') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   { smul := (· • ·)
@@ -389,28 +317,16 @@ instance leftDistribMulAction : DistribMulAction R' (M ⊗[R] N) :=
 instance : DistribMulAction R (M ⊗[R] N) :=
   TensorProduct.leftDistribMulAction
 
-/- warning: tensor_product.smul_tmul' -> TensorProduct.smul_tmul' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.smul_tmul' TensorProduct.smul_tmul'ₓ'. -/
 theorem smul_tmul' (r : R') (m : M) (n : N) : r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n :=
   rfl
 #align tensor_product.smul_tmul' TensorProduct.smul_tmul'
 
-/- warning: tensor_product.tmul_smul -> TensorProduct.tmul_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.tmul_smul TensorProduct.tmul_smulₓ'. -/
 @[simp]
 theorem tmul_smul [DistribMulAction R' N] [CompatibleSMul R R' M N] (r : R') (x : M) (y : N) :
     x ⊗ₜ (r • y) = r • x ⊗ₜ[R] y :=
   (smul_tmul _ _ _).symm
 #align tensor_product.tmul_smul TensorProduct.tmul_smul
 
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-Case conversion may be inaccurate. Consider using '#align tensor_product.smul_tmul_smul TensorProduct.smul_tmul_smulₓ'. -/
 theorem smul_tmul_smul (r s : R) (m : M) (n : N) : (r • m) ⊗ₜ[R] (s • n) = (r * s) • m ⊗ₜ[R] n := by
   simp only [tmul_smul, smul_tmul, mul_smul]
 #align tensor_product.smul_tmul_smul TensorProduct.smul_tmul_smul
@@ -440,9 +356,6 @@ variable {R'₂ : Type _} [Monoid R'₂] [DistribMulAction R'₂ M]
 
 variable [SMulCommClass R R'₂ M] [SMul R'₂ R']
 
-/- warning: tensor_product.is_scalar_tower_left -> TensorProduct.isScalarTower_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.is_scalar_tower_left TensorProduct.isScalarTower_leftₓ'. -/
 /-- `is_scalar_tower R'₂ R' M` implies `is_scalar_tower R'₂ R' (M ⊗[R] N)` -/
 instance isScalarTower_left [IsScalarTower R'₂ R' M] : IsScalarTower R'₂ R' (M ⊗[R] N) :=
   ⟨fun s r x =>
@@ -455,9 +368,6 @@ variable [DistribMulAction R'₂ N] [DistribMulAction R' N]
 
 variable [CompatibleSMul R R'₂ M N] [CompatibleSMul R R' M N]
 
-/- warning: tensor_product.is_scalar_tower_right -> TensorProduct.isScalarTower_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.is_scalar_tower_right TensorProduct.isScalarTower_rightₓ'. -/
 /-- `is_scalar_tower R'₂ R' N` implies `is_scalar_tower R'₂ R' (M ⊗[R] N)` -/
 instance isScalarTower_right [IsScalarTower R'₂ R' N] : IsScalarTower R'₂ R' (M ⊗[R] N) :=
   ⟨fun s r x =>
@@ -468,12 +378,6 @@ instance isScalarTower_right [IsScalarTower R'₂ R' N] : IsScalarTower R'₂ R'
 
 end
 
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 /-- A short-cut instance for the common case, where the requirements for the `compatible_smul`
 instances are sufficient. -/
 instance isScalarTower [SMul R' R] [IsScalarTower R' R M] : IsScalarTower R' R (M ⊗[R] N) :=
@@ -483,12 +387,6 @@ instance isScalarTower [SMul R' R] [IsScalarTower R' R M] : IsScalarTower R' R (
 -- or right
 variable (R M N)
 
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-Case conversion may be inaccurate. Consider using '#align tensor_product.mk TensorProduct.mkₓ'. -/
 /-- The canonical bilinear map `M → N → M ⊗[R] N`. -/
 def mk : M →ₗ[R] N →ₗ[R] M ⊗[R] N :=
   LinearMap.mk₂ R (· ⊗ₜ ·) add_tmul (fun c m n => by rw [smul_tmul, tmul_smul]) tmul_add tmul_smul
@@ -496,30 +394,15 @@ def mk : M →ₗ[R] N →ₗ[R] M ⊗[R] N :=
 
 variable {R M N}
 
-/- warning: tensor_product.mk_apply -> TensorProduct.mk_apply is a dubious translation:
-<too large>
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 @[simp]
 theorem mk_apply (m : M) (n : N) : mk R M N m n = m ⊗ₜ n :=
   rfl
 #align tensor_product.mk_apply TensorProduct.mk_apply
 
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 theorem ite_tmul (x₁ : M) (x₂ : N) (P : Prop) [Decidable P] :
     (if P then x₁ else 0) ⊗ₜ[R] x₂ = if P then x₁ ⊗ₜ x₂ else 0 := by split_ifs <;> simp
 #align tensor_product.ite_tmul TensorProduct.ite_tmul
 
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 theorem tmul_ite (x₁ : M) (x₂ : N) (P : Prop) [Decidable P] :
     (x₁ ⊗ₜ[R] if P then x₂ else 0) = if P then x₁ ⊗ₜ x₂ else 0 := by split_ifs <;> simp
 #align tensor_product.tmul_ite TensorProduct.tmul_ite
@@ -528,12 +411,6 @@ section
 
 open BigOperators
 
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 theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
     (∑ a in s, m a) ⊗ₜ[R] n = ∑ a in s, m a ⊗ₜ[R] n := by
   classical
@@ -542,12 +419,6 @@ theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
     · simp [Finset.sum_insert has, add_tmul, ih]
 #align tensor_product.sum_tmul TensorProduct.sum_tmul
 
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 theorem tmul_sum (m : M) {α : Type _} (s : Finset α) (n : α → N) :
     (m ⊗ₜ[R] ∑ a in s, n a) = ∑ a in s, m ⊗ₜ[R] n a := by
   classical
@@ -560,12 +431,6 @@ end
 
 variable (R M N)
 
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 /-- The simple (aka pure) elements span the tensor product. -/
 theorem span_tmul_eq_top : Submodule.span R { t : M ⊗[R] N | ∃ m n, m ⊗ₜ n = t } = ⊤ :=
   by
@@ -576,12 +441,6 @@ theorem span_tmul_eq_top : Submodule.span R { t : M ⊗[R] N | ∃ m n, m ⊗ₜ
   · intro t₁ t₂ ht₁ ht₂; exact Submodule.add_mem _ ht₁ ht₂
 #align tensor_product.span_tmul_eq_top TensorProduct.span_tmul_eq_top
 
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 @[simp]
 theorem map₂_mk_top_top_eq_top : Submodule.map₂ (mk R M N) ⊤ ⊤ = ⊤ :=
   by
@@ -624,18 +483,12 @@ def liftAux : M ⊗[R] N →+ P :=
 #align tensor_product.lift_aux TensorProduct.liftAux
 -/
 
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 theorem liftAux_tmul (m n) : liftAux f (m ⊗ₜ n) = f m n :=
   rfl
 #align tensor_product.lift_aux_tmul TensorProduct.liftAux_tmul
 
 variable {f}
 
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 @[simp]
 theorem liftAux.smul (r : R) (x) : liftAux f (r • x) = r • liftAux f x :=
   TensorProduct.induction_on x (smul_zero _).symm
@@ -657,65 +510,38 @@ def lift : M ⊗ N →ₗ[R] P :=
 
 variable {f}
 
-/- warning: tensor_product.lift.tmul -> TensorProduct.lift.tmul is a dubious translation:
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 @[simp]
 theorem lift.tmul (x y) : lift f (x ⊗ₜ y) = f x y :=
   rfl
 #align tensor_product.lift.tmul TensorProduct.lift.tmul
 
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 @[simp]
 theorem lift.tmul' (x y) : (lift f).1 (x ⊗ₜ y) = f x y :=
   rfl
 #align tensor_product.lift.tmul' TensorProduct.lift.tmul'
 
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 theorem ext' {g h : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x ⊗ₜ y)) : g = h :=
   LinearMap.ext fun z =>
     TensorProduct.induction_on z (by simp_rw [LinearMap.map_zero]) H fun x y ihx ihy => by
       rw [g.map_add, h.map_add, ihx, ihy]
 #align tensor_product.ext' TensorProduct.ext'
 
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 theorem lift.unique {g : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = f x y) : g = lift f :=
   ext' fun m n => by rw [H, lift.tmul]
 #align tensor_product.lift.unique TensorProduct.lift.unique
 
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 theorem lift_mk : lift (mk R M N) = LinearMap.id :=
   Eq.symm <| lift.unique fun x y => rfl
 #align tensor_product.lift_mk TensorProduct.lift_mk
 
-/- warning: tensor_product.lift_compr₂ -> TensorProduct.lift_compr₂ is a dubious translation:
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 theorem lift_compr₂ (g : P →ₗ[R] Q) : lift (f.compr₂ g) = g.comp (lift f) :=
   Eq.symm <| lift.unique fun x y => by simp
 #align tensor_product.lift_compr₂ TensorProduct.lift_compr₂
 
-/- warning: tensor_product.lift_mk_compr₂ -> TensorProduct.lift_mk_compr₂ is a dubious translation:
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 theorem lift_mk_compr₂ (f : M ⊗ N →ₗ[R] P) : lift ((mk R M N).compr₂ f) = f := by
   rw [lift_compr₂ f, lift_mk, LinearMap.comp_id]
 #align tensor_product.lift_mk_compr₂ TensorProduct.lift_mk_compr₂
 
-/- warning: tensor_product.ext -> TensorProduct.ext is a dubious translation:
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 /-- This used to be an `@[ext]` lemma, but it fails very slowly when the `ext` tactic tries to apply
 it in some cases, notably when one wants to show equality of two linear maps. The `@[ext]`
 attribute is now added locally where it is needed. Using this as the `@[ext]` lemma instead of
@@ -743,9 +569,6 @@ def uncurry : (M →ₗ[R] N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] P :=
 
 variable {R M N P}
 
-/- warning: tensor_product.uncurry_apply -> TensorProduct.uncurry_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.uncurry_apply TensorProduct.uncurry_applyₓ'. -/
 @[simp]
 theorem uncurry_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
     uncurry R M N P f (m ⊗ₜ n) = f m n := by rw [uncurry, LinearMap.flip_apply, lift.tmul] <;> rfl
@@ -765,27 +588,18 @@ def lift.equiv : (M →ₗ[R] N →ₗ[R] P) ≃ₗ[R] M ⊗ N →ₗ[R] P :=
 #align tensor_product.lift.equiv TensorProduct.lift.equiv
 -/
 
-/- warning: tensor_product.lift.equiv_apply -> TensorProduct.lift.equiv_apply is a dubious translation:
-<too large>
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 @[simp]
 theorem lift.equiv_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
     lift.equiv R M N P f (m ⊗ₜ n) = f m n :=
   uncurry_apply f m n
 #align tensor_product.lift.equiv_apply TensorProduct.lift.equiv_apply
 
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 @[simp]
 theorem lift.equiv_symm_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) :
     (lift.equiv R M N P).symm f m n = f (m ⊗ₜ n) :=
   rfl
 #align tensor_product.lift.equiv_symm_apply TensorProduct.lift.equiv_symm_apply
 
-/- warning: tensor_product.lcurry -> TensorProduct.lcurry is a dubious translation:
-<too large>
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 /-- Given a linear map `M ⊗ N → P`, compose it with the canonical bilinear map `M → N → M ⊗ N` to
 form a bilinear map `M → N → P`. -/
 def lcurry : (M ⊗[R] N →ₗ[R] P) →ₗ[R] M →ₗ[R] N →ₗ[R] P :=
@@ -794,47 +608,26 @@ def lcurry : (M ⊗[R] N →ₗ[R] P) →ₗ[R] M →ₗ[R] N →ₗ[R] P :=
 
 variable {R M N P}
 
-/- warning: tensor_product.lcurry_apply -> TensorProduct.lcurry_apply is a dubious translation:
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 @[simp]
 theorem lcurry_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) : lcurry R M N P f m n = f (m ⊗ₜ n) :=
   rfl
 #align tensor_product.lcurry_apply TensorProduct.lcurry_apply
 
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 /-- Given a linear map `M ⊗ N → P`, compose it with the canonical bilinear map `M → N → M ⊗ N` to
 form a bilinear map `M → N → P`. -/
 def curry (f : M ⊗ N →ₗ[R] P) : M →ₗ[R] N →ₗ[R] P :=
   lcurry R M N P f
 #align tensor_product.curry TensorProduct.curry
 
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 @[simp]
 theorem curry_apply (f : M ⊗ N →ₗ[R] P) (m : M) (n : N) : curry f m n = f (m ⊗ₜ n) :=
   rfl
 #align tensor_product.curry_apply TensorProduct.curry_apply
 
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 theorem curry_injective : Function.Injective (curry : (M ⊗[R] N →ₗ[R] P) → M →ₗ[R] N →ₗ[R] P) :=
   fun g h H => ext H
 #align tensor_product.curry_injective TensorProduct.curry_injective
 
-/- warning: tensor_product.ext_threefold -> TensorProduct.ext_threefold is a dubious translation:
-<too large>
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 theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
     (H : ∀ x y z, g (x ⊗ₜ y ⊗ₜ z) = h (x ⊗ₜ y ⊗ₜ z)) : g = h :=
   by
@@ -842,9 +635,6 @@ theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
   exact H x y z
 #align tensor_product.ext_threefold TensorProduct.ext_threefold
 
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-<too large>
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 -- We'll need this one for checking the pentagon identity!
 theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
     (H : ∀ w x y z, g (w ⊗ₜ x ⊗ₜ y ⊗ₜ z) = h (w ⊗ₜ x ⊗ₜ y ⊗ₜ z)) : g = h :=
@@ -853,9 +643,6 @@ theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
   exact H w x y z
 #align tensor_product.ext_fourfold TensorProduct.ext_fourfold
 
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 /-- Two linear maps (M ⊗ N) ⊗ (P ⊗ Q) → S which agree on all elements of the
 form (m ⊗ₜ n) ⊗ₜ (p ⊗ₜ q) are equal. -/
 theorem ext_fourfold' {φ ψ : (M ⊗[R] N) ⊗[R] P ⊗[R] Q →ₗ[R] S}
@@ -873,12 +660,6 @@ section
 
 variable (R M)
 
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 /-- The base ring is a left identity for the tensor product of modules, up to linear equivalence.
 -/
 protected def lid : R ⊗ M ≃ₗ[R] M :=
@@ -888,9 +669,6 @@ protected def lid : R ⊗ M ≃ₗ[R] M :=
 
 end
 
-/- warning: tensor_product.lid_tmul -> TensorProduct.lid_tmul is a dubious translation:
-<too large>
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 @[simp]
 theorem lid_tmul (m : M) (r : R) : (TensorProduct.lid R M : R ⊗ M → M) (r ⊗ₜ m) = r • m :=
   by
@@ -898,9 +676,6 @@ theorem lid_tmul (m : M) (r : R) : (TensorProduct.lid R M : R ⊗ M → M) (r 
   simp
 #align tensor_product.lid_tmul TensorProduct.lid_tmul
 
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-<too large>
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 @[simp]
 theorem lid_symm_apply (m : M) : (TensorProduct.lid R M).symm m = 1 ⊗ₜ m :=
   rfl
@@ -910,12 +685,6 @@ section
 
 variable (R M N)
 
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-Case conversion may be inaccurate. Consider using '#align tensor_product.comm TensorProduct.commₓ'. -/
 /-- The tensor product of modules is commutative, up to linear equivalence.
 -/
 protected def comm : M ⊗ N ≃ₗ[R] N ⊗ M :=
@@ -923,17 +692,11 @@ protected def comm : M ⊗ N ≃ₗ[R] N ⊗ M :=
     (ext' fun m n => rfl)
 #align tensor_product.comm TensorProduct.comm
 
-/- warning: tensor_product.comm_tmul -> TensorProduct.comm_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.comm_tmul TensorProduct.comm_tmulₓ'. -/
 @[simp]
 theorem comm_tmul (m : M) (n : N) : (TensorProduct.comm R M N) (m ⊗ₜ n) = n ⊗ₜ m :=
   rfl
 #align tensor_product.comm_tmul TensorProduct.comm_tmul
 
-/- warning: tensor_product.comm_symm_tmul -> TensorProduct.comm_symm_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.comm_symm_tmul TensorProduct.comm_symm_tmulₓ'. -/
 @[simp]
 theorem comm_symm_tmul (m : M) (n : N) : (TensorProduct.comm R M N).symm (n ⊗ₜ m) = m ⊗ₜ n :=
   rfl
@@ -945,12 +708,6 @@ section
 
 variable (R M)
 
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 /-- The base ring is a right identity for the tensor product of modules, up to linear equivalence.
 -/
 protected def rid : M ⊗[R] R ≃ₗ[R] M :=
@@ -959,9 +716,6 @@ protected def rid : M ⊗[R] R ≃ₗ[R] M :=
 
 end
 
-/- warning: tensor_product.rid_tmul -> TensorProduct.rid_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.rid_tmul TensorProduct.rid_tmulₓ'. -/
 @[simp]
 theorem rid_tmul (m : M) (r : R) : (TensorProduct.rid R M) (m ⊗ₜ r) = r • m :=
   by
@@ -969,9 +723,6 @@ theorem rid_tmul (m : M) (r : R) : (TensorProduct.rid R M) (m ⊗ₜ r) = r •
   simp
 #align tensor_product.rid_tmul TensorProduct.rid_tmul
 
-/- warning: tensor_product.rid_symm_apply -> TensorProduct.rid_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.rid_symm_apply TensorProduct.rid_symm_applyₓ'. -/
 @[simp]
 theorem rid_symm_apply (m : M) : (TensorProduct.rid R M).symm m = m ⊗ₜ 1 :=
   rfl
@@ -983,9 +734,6 @@ section
 
 variable (R M N P)
 
-/- warning: tensor_product.assoc -> TensorProduct.assoc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.assoc TensorProduct.assocₓ'. -/
 /-- The associator for tensor product of R-modules, as a linear equivalence. -/
 protected def assoc : (M ⊗[R] N) ⊗[R] P ≃ₗ[R] M ⊗[R] N ⊗[R] P := by
   refine'
@@ -1000,46 +748,28 @@ protected def assoc : (M ⊗[R] N) ⊗[R] P ≃ₗ[R] M ⊗[R] N ⊗[R] P := by
 
 end
 
-/- warning: tensor_product.assoc_tmul -> TensorProduct.assoc_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.assoc_tmul TensorProduct.assoc_tmulₓ'. -/
 @[simp]
 theorem assoc_tmul (m : M) (n : N) (p : P) :
     (TensorProduct.assoc R M N P) (m ⊗ₜ n ⊗ₜ p) = m ⊗ₜ (n ⊗ₜ p) :=
   rfl
 #align tensor_product.assoc_tmul TensorProduct.assoc_tmul
 
-/- warning: tensor_product.assoc_symm_tmul -> TensorProduct.assoc_symm_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.assoc_symm_tmul TensorProduct.assoc_symm_tmulₓ'. -/
 @[simp]
 theorem assoc_symm_tmul (m : M) (n : N) (p : P) :
     (TensorProduct.assoc R M N P).symm (m ⊗ₜ (n ⊗ₜ p)) = m ⊗ₜ n ⊗ₜ p :=
   rfl
 #align tensor_product.assoc_symm_tmul TensorProduct.assoc_symm_tmul
 
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-Case conversion may be inaccurate. Consider using '#align tensor_product.map TensorProduct.mapₓ'. -/
 /-- The tensor product of a pair of linear maps between modules. -/
 def map (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : M ⊗ N →ₗ[R] P ⊗ Q :=
   lift <| comp (compl₂ (mk _ _ _) g) f
 #align tensor_product.map TensorProduct.map
 
-/- warning: tensor_product.map_tmul -> TensorProduct.map_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.map_tmul TensorProduct.map_tmulₓ'. -/
 @[simp]
 theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f g (m ⊗ₜ n) = f m ⊗ₜ g n :=
   rfl
 #align tensor_product.map_tmul TensorProduct.map_tmul
 
-/- warning: tensor_product.map_range_eq_span_tmul -> TensorProduct.map_range_eq_span_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.map_range_eq_span_tmul TensorProduct.map_range_eq_span_tmulₓ'. -/
 theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (map f g).range = Submodule.span R { t | ∃ m n, f m ⊗ₜ g n = t } :=
   by
@@ -1051,9 +781,6 @@ theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
   · rintro ⟨m, n, rfl⟩; use m ⊗ₜ n, m, n; simp only [map_tmul]
 #align tensor_product.map_range_eq_span_tmul TensorProduct.map_range_eq_span_tmul
 
-/- warning: tensor_product.map_incl -> TensorProduct.mapIncl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.map_incl TensorProduct.mapInclₓ'. -/
 /-- Given submodules `p ⊆ P` and `q ⊆ Q`, this is the natural map: `p ⊗ q → P ⊗ Q`. -/
 @[simp]
 def mapIncl (p : Submodule R P) (q : Submodule R Q) : p ⊗[R] q →ₗ[R] P ⊗[R] Q :=
@@ -1068,17 +795,11 @@ variable [AddCommMonoid P'] [Module R P']
 
 variable [AddCommMonoid Q'] [Module R Q']
 
-/- warning: tensor_product.map_comp -> TensorProduct.map_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.map_comp TensorProduct.map_compₓ'. -/
 theorem map_comp (f₂ : P →ₗ[R] P') (f₁ : M →ₗ[R] P) (g₂ : Q →ₗ[R] Q') (g₁ : N →ₗ[R] Q) :
     map (f₂.comp f₁) (g₂.comp g₁) = (map f₂ g₂).comp (map f₁ g₁) :=
   ext' fun _ _ => rfl
 #align tensor_product.map_comp TensorProduct.map_comp
 
-/- warning: tensor_product.lift_comp_map -> TensorProduct.lift_comp_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.lift_comp_map TensorProduct.lift_comp_mapₓ'. -/
 theorem lift_comp_map (i : P →ₗ[R] Q →ₗ[R] Q') (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (lift i).comp (map f g) = lift ((i.comp f).compl₂ g) :=
   ext' fun _ _ => rfl
@@ -1086,36 +807,21 @@ theorem lift_comp_map (i : P →ₗ[R] Q →ₗ[R] Q') (f : M →ₗ[R] P) (g :
 
 attribute [local ext] ext
 
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 @[simp]
 theorem map_id : map (id : M →ₗ[R] M) (id : N →ₗ[R] N) = id := by ext;
   simp only [mk_apply, id_coe, compr₂_apply, id.def, map_tmul]
 #align tensor_product.map_id TensorProduct.map_id
 
-/- warning: tensor_product.map_one -> TensorProduct.map_one is a dubious translation:
-<too large>
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 @[simp]
 theorem map_one : map (1 : M →ₗ[R] M) (1 : N →ₗ[R] N) = 1 :=
   map_id
 #align tensor_product.map_one TensorProduct.map_one
 
-/- warning: tensor_product.map_mul -> TensorProduct.map_mul is a dubious translation:
-<too large>
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 theorem map_mul (f₁ f₂ : M →ₗ[R] M) (g₁ g₂ : N →ₗ[R] N) :
     map (f₁ * f₂) (g₁ * g₂) = map f₁ g₁ * map f₂ g₂ :=
   map_comp f₁ f₂ g₁ g₂
 #align tensor_product.map_mul TensorProduct.map_mul
 
-/- warning: tensor_product.map_pow -> TensorProduct.map_pow is a dubious translation:
-<too large>
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 @[simp]
 protected theorem map_pow (f : M →ₗ[R] M) (g : N →ₗ[R] N) (n : ℕ) :
     map f g ^ n = map (f ^ n) (g ^ n) :=
@@ -1125,39 +831,24 @@ protected theorem map_pow (f : M →ₗ[R] M) (g : N →ₗ[R] N) (n : ℕ) :
   · simp only [pow_succ', ih, map_mul]
 #align tensor_product.map_pow TensorProduct.map_pow
 
-/- warning: tensor_product.map_add_left -> TensorProduct.map_add_left is a dubious translation:
-<too large>
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 theorem map_add_left (f₁ f₂ : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (f₁ + f₂) g = map f₁ g + map f₂ g :=
   by ext; simp only [add_tmul, compr₂_apply, mk_apply, map_tmul, add_apply]
 #align tensor_product.map_add_left TensorProduct.map_add_left
 
-/- warning: tensor_product.map_add_right -> TensorProduct.map_add_right is a dubious translation:
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 theorem map_add_right (f : M →ₗ[R] P) (g₁ g₂ : N →ₗ[R] Q) : map f (g₁ + g₂) = map f g₁ + map f g₂ :=
   by ext; simp only [tmul_add, compr₂_apply, mk_apply, map_tmul, add_apply]
 #align tensor_product.map_add_right TensorProduct.map_add_right
 
-/- warning: tensor_product.map_smul_left -> TensorProduct.map_smul_left is a dubious translation:
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 theorem map_smul_left (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (r • f) g = r • map f g := by
   ext; simp only [smul_tmul, compr₂_apply, mk_apply, map_tmul, smul_apply, tmul_smul]
 #align tensor_product.map_smul_left TensorProduct.map_smul_left
 
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 theorem map_smul_right (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map f (r • g) = r • map f g := by
   ext; simp only [smul_tmul, compr₂_apply, mk_apply, map_tmul, smul_apply, tmul_smul]
 #align tensor_product.map_smul_right TensorProduct.map_smul_right
 
 variable (R M N P Q)
 
-/- warning: tensor_product.map_bilinear -> TensorProduct.mapBilinear is a dubious translation:
-<too large>
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 /-- The tensor product of a pair of linear maps between modules, bilinear in both maps. -/
 def mapBilinear : (M →ₗ[R] P) →ₗ[R] (N →ₗ[R] Q) →ₗ[R] M ⊗[R] N →ₗ[R] P ⊗[R] Q :=
   LinearMap.mk₂ R map map_add_left map_smul_left map_add_right map_smul_right
@@ -1187,35 +878,23 @@ def homTensorHomMap : (M →ₗ[R] P) ⊗[R] (N →ₗ[R] Q) →ₗ[R] M ⊗[R]
 
 variable {R M N P Q}
 
-/- warning: tensor_product.map_bilinear_apply -> TensorProduct.mapBilinear_apply is a dubious translation:
-<too large>
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 @[simp]
 theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear R M N P Q f g = map f g :=
   rfl
 #align tensor_product.map_bilinear_apply TensorProduct.mapBilinear_apply
 
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-<too large>
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 @[simp]
 theorem lTensorHomToHomLTensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
     lTensorHomToHomLTensor R M P Q (p ⊗ₜ f) m = p ⊗ₜ f m :=
   rfl
 #align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.lTensorHomToHomLTensor_apply
 
-/- warning: tensor_product.rtensor_hom_to_hom_rtensor_apply -> TensorProduct.rTensorHomToHomRTensor_apply is a dubious translation:
-<too large>
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 @[simp]
 theorem rTensorHomToHomRTensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
     rTensorHomToHomRTensor R M P Q (f ⊗ₜ q) m = f m ⊗ₜ q :=
   rfl
 #align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rTensorHomToHomRTensor_apply
 
-/- warning: tensor_product.hom_tensor_hom_map_apply -> TensorProduct.homTensorHomMap_apply is a dubious translation:
-<too large>
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 @[simp]
 theorem homTensorHomMap_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     homTensorHomMap R M N P Q (f ⊗ₜ g) = map f g :=
@@ -1224,12 +903,6 @@ theorem homTensorHomMap_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
 
 end
 
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 /-- If `M` and `P` are linearly equivalent and `N` and `Q` are linearly equivalent
 then `M ⊗ N` and `P ⊗ Q` are linearly equivalent. -/
 def congr (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) : M ⊗ N ≃ₗ[R] P ⊗ Q :=
@@ -1238,18 +911,12 @@ def congr (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) : M ⊗ N ≃ₗ[R] P ⊗ Q :=
     (ext' fun m n => by simp <;> simp only [LinearEquiv.symm_apply_apply])
 #align tensor_product.congr TensorProduct.congr
 
-/- warning: tensor_product.congr_tmul -> TensorProduct.congr_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.congr_tmul TensorProduct.congr_tmulₓ'. -/
 @[simp]
 theorem congr_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (m : M) (n : N) :
     congr f g (m ⊗ₜ n) = f m ⊗ₜ g n :=
   rfl
 #align tensor_product.congr_tmul TensorProduct.congr_tmul
 
-/- warning: tensor_product.congr_symm_tmul -> TensorProduct.congr_symm_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.congr_symm_tmul TensorProduct.congr_symm_tmulₓ'. -/
 @[simp]
 theorem congr_symm_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (p : P) (q : Q) :
     (congr f g).symm (p ⊗ₜ q) = f.symm p ⊗ₜ g.symm q :=
@@ -1258,12 +925,6 @@ theorem congr_symm_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (p : P) (q : Q)
 
 variable (R M N P Q)
 
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-Case conversion may be inaccurate. Consider using '#align tensor_product.left_comm TensorProduct.leftCommₓ'. -/
 /-- A tensor product analogue of `mul_left_comm`. -/
 def leftComm : M ⊗[R] N ⊗[R] P ≃ₗ[R] N ⊗[R] M ⊗[R] P :=
   let e₁ := (TensorProduct.assoc R M N P).symm
@@ -1274,17 +935,11 @@ def leftComm : M ⊗[R] N ⊗[R] P ≃ₗ[R] N ⊗[R] M ⊗[R] P :=
 
 variable {M N P Q}
 
-/- warning: tensor_product.left_comm_tmul -> TensorProduct.leftComm_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.left_comm_tmul TensorProduct.leftComm_tmulₓ'. -/
 @[simp]
 theorem leftComm_tmul (m : M) (n : N) (p : P) : leftComm R M N P (m ⊗ₜ (n ⊗ₜ p)) = n ⊗ₜ (m ⊗ₜ p) :=
   rfl
 #align tensor_product.left_comm_tmul TensorProduct.leftComm_tmul
 
-/- warning: tensor_product.left_comm_symm_tmul -> TensorProduct.leftComm_symm_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.left_comm_symm_tmul TensorProduct.leftComm_symm_tmulₓ'. -/
 @[simp]
 theorem leftComm_symm_tmul (m : M) (n : N) (p : P) :
     (leftComm R M N P).symm (n ⊗ₜ (m ⊗ₜ p)) = m ⊗ₜ (n ⊗ₜ p) :=
@@ -1293,9 +948,6 @@ theorem leftComm_symm_tmul (m : M) (n : N) (p : P) :
 
 variable (M N P Q)
 
-/- warning: tensor_product.tensor_tensor_tensor_comm -> TensorProduct.tensorTensorTensorComm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_comm TensorProduct.tensorTensorTensorCommₓ'. -/
 /-- This special case is worth defining explicitly since it is useful for defining multiplication
 on tensor products of modules carrying multiplications (e.g., associative rings, Lie rings, ...).
 
@@ -1315,18 +967,12 @@ def tensorTensorTensorComm : (M ⊗[R] N) ⊗[R] P ⊗[R] Q ≃ₗ[R] (M ⊗[R]
 
 variable {M N P Q}
 
-/- warning: tensor_product.tensor_tensor_tensor_comm_tmul -> TensorProduct.tensorTensorTensorComm_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_comm_tmul TensorProduct.tensorTensorTensorComm_tmulₓ'. -/
 @[simp]
 theorem tensorTensorTensorComm_tmul (m : M) (n : N) (p : P) (q : Q) :
     tensorTensorTensorComm R M N P Q (m ⊗ₜ n ⊗ₜ (p ⊗ₜ q)) = m ⊗ₜ p ⊗ₜ (n ⊗ₜ q) :=
   rfl
 #align tensor_product.tensor_tensor_tensor_comm_tmul TensorProduct.tensorTensorTensorComm_tmul
 
-/- warning: tensor_product.tensor_tensor_tensor_comm_symm -> TensorProduct.tensorTensorTensorComm_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_comm_symm TensorProduct.tensorTensorTensorComm_symmₓ'. -/
 @[simp]
 theorem tensorTensorTensorComm_symm :
     (tensorTensorTensorComm R M N P Q).symm = tensorTensorTensorComm R M P N Q :=
@@ -1335,9 +981,6 @@ theorem tensorTensorTensorComm_symm :
 
 variable (M N P Q)
 
-/- warning: tensor_product.tensor_tensor_tensor_assoc -> TensorProduct.tensorTensorTensorAssoc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_assoc TensorProduct.tensorTensorTensorAssocₓ'. -/
 /-- This special case is useful for describing the interplay between `dual_tensor_hom_equiv` and
 composition of linear maps.
 
@@ -1353,18 +996,12 @@ def tensorTensorTensorAssoc : (M ⊗[R] N) ⊗[R] P ⊗[R] Q ≃ₗ[R] (M ⊗[R]
 
 variable {M N P Q}
 
-/- warning: tensor_product.tensor_tensor_tensor_assoc_tmul -> TensorProduct.tensorTensorTensorAssoc_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_assoc_tmul TensorProduct.tensorTensorTensorAssoc_tmulₓ'. -/
 @[simp]
 theorem tensorTensorTensorAssoc_tmul (m : M) (n : N) (p : P) (q : Q) :
     tensorTensorTensorAssoc R M N P Q (m ⊗ₜ n ⊗ₜ (p ⊗ₜ q)) = m ⊗ₜ (n ⊗ₜ p) ⊗ₜ q :=
   rfl
 #align tensor_product.tensor_tensor_tensor_assoc_tmul TensorProduct.tensorTensorTensorAssoc_tmul
 
-/- warning: tensor_product.tensor_tensor_tensor_assoc_symm_tmul -> TensorProduct.tensorTensorTensorAssoc_symm_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_assoc_symm_tmul TensorProduct.tensorTensorTensorAssoc_symm_tmulₓ'. -/
 @[simp]
 theorem tensorTensorTensorAssoc_symm_tmul (m : M) (n : N) (p : P) (q : Q) :
     (tensorTensorTensorAssoc R M N P Q).symm (m ⊗ₜ (n ⊗ₜ p) ⊗ₜ q) = m ⊗ₜ n ⊗ₜ (p ⊗ₜ q) :=
@@ -1377,23 +1014,11 @@ namespace LinearMap
 
 variable {R} (M) {N P Q}
 
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-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor LinearMap.lTensorₓ'. -/
 /-- `ltensor M f : M ⊗ N →ₗ M ⊗ P` is the natural linear map induced by `f : N →ₗ P`. -/
 def lTensor (f : N →ₗ[R] P) : M ⊗ N →ₗ[R] M ⊗ P :=
   TensorProduct.map id f
 #align linear_map.ltensor LinearMap.lTensor
 
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-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor LinearMap.rTensorₓ'. -/
 /-- `rtensor f M : N₁ ⊗ M →ₗ N₂ ⊗ M` is the natural linear map induced by `f : N₁ →ₗ N₂`. -/
 def rTensor (f : N →ₗ[R] P) : N ⊗ M →ₗ[R] P ⊗ M :=
   TensorProduct.map f id
@@ -1401,17 +1026,11 @@ def rTensor (f : N →ₗ[R] P) : N ⊗ M →ₗ[R] P ⊗ M :=
 
 variable (g : P →ₗ[R] Q) (f : N →ₗ[R] P)
 
-/- warning: linear_map.ltensor_tmul -> LinearMap.lTensor_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_tmul LinearMap.lTensor_tmulₓ'. -/
 @[simp]
 theorem lTensor_tmul (m : M) (n : N) : f.lTensor M (m ⊗ₜ n) = m ⊗ₜ f n :=
   rfl
 #align linear_map.ltensor_tmul LinearMap.lTensor_tmul
 
-/- warning: linear_map.rtensor_tmul -> LinearMap.rTensor_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_tmul LinearMap.rTensor_tmulₓ'. -/
 @[simp]
 theorem rTensor_tmul (m : M) (n : N) : f.rTensor M (n ⊗ₜ m) = f n ⊗ₜ m :=
   rfl
@@ -1421,9 +1040,6 @@ open TensorProduct
 
 attribute [local ext] TensorProduct.ext
 
-/- warning: linear_map.ltensor_hom -> LinearMap.lTensorHom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_hom LinearMap.lTensorHomₓ'. -/
 /-- `ltensor_hom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
 def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
     where
@@ -1434,9 +1050,6 @@ def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
     simp only [compr₂_apply, mk_apply, tmul_smul, smul_apply, ltensor_tmul]
 #align linear_map.ltensor_hom LinearMap.lTensorHom
 
-/- warning: linear_map.rtensor_hom -> LinearMap.rTensorHom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_hom LinearMap.rTensorHomₓ'. -/
 /-- `rtensor_hom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
 def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
     where
@@ -1447,147 +1060,87 @@ def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
     simp only [compr₂_apply, mk_apply, smul_tmul, tmul_smul, smul_apply, rtensor_tmul]
 #align linear_map.rtensor_hom LinearMap.rTensorHom
 
-/- warning: linear_map.coe_ltensor_hom -> LinearMap.coe_lTensorHom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.coe_ltensor_hom LinearMap.coe_lTensorHomₓ'. -/
 @[simp]
 theorem coe_lTensorHom : (lTensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R] M ⊗[R] P) = lTensor M :=
   rfl
 #align linear_map.coe_ltensor_hom LinearMap.coe_lTensorHom
 
-/- warning: linear_map.coe_rtensor_hom -> LinearMap.coe_rTensorHom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.coe_rtensor_hom LinearMap.coe_rTensorHomₓ'. -/
 @[simp]
 theorem coe_rTensorHom : (rTensorHom M : (N →ₗ[R] P) → N ⊗[R] M →ₗ[R] P ⊗[R] M) = rTensor M :=
   rfl
 #align linear_map.coe_rtensor_hom LinearMap.coe_rTensorHom
 
-/- warning: linear_map.ltensor_add -> LinearMap.lTensor_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_add LinearMap.lTensor_addₓ'. -/
 @[simp]
 theorem lTensor_add (f g : N →ₗ[R] P) : (f + g).lTensor M = f.lTensor M + g.lTensor M :=
   (lTensorHom M).map_add f g
 #align linear_map.ltensor_add LinearMap.lTensor_add
 
-/- warning: linear_map.rtensor_add -> LinearMap.rTensor_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_add LinearMap.rTensor_addₓ'. -/
 @[simp]
 theorem rTensor_add (f g : N →ₗ[R] P) : (f + g).rTensor M = f.rTensor M + g.rTensor M :=
   (rTensorHom M).map_add f g
 #align linear_map.rtensor_add LinearMap.rTensor_add
 
-/- warning: linear_map.ltensor_zero -> LinearMap.lTensor_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_zero LinearMap.lTensor_zeroₓ'. -/
 @[simp]
 theorem lTensor_zero : lTensor M (0 : N →ₗ[R] P) = 0 :=
   (lTensorHom M).map_zero
 #align linear_map.ltensor_zero LinearMap.lTensor_zero
 
-/- warning: linear_map.rtensor_zero -> LinearMap.rTensor_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_zero LinearMap.rTensor_zeroₓ'. -/
 @[simp]
 theorem rTensor_zero : rTensor M (0 : N →ₗ[R] P) = 0 :=
   (rTensorHom M).map_zero
 #align linear_map.rtensor_zero LinearMap.rTensor_zero
 
-/- warning: linear_map.ltensor_smul -> LinearMap.lTensor_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_smul LinearMap.lTensor_smulₓ'. -/
 @[simp]
 theorem lTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).lTensor M = r • f.lTensor M :=
   (lTensorHom M).map_smul r f
 #align linear_map.ltensor_smul LinearMap.lTensor_smul
 
-/- warning: linear_map.rtensor_smul -> LinearMap.rTensor_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_smul LinearMap.rTensor_smulₓ'. -/
 @[simp]
 theorem rTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).rTensor M = r • f.rTensor M :=
   (rTensorHom M).map_smul r f
 #align linear_map.rtensor_smul LinearMap.rTensor_smul
 
-/- warning: linear_map.ltensor_comp -> LinearMap.lTensor_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp LinearMap.lTensor_compₓ'. -/
 theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) := by ext (m n);
   simp only [compr₂_apply, mk_apply, comp_apply, ltensor_tmul]
 #align linear_map.ltensor_comp LinearMap.lTensor_comp
 
-/- warning: linear_map.ltensor_comp_apply -> LinearMap.lTensor_comp_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_apply LinearMap.lTensor_comp_applyₓ'. -/
 theorem lTensor_comp_apply (x : M ⊗[R] N) :
     (g.comp f).lTensor M x = (g.lTensor M) ((f.lTensor M) x) := by rw [ltensor_comp, coe_comp]
 #align linear_map.ltensor_comp_apply LinearMap.lTensor_comp_apply
 
-/- warning: linear_map.rtensor_comp -> LinearMap.rTensor_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp LinearMap.rTensor_compₓ'. -/
 theorem rTensor_comp : (g.comp f).rTensor M = (g.rTensor M).comp (f.rTensor M) := by ext (m n);
   simp only [compr₂_apply, mk_apply, comp_apply, rtensor_tmul]
 #align linear_map.rtensor_comp LinearMap.rTensor_comp
 
-/- warning: linear_map.rtensor_comp_apply -> LinearMap.rTensor_comp_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_apply LinearMap.rTensor_comp_applyₓ'. -/
 theorem rTensor_comp_apply (x : N ⊗[R] M) :
     (g.comp f).rTensor M x = (g.rTensor M) ((f.rTensor M) x) := by rw [rtensor_comp, coe_comp]
 #align linear_map.rtensor_comp_apply LinearMap.rTensor_comp_apply
 
-/- warning: linear_map.ltensor_mul -> LinearMap.lTensor_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_mul LinearMap.lTensor_mulₓ'. -/
 theorem lTensor_mul (f g : Module.End R N) : (f * g).lTensor M = f.lTensor M * g.lTensor M :=
   lTensor_comp M f g
 #align linear_map.ltensor_mul LinearMap.lTensor_mul
 
-/- warning: linear_map.rtensor_mul -> LinearMap.rTensor_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_mul LinearMap.rTensor_mulₓ'. -/
 theorem rTensor_mul (f g : Module.End R N) : (f * g).rTensor M = f.rTensor M * g.rTensor M :=
   rTensor_comp M f g
 #align linear_map.rtensor_mul LinearMap.rTensor_mul
 
 variable (N)
 
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 @[simp]
 theorem lTensor_id : (id : N →ₗ[R] N).lTensor M = id :=
   map_id
 #align linear_map.ltensor_id LinearMap.lTensor_id
 
-/- warning: linear_map.ltensor_id_apply -> LinearMap.lTensor_id_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_id_apply LinearMap.lTensor_id_applyₓ'. -/
 -- `simp` can prove this.
 theorem lTensor_id_apply (x : M ⊗[R] N) : (LinearMap.id : N →ₗ[R] N).lTensor M x = x := by
   rw [ltensor_id, id_coe, id.def]
 #align linear_map.ltensor_id_apply LinearMap.lTensor_id_apply
 
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 @[simp]
 theorem rTensor_id : (id : N →ₗ[R] N).rTensor M = id :=
   map_id
 #align linear_map.rtensor_id LinearMap.rTensor_id
 
-/- warning: linear_map.rtensor_id_apply -> LinearMap.rTensor_id_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_id_apply LinearMap.rTensor_id_applyₓ'. -/
 -- `simp` can prove this.
 theorem rTensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rTensor M x = x := by
   rw [rtensor_id, id_coe, id.def]
@@ -1595,54 +1148,36 @@ theorem rTensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rTens
 
 variable {N}
 
-/- warning: linear_map.ltensor_comp_rtensor -> LinearMap.lTensor_comp_rTensor is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_rtensor LinearMap.lTensor_comp_rTensorₓ'. -/
 @[simp]
 theorem lTensor_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (g.lTensor P).comp (f.rTensor N) = map f g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.ltensor_comp_rtensor LinearMap.lTensor_comp_rTensor
 
-/- warning: linear_map.rtensor_comp_ltensor -> LinearMap.rTensor_comp_lTensor is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_ltensor LinearMap.rTensor_comp_lTensorₓ'. -/
 @[simp]
 theorem rTensor_comp_lTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (f.rTensor Q).comp (g.lTensor M) = map f g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.rtensor_comp_ltensor LinearMap.rTensor_comp_lTensor
 
-/- warning: linear_map.map_comp_rtensor -> LinearMap.map_comp_rTensor is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.map_comp_rtensor LinearMap.map_comp_rTensorₓ'. -/
 @[simp]
 theorem map_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (f' : S →ₗ[R] M) :
     (map f g).comp (f'.rTensor _) = map (f.comp f') g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.map_comp_rtensor LinearMap.map_comp_rTensor
 
-/- warning: linear_map.map_comp_ltensor -> LinearMap.map_comp_lTensor is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.map_comp_ltensor LinearMap.map_comp_lTensorₓ'. -/
 @[simp]
 theorem map_comp_lTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (g' : S →ₗ[R] N) :
     (map f g).comp (g'.lTensor _) = map f (g.comp g') := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.map_comp_ltensor LinearMap.map_comp_lTensor
 
-/- warning: linear_map.rtensor_comp_map -> LinearMap.rTensor_comp_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_map LinearMap.rTensor_comp_mapₓ'. -/
 @[simp]
 theorem rTensor_comp_map (f' : P →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (f'.rTensor _).comp (map f g) = map (f'.comp f) g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.rtensor_comp_map LinearMap.rTensor_comp_map
 
-/- warning: linear_map.ltensor_comp_map -> LinearMap.lTensor_comp_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_map LinearMap.lTensor_comp_mapₓ'. -/
 @[simp]
 theorem lTensor_comp_map (g' : Q →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (g'.lTensor _).comp (map f g) = map f (g'.comp g) := by
@@ -1651,17 +1186,11 @@ theorem lTensor_comp_map (g' : Q →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[
 
 variable {M}
 
-/- warning: linear_map.rtensor_pow -> LinearMap.rTensor_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_pow LinearMap.rTensor_powₓ'. -/
 @[simp]
 theorem rTensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rTensor N ^ n = (f ^ n).rTensor N := by
   have h := TensorProduct.map_pow f (id : N →ₗ[R] N) n; rwa [id_pow] at h
 #align linear_map.rtensor_pow LinearMap.rTensor_pow
 
-/- warning: linear_map.ltensor_pow -> LinearMap.lTensor_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_pow LinearMap.lTensor_powₓ'. -/
 @[simp]
 theorem lTensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.lTensor M ^ n = (f ^ n).lTensor M := by
   have h := TensorProduct.map_pow (id : M →ₗ[R] M) f n; rwa [id_pow] at h
@@ -1689,12 +1218,6 @@ open LinearMap
 
 variable (R)
 
-/- warning: tensor_product.neg.aux -> TensorProduct.Neg.aux is a dubious translation:
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 /-- Auxiliary function to defining negation multiplication on tensor product. -/
 def Neg.aux : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
   FreeAddMonoid.lift fun p : M × N => (-p.1) ⊗ₜ p.2
@@ -1702,9 +1225,6 @@ def Neg.aux : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
 
 variable {R}
 
-/- warning: tensor_product.neg.aux_of -> TensorProduct.Neg.aux_of is a dubious translation:
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 theorem Neg.aux_of (m : M) (n : N) : Neg.aux R (FreeAddMonoid.of (m, n)) = (-m) ⊗ₜ[R] n :=
   rfl
 #align tensor_product.neg.aux_of TensorProduct.Neg.aux_of
@@ -1728,12 +1248,6 @@ instance : Neg (M ⊗[R] N)
         | _, _, eqv.add_comm x y =>
           (AddCon.ker_rel _).2 <| by simp_rw [AddMonoidHom.map_add, add_comm]
 
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 protected theorem add_left_neg (x : M ⊗[R] N) : -x + x = 0 :=
   TensorProduct.induction_on x (by rw [add_zero]; apply (neg.aux R).map_zero)
     (fun x y => by convert(add_tmul (-x) x y).symm; rw [add_left_neg, zero_tmul]) fun x y hx hy =>
@@ -1760,52 +1274,22 @@ instance : AddCommGroup (M ⊗[R] N) :=
         add_smul, ← sub_eq_add_neg, sub_self, zero_smul, add_zero]
       rfl }
 
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 theorem neg_tmul (m : M) (n : N) : (-m) ⊗ₜ n = -m ⊗ₜ[R] n :=
   rfl
 #align tensor_product.neg_tmul TensorProduct.neg_tmul
 
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 theorem tmul_neg (m : M) (n : N) : m ⊗ₜ (-n) = -m ⊗ₜ[R] n :=
   (mk R M N _).map_neg _
 #align tensor_product.tmul_neg TensorProduct.tmul_neg
 
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 theorem tmul_sub (m : M) (n₁ n₂ : N) : m ⊗ₜ (n₁ - n₂) = m ⊗ₜ[R] n₁ - m ⊗ₜ[R] n₂ :=
   (mk R M N _).map_sub _ _
 #align tensor_product.tmul_sub TensorProduct.tmul_sub
 
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 theorem sub_tmul (m₁ m₂ : M) (n : N) : (m₁ - m₂) ⊗ₜ n = m₁ ⊗ₜ[R] n - m₂ ⊗ₜ[R] n :=
   (mk R M N).map_sub₂ _ _ _
 #align tensor_product.sub_tmul TensorProduct.sub_tmul
 
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 /-- While the tensor product will automatically inherit a ℤ-module structure from
 `add_comm_group.int_module`, that structure won't be compatible with lemmas like `tmul_smul` unless
 we use a `ℤ-module` instance provided by `tensor_product.left_module`.
@@ -1820,12 +1304,6 @@ instance CompatibleSMul.int : CompatibleSMul R ℤ M N :=
       fun r ih => by simpa [sub_smul, tmul_sub, sub_tmul] using ih⟩
 #align tensor_product.compatible_smul.int TensorProduct.CompatibleSMul.int
 
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 instance CompatibleSMul.unit {S} [Monoid S] [DistribMulAction S M] [DistribMulAction S N]
     [CompatibleSMul R S M N] : CompatibleSMul R Sˣ M N :=
   ⟨fun s m n => (CompatibleSMul.smul_tmul (s : S) m n : _)⟩
@@ -1835,33 +1313,21 @@ end TensorProduct
 
 namespace LinearMap
 
-/- warning: linear_map.ltensor_sub -> LinearMap.lTensor_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_sub LinearMap.lTensor_subₓ'. -/
 @[simp]
 theorem lTensor_sub (f g : N →ₗ[R] P) : (f - g).lTensor M = f.lTensor M - g.lTensor M := by
   simp only [← coe_ltensor_hom, map_sub]
 #align linear_map.ltensor_sub LinearMap.lTensor_sub
 
-/- warning: linear_map.rtensor_sub -> LinearMap.rTensor_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_sub LinearMap.rTensor_subₓ'. -/
 @[simp]
 theorem rTensor_sub (f g : N →ₗ[R] P) : (f - g).rTensor M = f.rTensor M - g.rTensor M := by
   simp only [← coe_rtensor_hom, map_sub]
 #align linear_map.rtensor_sub LinearMap.rTensor_sub
 
-/- warning: linear_map.ltensor_neg -> LinearMap.lTensor_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_neg LinearMap.lTensor_negₓ'. -/
 @[simp]
 theorem lTensor_neg (f : N →ₗ[R] P) : (-f).lTensor M = -f.lTensor M := by
   simp only [← coe_ltensor_hom, map_neg]
 #align linear_map.ltensor_neg LinearMap.lTensor_neg
 
-/- warning: linear_map.rtensor_neg -> LinearMap.rTensor_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_neg LinearMap.rTensor_negₓ'. -/
 @[simp]
 theorem rTensor_neg (f : N →ₗ[R] P) : (-f).rTensor M = -f.rTensor M := by
   simp only [← coe_rtensor_hom, map_neg]

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

@@ -153,10 +153,7 @@ Case conversion may be inaccurate. Consider using '#align tensor_product.inducti
 protected theorem induction_on {C : M ⊗[R] N → Prop} (z : M ⊗[R] N) (C0 : C 0)
     (C1 : ∀ {x y}, C <| x ⊗ₜ[R] y) (Cp : ∀ {x y}, C x → C y → C (x + y)) : C z :=
   AddCon.induction_on z fun x =>
-    FreeAddMonoid.recOn x C0 fun ⟨m, n⟩ y ih =>
-      by
-      rw [AddCon.coe_add]
-      exact Cp C1 ih
+    FreeAddMonoid.recOn x C0 fun ⟨m, n⟩ y ih => by rw [AddCon.coe_add]; exact Cp C1 ih
 #align tensor_product.induction_on TensorProduct.induction_on
 
 variable (M)
@@ -360,10 +357,8 @@ Case conversion may be inaccurate. Consider using '#align tensor_product.add_smu
 protected theorem add_smul (r s : R'') (x : M ⊗[R] N) : (r + s) • x = r • x + s • x :=
   have : ∀ (r : R'') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   TensorProduct.induction_on x (by simp_rw [TensorProduct.smul_zero, add_zero])
-    (fun m n => by simp_rw [this, add_smul, add_tmul]) fun x y ihx ihy =>
-    by
-    simp_rw [TensorProduct.smul_add]
-    rw [ihx, ihy, add_add_add_comm]
+    (fun m n => by simp_rw [this, add_smul, add_tmul]) fun x y ihx ihy => by
+    simp_rw [TensorProduct.smul_add]; rw [ihx, ihy, add_add_add_comm]
 #align tensor_product.add_smul TensorProduct.add_smul
 
 instance : AddCommMonoid (M ⊗[R] N) :=
@@ -385,10 +380,8 @@ instance leftDistribMulAction : DistribMulAction R' (M ⊗[R] N) :=
     smul_add := fun r x y => TensorProduct.smul_add r x y
     mul_smul := fun r s x =>
       TensorProduct.induction_on x (by simp_rw [TensorProduct.smul_zero])
-        (fun m n => by simp_rw [this, mul_smul]) fun x y ihx ihy =>
-        by
-        simp_rw [TensorProduct.smul_add]
-        rw [ihx, ihy]
+        (fun m n => by simp_rw [this, mul_smul]) fun x y ihx ihy => by
+        simp_rw [TensorProduct.smul_add]; rw [ihx, ihy]
     one_smul := TensorProduct.one_smul
     smul_zero := TensorProduct.smul_zero }
 #align tensor_product.left_distrib_mul_action TensorProduct.leftDistribMulAction
@@ -579,11 +572,8 @@ theorem span_tmul_eq_top : Submodule.span R { t : M ⊗[R] N | ∃ m n, m ⊗ₜ
   ext t; simp only [Submodule.mem_top, iff_true_iff]
   apply t.induction_on
   · exact Submodule.zero_mem _
-  · intro m n
-    apply Submodule.subset_span
-    use m, n
-  · intro t₁ t₂ ht₁ ht₂
-    exact Submodule.add_mem _ ht₁ ht₂
+  · intro m n; apply Submodule.subset_span; use m, n
+  · intro t₁ t₂ ht₁ ht₂; exact Submodule.add_mem _ ht₁ ht₂
 #align tensor_product.span_tmul_eq_top TensorProduct.span_tmul_eq_top
 
 /- warning: tensor_product.map₂_mk_top_top_eq_top -> TensorProduct.map₂_mk_top_top_eq_top is a dubious translation:
@@ -1057,12 +1047,8 @@ theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     Set.mem_setOf_eq]
   congr ; ext t
   constructor
-  · rintro ⟨_, ⟨⟨m, n, rfl⟩, rfl⟩⟩
-    use m, n
-    simp only [map_tmul]
-  · rintro ⟨m, n, rfl⟩
-    use m ⊗ₜ n, m, n
-    simp only [map_tmul]
+  · rintro ⟨_, ⟨⟨m, n, rfl⟩, rfl⟩⟩; use m, n; simp only [map_tmul]
+  · rintro ⟨m, n, rfl⟩; use m ⊗ₜ n, m, n; simp only [map_tmul]
 #align tensor_product.map_range_eq_span_tmul TensorProduct.map_range_eq_span_tmul
 
 /- warning: tensor_product.map_incl -> TensorProduct.mapIncl is a dubious translation:
@@ -1107,9 +1093,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u3}} {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5], Eq.{max (succ u3) (succ u2)} (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, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (TensorProduct.map.{u1, u3, u2, u3, u2} R _inst_1 M N M N _inst_4 _inst_5 _inst_4 _inst_5 _inst_9 _inst_10 _inst_9 _inst_10 (LinearMap.id.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_9) (LinearMap.id.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)) (LinearMap.id.{u1, max u3 u2} R (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_id TensorProduct.map_idₓ'. -/
 @[simp]
-theorem map_id : map (id : M →ₗ[R] M) (id : N →ₗ[R] N) = id :=
-  by
-  ext
+theorem map_id : map (id : M →ₗ[R] M) (id : N →ₗ[R] N) = id := by ext;
   simp only [mk_apply, id_coe, compr₂_apply, id.def, map_tmul]
 #align tensor_product.map_id TensorProduct.map_id
 
@@ -1145,36 +1129,28 @@ protected theorem map_pow (f : M →ₗ[R] M) (g : N →ₗ[R] N) (n : ℕ) :
 <too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_add_left TensorProduct.map_add_leftₓ'. -/
 theorem map_add_left (f₁ f₂ : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (f₁ + f₂) g = map f₁ g + map f₂ g :=
-  by
-  ext
-  simp only [add_tmul, compr₂_apply, mk_apply, map_tmul, add_apply]
+  by ext; simp only [add_tmul, compr₂_apply, mk_apply, map_tmul, add_apply]
 #align tensor_product.map_add_left TensorProduct.map_add_left
 
 /- warning: tensor_product.map_add_right -> TensorProduct.map_add_right is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_add_right TensorProduct.map_add_rightₓ'. -/
 theorem map_add_right (f : M →ₗ[R] P) (g₁ g₂ : N →ₗ[R] Q) : map f (g₁ + g₂) = map f g₁ + map f g₂ :=
-  by
-  ext
-  simp only [tmul_add, compr₂_apply, mk_apply, map_tmul, add_apply]
+  by ext; simp only [tmul_add, compr₂_apply, mk_apply, map_tmul, add_apply]
 #align tensor_product.map_add_right TensorProduct.map_add_right
 
 /- warning: tensor_product.map_smul_left -> TensorProduct.map_smul_left is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_smul_left TensorProduct.map_smul_leftₓ'. -/
-theorem map_smul_left (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (r • f) g = r • map f g :=
-  by
-  ext
-  simp only [smul_tmul, compr₂_apply, mk_apply, map_tmul, smul_apply, tmul_smul]
+theorem map_smul_left (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (r • f) g = r • map f g := by
+  ext; simp only [smul_tmul, compr₂_apply, mk_apply, map_tmul, smul_apply, tmul_smul]
 #align tensor_product.map_smul_left TensorProduct.map_smul_left
 
 /- warning: tensor_product.map_smul_right -> TensorProduct.map_smul_right is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_smul_right TensorProduct.map_smul_rightₓ'. -/
-theorem map_smul_right (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map f (r • g) = r • map f g :=
-  by
-  ext
-  simp only [smul_tmul, compr₂_apply, mk_apply, map_tmul, smul_apply, tmul_smul]
+theorem map_smul_right (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map f (r • g) = r • map f g := by
+  ext; simp only [smul_tmul, compr₂_apply, mk_apply, map_tmul, smul_apply, tmul_smul]
 #align tensor_product.map_smul_right TensorProduct.map_smul_right
 
 variable (R M N P Q)
@@ -1452,12 +1428,9 @@ Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_hom
 def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
     where
   toFun := lTensor M
-  map_add' f g := by
-    ext (x y)
+  map_add' f g := by ext (x y);
     simp only [compr₂_apply, mk_apply, add_apply, ltensor_tmul, tmul_add]
-  map_smul' r f := by
-    dsimp
-    ext (x y)
+  map_smul' r f := by dsimp; ext (x y);
     simp only [compr₂_apply, mk_apply, tmul_smul, smul_apply, ltensor_tmul]
 #align linear_map.ltensor_hom LinearMap.lTensorHom
 
@@ -1468,12 +1441,9 @@ Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_hom
 def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
     where
   toFun f := f.rTensor M
-  map_add' f g := by
-    ext (x y)
+  map_add' f g := by ext (x y);
     simp only [compr₂_apply, mk_apply, add_apply, rtensor_tmul, add_tmul]
-  map_smul' r f := by
-    dsimp
-    ext (x y)
+  map_smul' r f := by dsimp; ext (x y);
     simp only [compr₂_apply, mk_apply, smul_tmul, tmul_smul, smul_apply, rtensor_tmul]
 #align linear_map.rtensor_hom LinearMap.rTensorHom
 
@@ -1544,9 +1514,7 @@ theorem rTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).rTensor M = r • f
 /- warning: linear_map.ltensor_comp -> LinearMap.lTensor_comp is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp LinearMap.lTensor_compₓ'. -/
-theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) :=
-  by
-  ext (m n)
+theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) := by ext (m n);
   simp only [compr₂_apply, mk_apply, comp_apply, ltensor_tmul]
 #align linear_map.ltensor_comp LinearMap.lTensor_comp
 
@@ -1560,9 +1528,7 @@ theorem lTensor_comp_apply (x : M ⊗[R] N) :
 /- warning: linear_map.rtensor_comp -> LinearMap.rTensor_comp is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp LinearMap.rTensor_compₓ'. -/
-theorem rTensor_comp : (g.comp f).rTensor M = (g.rTensor M).comp (f.rTensor M) :=
-  by
-  ext (m n)
+theorem rTensor_comp : (g.comp f).rTensor M = (g.rTensor M).comp (f.rTensor M) := by ext (m n);
   simp only [compr₂_apply, mk_apply, comp_apply, rtensor_tmul]
 #align linear_map.rtensor_comp LinearMap.rTensor_comp
 
@@ -1689,20 +1655,16 @@ variable {M}
 <too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_pow LinearMap.rTensor_powₓ'. -/
 @[simp]
-theorem rTensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rTensor N ^ n = (f ^ n).rTensor N :=
-  by
-  have h := TensorProduct.map_pow f (id : N →ₗ[R] N) n
-  rwa [id_pow] at h
+theorem rTensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rTensor N ^ n = (f ^ n).rTensor N := by
+  have h := TensorProduct.map_pow f (id : N →ₗ[R] N) n; rwa [id_pow] at h
 #align linear_map.rtensor_pow LinearMap.rTensor_pow
 
 /- warning: linear_map.ltensor_pow -> LinearMap.lTensor_pow is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_pow LinearMap.lTensor_powₓ'. -/
 @[simp]
-theorem lTensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.lTensor M ^ n = (f ^ n).lTensor M :=
-  by
-  have h := TensorProduct.map_pow (id : M →ₗ[R] M) f n
-  rwa [id_pow] at h
+theorem lTensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.lTensor M ^ n = (f ^ n).lTensor M := by
+  have h := TensorProduct.map_pow (id : M →ₗ[R] M) f n; rwa [id_pow] at h
 #align linear_map.ltensor_pow LinearMap.lTensor_pow
 
 end LinearMap
@@ -1773,14 +1735,9 @@ but is expected to have type
   forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u2}} {N : Type.{u1}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u1} N] [_inst_7 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3)] (x : TensorProduct.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8), Eq.{max (succ u2) (succ u1)} (TensorProduct.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8) (TensorProduct.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8) (TensorProduct.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8) (instHAdd.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8) (AddZeroClass.toAdd.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8) (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8))) (Neg.neg.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8) (TensorProduct.neg.{u3, u2, u1} R _inst_1 M N _inst_2 _inst_3 _inst_7 _inst_8) x) x) (OfNat.ofNat.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8) 0 (Zero.toOfNat0.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8) (AddMonoid.toZero.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_7 _inst_8)))))
 Case conversion may be inaccurate. Consider using '#align tensor_product.add_left_neg TensorProduct.add_left_negₓ'. -/
 protected theorem add_left_neg (x : M ⊗[R] N) : -x + x = 0 :=
-  TensorProduct.induction_on x
-    (by
-      rw [add_zero]
-      apply (neg.aux R).map_zero)
-    (fun x y => by
-      convert(add_tmul (-x) x y).symm
-      rw [add_left_neg, zero_tmul])
-    fun x y hx hy => by
+  TensorProduct.induction_on x (by rw [add_zero]; apply (neg.aux R).map_zero)
+    (fun x y => by convert(add_tmul (-x) x y).symm; rw [add_left_neg, zero_tmul]) fun x y hx hy =>
+    by
     unfold Neg.neg SubNegMonoid.neg
     rw [AddMonoidHom.map_add]
     ac_change -x + x + (-y + y) = 0

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

@@ -147,10 +147,7 @@ infixl:100 " ⊗ₜ " => tmul _
 notation:100 x " ⊗ₜ[" R "] " y:100 => tmul R x y
 
 /- warning: tensor_product.induction_on -> TensorProduct.induction_on is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.induction_on TensorProduct.induction_onₓ'. -/
 @[elab_as_elim]
 protected theorem induction_on {C : M ⊗[R] N → Prop} (z : M ⊗[R] N) (C0 : C 0)
@@ -252,10 +249,7 @@ instance (priority := 100) CompatibleSMul.isScalarTower [SMul R' R] [IsScalarTow
 #align tensor_product.compatible_smul.is_scalar_tower TensorProduct.CompatibleSMul.isScalarTower
 
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 Case conversion may be inaccurate. Consider using '#align tensor_product.smul_tmul TensorProduct.smul_tmulₓ'. -/
 /-- `smul` can be moved from one side of the product to the other .-/
 theorem smul_tmul [DistribMulAction R' N] [CompatibleSMul R R' M N] (r : R') (m : M) (n : N) :
@@ -275,10 +269,7 @@ def SMul.aux {R' : Type _} [SMul R' M] (r : R') : FreeAddMonoid (M × N) →+ M
 #align tensor_product.smul.aux TensorProduct.SMul.aux
 
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 Case conversion may be inaccurate. Consider using '#align tensor_product.smul.aux_of TensorProduct.SMul.aux_ofₓ'. -/
 theorem SMul.aux_of {R' : Type _} [SMul R' M] (r : R') (m : M) (n : N) :
     SMul.aux r (FreeAddMonoid.of (m, n)) = (r • m) ⊗ₜ[R] n :=
@@ -331,30 +322,21 @@ instance : SMul R (M ⊗[R] N) :=
   TensorProduct.leftHasSMul
 
 /- warning: tensor_product.smul_zero -> TensorProduct.smul_zero is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align tensor_product.smul_zero TensorProduct.smul_zeroₓ'. -/
 protected theorem smul_zero (r : R') : (r • 0 : M ⊗[R] N) = 0 :=
   AddMonoidHom.map_zero _
 #align tensor_product.smul_zero TensorProduct.smul_zero
 
 /- warning: tensor_product.smul_add -> TensorProduct.smul_add is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align tensor_product.smul_add TensorProduct.smul_addₓ'. -/
 protected theorem smul_add (r : R') (x y : M ⊗[R] N) : r • (x + y) = r • x + r • y :=
   AddMonoidHom.map_add _ _ _
 #align tensor_product.smul_add TensorProduct.smul_add
 
 /- warning: tensor_product.zero_smul -> TensorProduct.zero_smul is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align tensor_product.zero_smul TensorProduct.zero_smulₓ'. -/
 protected theorem zero_smul (x : M ⊗[R] N) : (0 : R'') • x = 0 :=
   have : ∀ (r : R'') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
@@ -364,10 +346,7 @@ protected theorem zero_smul (x : M ⊗[R] N) : (0 : R'') • x = 0 :=
 #align tensor_product.zero_smul TensorProduct.zero_smul
 
 /- warning: tensor_product.one_smul -> TensorProduct.one_smul is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align tensor_product.one_smul TensorProduct.one_smulₓ'. -/
 protected theorem one_smul (x : M ⊗[R] N) : (1 : R') • x = x :=
   have : ∀ (r : R') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
@@ -376,10 +355,7 @@ protected theorem one_smul (x : M ⊗[R] N) : (1 : R') • x = x :=
 #align tensor_product.one_smul TensorProduct.one_smul
 
 /- warning: tensor_product.add_smul -> TensorProduct.add_smul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.add_smul TensorProduct.add_smulₓ'. -/
 protected theorem add_smul (r s : R'') (x : M ⊗[R] N) : (r + s) • x = r • x + s • x :=
   have : ∀ (r : R'') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
@@ -421,20 +397,14 @@ instance : DistribMulAction R (M ⊗[R] N) :=
   TensorProduct.leftDistribMulAction
 
 /- warning: tensor_product.smul_tmul' -> TensorProduct.smul_tmul' is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align tensor_product.smul_tmul' TensorProduct.smul_tmul'ₓ'. -/
 theorem smul_tmul' (r : R') (m : M) (n : N) : r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n :=
   rfl
 #align tensor_product.smul_tmul' TensorProduct.smul_tmul'
 
 /- warning: tensor_product.tmul_smul -> TensorProduct.tmul_smul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] [_inst_18 : DistribMulAction.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5)] [_inst_19 : TensorProduct.CompatibleSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_18] (r : R') (x : M) (y : N), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x (SMul.smul.{u2, u4} R' N (SMulZeroClass.toHasSmul.{u2, u4} R' N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5))) (DistribSMul.toSmulZeroClass.{u2, u4} R' N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (DistribMulAction.toDistribSMul.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5) _inst_18))) r y)) (SMul.smul.{u2, max u3 u4} R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16) r (TensorProduct.tmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x y))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.tmul_smul TensorProduct.tmul_smulₓ'. -/
 @[simp]
 theorem tmul_smul [DistribMulAction R' N] [CompatibleSMul R R' M N] (r : R') (x : M) (y : N) :
@@ -478,10 +448,7 @@ variable {R'₂ : Type _} [Monoid R'₂] [DistribMulAction R'₂ M]
 variable [SMulCommClass R R'₂ M] [SMul R'₂ R']
 
 /- warning: tensor_product.is_scalar_tower_left -> TensorProduct.isScalarTower_left is a dubious translation:
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-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toSMul.{u2, u3} R' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] {R'₂ : Type.{u5}} [_inst_18 : Monoid.{u5} R'₂] [_inst_19 : DistribMulAction.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_20 : SMulCommClass.{u1, u5, u3} R R'₂ M (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_9)))) (SMulZeroClass.toSMul.{u5, u3} R'₂ M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u5, u3} R'₂ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_19)))] [_inst_21 : SMul.{u5, u2} R'₂ R'] [_inst_22 : IsScalarTower.{u5, u2, u3} R'₂ R' M _inst_21 (SMulZeroClass.toSMul.{u2, u3} R' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14))) (SMulZeroClass.toSMul.{u5, u3} R'₂ M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u5, u3} R'₂ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_19)))], IsScalarTower.{u5, u2, max u4 u3} R'₂ R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_21 (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16) (TensorProduct.leftHasSMul.{u1, u5, u3, u4} R _inst_1 R'₂ _inst_18 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_19 _inst_20)
+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.is_scalar_tower_left TensorProduct.isScalarTower_leftₓ'. -/
 /-- `is_scalar_tower R'₂ R' M` implies `is_scalar_tower R'₂ R' (M ⊗[R] N)` -/
 instance isScalarTower_left [IsScalarTower R'₂ R' M] : IsScalarTower R'₂ R' (M ⊗[R] N) :=
@@ -496,10 +463,7 @@ variable [DistribMulAction R'₂ N] [DistribMulAction R' N]
 variable [CompatibleSMul R R'₂ M N] [CompatibleSMul R R' M N]
 
 /- warning: tensor_product.is_scalar_tower_right -> TensorProduct.isScalarTower_right is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.is_scalar_tower_right TensorProduct.isScalarTower_rightₓ'. -/
 /-- `is_scalar_tower R'₂ R' N` implies `is_scalar_tower R'₂ R' (M ⊗[R] N)` -/
 instance isScalarTower_right [IsScalarTower R'₂ R' N] : IsScalarTower R'₂ R' (M ⊗[R] N) :=
@@ -540,10 +504,7 @@ def mk : M →ₗ[R] N →ₗ[R] M ⊗[R] N :=
 variable {R M N}
 
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 Case conversion may be inaccurate. Consider using '#align tensor_product.mk_apply TensorProduct.mk_applyₓ'. -/
 @[simp]
 theorem mk_apply (m : M) (n : N) : mk R M N m n = m ⊗ₜ n :=
@@ -674,10 +635,7 @@ def liftAux : M ⊗[R] N →+ P :=
 -/
 
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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift_aux_tmul TensorProduct.liftAux_tmulₓ'. -/
 theorem liftAux_tmul (m n) : liftAux f (m ⊗ₜ n) = f m n :=
   rfl
@@ -686,10 +644,7 @@ theorem liftAux_tmul (m n) : liftAux f (m ⊗ₜ n) = f m n :=
 variable {f}
 
 /- warning: tensor_product.lift_aux.smul -> TensorProduct.liftAux.smul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.lift_aux.smul TensorProduct.liftAux.smulₓ'. -/
 @[simp]
 theorem liftAux.smul (r : R) (x) : liftAux f (r • x) = r • liftAux f x :=
@@ -713,10 +668,7 @@ def lift : M ⊗ N →ₗ[R] P :=
 variable {f}
 
 /- warning: tensor_product.lift.tmul -> TensorProduct.lift.tmul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.tmul TensorProduct.lift.tmulₓ'. -/
 @[simp]
 theorem lift.tmul (x y) : lift f (x ⊗ₜ y) = f x y :=
@@ -724,10 +676,7 @@ theorem lift.tmul (x y) : lift f (x ⊗ₜ y) = f x y :=
 #align tensor_product.lift.tmul TensorProduct.lift.tmul
 
 /- warning: tensor_product.lift.tmul' -> TensorProduct.lift.tmul' is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.tmul' TensorProduct.lift.tmul'ₓ'. -/
 @[simp]
 theorem lift.tmul' (x y) : (lift f).1 (x ⊗ₜ y) = f x y :=
@@ -735,10 +684,7 @@ theorem lift.tmul' (x y) : (lift f).1 (x ⊗ₜ y) = f x y :=
 #align tensor_product.lift.tmul' TensorProduct.lift.tmul'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.ext' TensorProduct.ext'ₓ'. -/
 theorem ext' {g h : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x ⊗ₜ y)) : g = h :=
   LinearMap.ext fun z =>
@@ -747,10 +693,7 @@ theorem ext' {g h : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x
 #align tensor_product.ext' TensorProduct.ext'
 
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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.unique TensorProduct.lift.uniqueₓ'. -/
 theorem lift.unique {g : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = f x y) : g = lift f :=
   ext' fun m n => by rw [H, lift.tmul]
@@ -767,30 +710,21 @@ theorem lift_mk : lift (mk R M N) = LinearMap.id :=
 #align tensor_product.lift_mk TensorProduct.lift_mk
 
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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift_compr₂ TensorProduct.lift_compr₂ₓ'. -/
 theorem lift_compr₂ (g : P →ₗ[R] Q) : lift (f.compr₂ g) = g.comp (lift f) :=
   Eq.symm <| lift.unique fun x y => by simp
 #align tensor_product.lift_compr₂ TensorProduct.lift_compr₂
 
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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift_mk_compr₂ TensorProduct.lift_mk_compr₂ₓ'. -/
 theorem lift_mk_compr₂ (f : M ⊗ N →ₗ[R] P) : lift ((mk R M N).compr₂ f) = f := by
   rw [lift_compr₂ f, lift_mk, LinearMap.comp_id]
 #align tensor_product.lift_mk_compr₂ TensorProduct.lift_mk_compr₂
 
 /- warning: tensor_product.ext -> TensorProduct.ext is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.ext TensorProduct.extₓ'. -/
 /-- This used to be an `@[ext]` lemma, but it fails very slowly when the `ext` tactic tries to apply
 it in some cases, notably when one wants to show equality of two linear maps. The `@[ext]`
@@ -820,10 +754,7 @@ def uncurry : (M →ₗ[R] N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] P :=
 variable {R M N P}
 
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(LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P 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 Case conversion may be inaccurate. Consider using '#align tensor_product.uncurry_apply TensorProduct.uncurry_applyₓ'. -/
 @[simp]
 theorem uncurry_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
@@ -845,10 +776,7 @@ def lift.equiv : (M →ₗ[R] N →ₗ[R] P) ≃ₗ[R] M ⊗ N →ₗ[R] P :=
 -/
 
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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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toZero.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) 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_inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R 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R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, max u1 u2} R R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) 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R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u4, u4, u4, u4, u1, u2} R R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) 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_inst_10) _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u2} R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u2} R R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (SemilinearMapClass.distribMulActionHomClass.{u4, max (max u3 u1) u2, max (max u3 u1) u2, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.equiv_apply TensorProduct.lift.equiv_applyₓ'. -/
 @[simp]
 theorem lift.equiv_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
@@ -857,10 +785,7 @@ theorem lift.equiv_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
 #align tensor_product.lift.equiv_apply TensorProduct.lift.equiv_apply
 
 /- warning: tensor_product.lift.equiv_symm_apply -> TensorProduct.lift.equiv_symm_apply is a dubious translation:
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u1} R (LinearMap.{u4, u4, max u3 u2, u1} 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, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, max u2 u3, u1} R R (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u2 u3, u1} R R R (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))))))) (SMulZeroClass.toSMul.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, 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(smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u4, u4, u4, u4, u3, u1} R R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P 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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, u4, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{u4, u4, max (max u2 u3) u1, max (max u2 u3) u1} 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))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, max u3 u2, u1} 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, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, 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(CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R 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u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u2 u3, u1} R R R (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.equiv_symm_apply TensorProduct.lift.equiv_symm_applyₓ'. -/
 @[simp]
 theorem lift.equiv_symm_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) :
@@ -869,10 +794,7 @@ theorem lift.equiv_symm_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) :
 #align tensor_product.lift.equiv_symm_apply TensorProduct.lift.equiv_symm_apply
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.lcurry TensorProduct.lcurryₓ'. -/
 /-- Given a linear map `M ⊗ N → P`, compose it with the canonical bilinear map `M → N → M ⊗ N` to
 form a bilinear map `M → N → P`. -/
@@ -883,10 +805,7 @@ def lcurry : (M ⊗[R] N →ₗ[R] P) →ₗ[R] M →ₗ[R] N →ₗ[R] P :=
 variable {R M N P}
 
 /- warning: tensor_product.lcurry_apply -> TensorProduct.lcurry_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.lcurry_apply TensorProduct.lcurry_applyₓ'. -/
 @[simp]
 theorem lcurry_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) : lcurry R M N P f m n = f (m ⊗ₜ n) :=
@@ -906,10 +825,7 @@ def curry (f : M ⊗ N →ₗ[R] P) : M →ₗ[R] N →ₗ[R] P :=
 #align tensor_product.curry TensorProduct.curry
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.curry_apply TensorProduct.curry_applyₓ'. -/
 @[simp]
 theorem curry_apply (f : M ⊗ N →ₗ[R] P) (m : M) (n : N) : curry f m n = f (m ⊗ₜ n) :=
@@ -927,10 +843,7 @@ theorem curry_injective : Function.Injective (curry : (M ⊗[R] N →ₗ[R] P) 
 #align tensor_product.curry_injective TensorProduct.curry_injective
 
 /- warning: tensor_product.ext_threefold -> TensorProduct.ext_threefold is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.ext_threefold TensorProduct.ext_threefoldₓ'. -/
 theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
     (H : ∀ x y z, g (x ⊗ₜ y ⊗ₜ z) = h (x ⊗ₜ y ⊗ₜ z)) : g = h :=
@@ -940,10 +853,7 @@ theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
 #align tensor_product.ext_threefold TensorProduct.ext_threefold
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.ext_fourfold TensorProduct.ext_fourfoldₓ'. -/
 -- We'll need this one for checking the pentagon identity!
 theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
@@ -954,10 +864,7 @@ theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
 #align tensor_product.ext_fourfold TensorProduct.ext_fourfold
 
 /- warning: tensor_product.ext_fourfold' -> TensorProduct.ext_fourfold' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.ext_fourfold' TensorProduct.ext_fourfold'ₓ'. -/
 /-- Two linear maps (M ⊗ N) ⊗ (P ⊗ Q) → S which agree on all elements of the
 form (m ⊗ₜ n) ⊗ₜ (p ⊗ₜ q) are equal. -/
@@ -992,10 +899,7 @@ protected def lid : R ⊗ M ≃ₗ[R] M :=
 end
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.lid_tmul TensorProduct.lid_tmulₓ'. -/
 @[simp]
 theorem lid_tmul (m : M) (r : R) : (TensorProduct.lid R M : R ⊗ M → M) (r ⊗ₜ m) = r • m :=
@@ -1005,10 +909,7 @@ theorem lid_tmul (m : M) (r : R) : (TensorProduct.lid R M : R ⊗ M → M) (r 
 #align tensor_product.lid_tmul TensorProduct.lid_tmul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.lid_symm_apply TensorProduct.lid_symm_applyₓ'. -/
 @[simp]
 theorem lid_symm_apply (m : M) : (TensorProduct.lid R M).symm m = 1 ⊗ₜ m :=
@@ -1033,10 +934,7 @@ protected def comm : M ⊗ N ≃ₗ[R] N ⊗ M :=
 #align tensor_product.comm TensorProduct.comm
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.comm_tmul TensorProduct.comm_tmulₓ'. -/
 @[simp]
 theorem comm_tmul (m : M) (n : N) : (TensorProduct.comm R M N) (m ⊗ₜ n) = n ⊗ₜ m :=
@@ -1044,10 +942,7 @@ theorem comm_tmul (m : M) (n : N) : (TensorProduct.comm R M N) (m ⊗ₜ n) = n
 #align tensor_product.comm_tmul TensorProduct.comm_tmul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.comm_symm_tmul TensorProduct.comm_symm_tmulₓ'. -/
 @[simp]
 theorem comm_symm_tmul (m : M) (n : N) : (TensorProduct.comm R M N).symm (n ⊗ₜ m) = m ⊗ₜ n :=
@@ -1075,10 +970,7 @@ protected def rid : M ⊗[R] R ≃ₗ[R] M :=
 end
 
 /- warning: tensor_product.rid_tmul -> TensorProduct.rid_tmul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.rid_tmul TensorProduct.rid_tmulₓ'. -/
 @[simp]
 theorem rid_tmul (m : M) (r : R) : (TensorProduct.rid R M) (m ⊗ₜ r) = r • m :=
@@ -1088,10 +980,7 @@ theorem rid_tmul (m : M) (r : R) : (TensorProduct.rid R M) (m ⊗ₜ r) = r •
 #align tensor_product.rid_tmul TensorProduct.rid_tmul
 
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(CommSemiring.toSemiring.{u2} R _inst_1)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.rid_symm_apply TensorProduct.rid_symm_applyₓ'. -/
 @[simp]
 theorem rid_symm_apply (m : M) : (TensorProduct.rid R M).symm m = m ⊗ₜ 1 :=
@@ -1105,10 +994,7 @@ section
 variable (R M N P)
 
 /- warning: tensor_product.assoc -> TensorProduct.assoc is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.assoc TensorProduct.assocₓ'. -/
 /-- The associator for tensor product of R-modules, as a linear equivalence. -/
 protected def assoc : (M ⊗[R] N) ⊗[R] P ≃ₗ[R] M ⊗[R] N ⊗[R] P := by
@@ -1125,10 +1011,7 @@ protected def assoc : (M ⊗[R] N) ⊗[R] P ≃ₗ[R] M ⊗[R] N ⊗[R] P := by
 end
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.assoc_tmul TensorProduct.assoc_tmulₓ'. -/
 @[simp]
 theorem assoc_tmul (m : M) (n : N) (p : P) :
@@ -1137,10 +1020,7 @@ theorem assoc_tmul (m : M) (n : N) (p : P) :
 #align tensor_product.assoc_tmul TensorProduct.assoc_tmul
 
 /- warning: tensor_product.assoc_symm_tmul -> TensorProduct.assoc_symm_tmul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.assoc_symm_tmul TensorProduct.assoc_symm_tmulₓ'. -/
 @[simp]
 theorem assoc_symm_tmul (m : M) (n : N) (p : P) :
@@ -1160,10 +1040,7 @@ def map (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : M ⊗ N →ₗ[R] P ⊗ Q :=
 #align tensor_product.map TensorProduct.map
 
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 Case conversion may be inaccurate. Consider using '#align tensor_product.map_tmul TensorProduct.map_tmulₓ'. -/
 @[simp]
 theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f g (m ⊗ₜ n) = f m ⊗ₜ g n :=
@@ -1171,10 +1048,7 @@ theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f
 #align tensor_product.map_tmul TensorProduct.map_tmul
 
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 Case conversion may be inaccurate. Consider using '#align tensor_product.map_range_eq_span_tmul TensorProduct.map_range_eq_span_tmulₓ'. -/
 theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (map f g).range = Submodule.span R { t | ∃ m n, f m ⊗ₜ g n = t } :=
@@ -1192,10 +1066,7 @@ theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
 #align tensor_product.map_range_eq_span_tmul TensorProduct.map_range_eq_span_tmul
 
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 Case conversion may be inaccurate. Consider using '#align tensor_product.map_incl TensorProduct.mapInclₓ'. -/
 /-- Given submodules `p ⊆ P` and `q ⊆ Q`, this is the natural map: `p ⊗ q → P ⊗ Q`. -/
 @[simp]
@@ -1212,10 +1083,7 @@ variable [AddCommMonoid P'] [Module R P']
 variable [AddCommMonoid Q'] [Module R Q']
 
 /- warning: tensor_product.map_comp -> TensorProduct.map_comp is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_comp TensorProduct.map_compₓ'. -/
 theorem map_comp (f₂ : P →ₗ[R] P') (f₁ : M →ₗ[R] P) (g₂ : Q →ₗ[R] Q') (g₁ : N →ₗ[R] Q) :
     map (f₂.comp f₁) (g₂.comp g₁) = (map f₂ g₂).comp (map f₁ g₁) :=
@@ -1223,10 +1091,7 @@ theorem map_comp (f₂ : P →ₗ[R] P') (f₁ : M →ₗ[R] P) (g₂ : Q →ₗ
 #align tensor_product.map_comp TensorProduct.map_comp
 
 /- warning: tensor_product.lift_comp_map -> TensorProduct.lift_comp_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.lift_comp_map TensorProduct.lift_comp_mapₓ'. -/
 theorem lift_comp_map (i : P →ₗ[R] Q →ₗ[R] Q') (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (lift i).comp (map f g) = lift ((i.comp f).compl₂ g) :=
@@ -1249,10 +1114,7 @@ theorem map_id : map (id : M →ₗ[R] M) (id : N →ₗ[R] N) = id :=
 #align tensor_product.map_id TensorProduct.map_id
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_one TensorProduct.map_oneₓ'. -/
 @[simp]
 theorem map_one : map (1 : M →ₗ[R] M) (1 : N →ₗ[R] N) = 1 :=
@@ -1260,10 +1122,7 @@ theorem map_one : map (1 : M →ₗ[R] M) (1 : N →ₗ[R] N) = 1 :=
 #align tensor_product.map_one TensorProduct.map_one
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_mul TensorProduct.map_mulₓ'. -/
 theorem map_mul (f₁ f₂ : M →ₗ[R] M) (g₁ g₂ : N →ₗ[R] N) :
     map (f₁ * f₂) (g₁ * g₂) = map f₁ g₁ * map f₂ g₂ :=
@@ -1271,10 +1130,7 @@ theorem map_mul (f₁ f₂ : M →ₗ[R] M) (g₁ g₂ : N →ₗ[R] N) :
 #align tensor_product.map_mul TensorProduct.map_mul
 
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 Case conversion may be inaccurate. Consider using '#align tensor_product.map_pow TensorProduct.map_powₓ'. -/
 @[simp]
 protected theorem map_pow (f : M →ₗ[R] M) (g : N →ₗ[R] N) (n : ℕ) :
@@ -1286,10 +1142,7 @@ protected theorem map_pow (f : M →ₗ[R] M) (g : N →ₗ[R] N) (n : ℕ) :
 #align tensor_product.map_pow TensorProduct.map_pow
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_add_left TensorProduct.map_add_leftₓ'. -/
 theorem map_add_left (f₁ f₂ : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (f₁ + f₂) g = map f₁ g + map f₂ g :=
   by
@@ -1298,10 +1151,7 @@ theorem map_add_left (f₁ f₂ : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (f₁
 #align tensor_product.map_add_left TensorProduct.map_add_left
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_add_right TensorProduct.map_add_rightₓ'. -/
 theorem map_add_right (f : M →ₗ[R] P) (g₁ g₂ : N →ₗ[R] Q) : map f (g₁ + g₂) = map f g₁ + map f g₂ :=
   by
@@ -1310,10 +1160,7 @@ theorem map_add_right (f : M →ₗ[R] P) (g₁ g₂ : N →ₗ[R] Q) : map f (g
 #align tensor_product.map_add_right TensorProduct.map_add_right
 
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 Case conversion may be inaccurate. Consider using '#align tensor_product.map_smul_left TensorProduct.map_smul_leftₓ'. -/
 theorem map_smul_left (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (r • f) g = r • map f g :=
   by
@@ -1322,10 +1169,7 @@ theorem map_smul_left (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (r 
 #align tensor_product.map_smul_left TensorProduct.map_smul_left
 
 /- warning: tensor_product.map_smul_right -> TensorProduct.map_smul_right is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_smul_right TensorProduct.map_smul_rightₓ'. -/
 theorem map_smul_right (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map f (r • g) = r • map f g :=
   by
@@ -1336,10 +1180,7 @@ theorem map_smul_right (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map f (
 variable (R M N P Q)
 
 /- warning: tensor_product.map_bilinear -> TensorProduct.mapBilinear is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_bilinear TensorProduct.mapBilinearₓ'. -/
 /-- The tensor product of a pair of linear maps between modules, bilinear in both maps. -/
 def mapBilinear : (M →ₗ[R] P) →ₗ[R] (N →ₗ[R] Q) →ₗ[R] M ⊗[R] N →ₗ[R] P ⊗[R] Q :=
@@ -1371,10 +1212,7 @@ def homTensorHomMap : (M →ₗ[R] P) ⊗[R] (N →ₗ[R] Q) →ₗ[R] M ⊗[R]
 variable {R M N P Q}
 
 /- warning: tensor_product.map_bilinear_apply -> TensorProduct.mapBilinear_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_bilinear_apply TensorProduct.mapBilinear_applyₓ'. -/
 @[simp]
 theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear R M N P Q f g = map f g :=
@@ -1382,10 +1220,7 @@ theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear
 #align tensor_product.map_bilinear_apply TensorProduct.mapBilinear_apply
 
 /- warning: tensor_product.ltensor_hom_to_hom_ltensor_apply -> TensorProduct.lTensorHomToHomLTensor_apply is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.lTensorHomToHomLTensor_applyₓ'. -/
 @[simp]
 theorem lTensorHomToHomLTensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
@@ -1394,10 +1229,7 @@ theorem lTensorHomToHomLTensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
 #align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.lTensorHomToHomLTensor_apply
 
 /- warning: tensor_product.rtensor_hom_to_hom_rtensor_apply -> TensorProduct.rTensorHomToHomRTensor_apply is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rTensorHomToHomRTensor_applyₓ'. -/
 @[simp]
 theorem rTensorHomToHomRTensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
@@ -1406,10 +1238,7 @@ theorem rTensorHomToHomRTensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
 #align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rTensorHomToHomRTensor_apply
 
 /- warning: tensor_product.hom_tensor_hom_map_apply -> TensorProduct.homTensorHomMap_apply is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.hom_tensor_hom_map_apply TensorProduct.homTensorHomMap_applyₓ'. -/
 @[simp]
 theorem homTensorHomMap_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
@@ -1434,10 +1263,7 @@ def congr (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) : M ⊗ N ≃ₗ[R] P ⊗ Q :=
 #align tensor_product.congr TensorProduct.congr
 
 /- warning: tensor_product.congr_tmul -> TensorProduct.congr_tmul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.congr_tmul TensorProduct.congr_tmulₓ'. -/
 @[simp]
 theorem congr_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (m : M) (n : N) :
@@ -1446,10 +1272,7 @@ theorem congr_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (m : M) (n : N) :
 #align tensor_product.congr_tmul TensorProduct.congr_tmul
 
 /- warning: tensor_product.congr_symm_tmul -> TensorProduct.congr_symm_tmul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.congr_symm_tmul TensorProduct.congr_symm_tmulₓ'. -/
 @[simp]
 theorem congr_symm_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (p : P) (q : Q) :
@@ -1476,10 +1299,7 @@ def leftComm : M ⊗[R] N ⊗[R] P ≃ₗ[R] N ⊗[R] M ⊗[R] P :=
 variable {M N P Q}
 
 /- warning: tensor_product.left_comm_tmul -> TensorProduct.leftComm_tmul is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align tensor_product.left_comm_tmul TensorProduct.leftComm_tmulₓ'. -/
 @[simp]
 theorem leftComm_tmul (m : M) (n : N) (p : P) : leftComm R M N P (m ⊗ₜ (n ⊗ₜ p)) = n ⊗ₜ (m ⊗ₜ p) :=
@@ -1487,10 +1307,7 @@ theorem leftComm_tmul (m : M) (n : N) (p : P) : leftComm R M N P (m ⊗ₜ (n 
 #align tensor_product.left_comm_tmul TensorProduct.leftComm_tmul
 
 /- warning: tensor_product.left_comm_symm_tmul -> TensorProduct.leftComm_symm_tmul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.left_comm_symm_tmul TensorProduct.leftComm_symm_tmulₓ'. -/
 @[simp]
 theorem leftComm_symm_tmul (m : M) (n : N) (p : P) :
@@ -1501,10 +1318,7 @@ theorem leftComm_symm_tmul (m : M) (n : N) (p : P) :
 variable (M N P Q)
 
 /- warning: tensor_product.tensor_tensor_tensor_comm -> TensorProduct.tensorTensorTensorComm is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_comm TensorProduct.tensorTensorTensorCommₓ'. -/
 /-- This special case is worth defining explicitly since it is useful for defining multiplication
 on tensor products of modules carrying multiplications (e.g., associative rings, Lie rings, ...).
@@ -1526,10 +1340,7 @@ def tensorTensorTensorComm : (M ⊗[R] N) ⊗[R] P ⊗[R] Q ≃ₗ[R] (M ⊗[R]
 variable {M N P Q}
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_comm_tmul TensorProduct.tensorTensorTensorComm_tmulₓ'. -/
 @[simp]
 theorem tensorTensorTensorComm_tmul (m : M) (n : N) (p : P) (q : Q) :
@@ -1538,10 +1349,7 @@ theorem tensorTensorTensorComm_tmul (m : M) (n : N) (p : P) (q : Q) :
 #align tensor_product.tensor_tensor_tensor_comm_tmul TensorProduct.tensorTensorTensorComm_tmul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_comm_symm TensorProduct.tensorTensorTensorComm_symmₓ'. -/
 @[simp]
 theorem tensorTensorTensorComm_symm :
@@ -1552,10 +1360,7 @@ theorem tensorTensorTensorComm_symm :
 variable (M N P Q)
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_assoc TensorProduct.tensorTensorTensorAssocₓ'. -/
 /-- This special case is useful for describing the interplay between `dual_tensor_hom_equiv` and
 composition of linear maps.
@@ -1573,10 +1378,7 @@ def tensorTensorTensorAssoc : (M ⊗[R] N) ⊗[R] P ⊗[R] Q ≃ₗ[R] (M ⊗[R]
 variable {M N P Q}
 
 /- warning: tensor_product.tensor_tensor_tensor_assoc_tmul -> TensorProduct.tensorTensorTensorAssoc_tmul is a dubious translation:
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N P _inst_5 _inst_6 _inst_10 _inst_11) m (TensorProduct.tmul.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11 n p)) q)
+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_assoc_tmul TensorProduct.tensorTensorTensorAssoc_tmulₓ'. -/
 @[simp]
 theorem tensorTensorTensorAssoc_tmul (m : M) (n : N) (p : P) (q : Q) :
@@ -1585,10 +1387,7 @@ theorem tensorTensorTensorAssoc_tmul (m : M) (n : N) (p : P) (q : Q) :
 #align tensor_product.tensor_tensor_tensor_assoc_tmul TensorProduct.tensorTensorTensorAssoc_tmul
 
 /- warning: tensor_product.tensor_tensor_tensor_assoc_symm_tmul -> TensorProduct.tensorTensorTensorAssoc_symm_tmul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_assoc_symm_tmul TensorProduct.tensorTensorTensorAssoc_symm_tmulₓ'. -/
 @[simp]
 theorem tensorTensorTensorAssoc_symm_tmul (m : M) (n : N) (p : P) (q : Q) :
@@ -1627,10 +1426,7 @@ def rTensor (f : N →ₗ[R] P) : N ⊗ M →ₗ[R] P ⊗ M :=
 variable (g : P →ₗ[R] Q) (f : N →ₗ[R] P)
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_tmul LinearMap.lTensor_tmulₓ'. -/
 @[simp]
 theorem lTensor_tmul (m : M) (n : N) : f.lTensor M (m ⊗ₜ n) = m ⊗ₜ f n :=
@@ -1638,10 +1434,7 @@ theorem lTensor_tmul (m : M) (n : N) : f.lTensor M (m ⊗ₜ n) = m ⊗ₜ f n :
 #align linear_map.ltensor_tmul LinearMap.lTensor_tmul
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_tmul LinearMap.rTensor_tmulₓ'. -/
 @[simp]
 theorem rTensor_tmul (m : M) (n : N) : f.rTensor M (n ⊗ₜ m) = f n ⊗ₜ m :=
@@ -1653,10 +1446,7 @@ open TensorProduct
 attribute [local ext] TensorProduct.ext
 
 /- warning: linear_map.ltensor_hom -> LinearMap.lTensorHom is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_hom LinearMap.lTensorHomₓ'. -/
 /-- `ltensor_hom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
 def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
@@ -1672,10 +1462,7 @@ def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
 #align linear_map.ltensor_hom LinearMap.lTensorHom
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_hom LinearMap.rTensorHomₓ'. -/
 /-- `rtensor_hom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
 def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
@@ -1691,10 +1478,7 @@ def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
 #align linear_map.rtensor_hom LinearMap.rTensorHom
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.coe_ltensor_hom LinearMap.coe_lTensorHomₓ'. -/
 @[simp]
 theorem coe_lTensorHom : (lTensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R] M ⊗[R] P) = lTensor M :=
@@ -1702,10 +1486,7 @@ theorem coe_lTensorHom : (lTensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R
 #align linear_map.coe_ltensor_hom LinearMap.coe_lTensorHom
 
 /- warning: linear_map.coe_rtensor_hom -> LinearMap.coe_rTensorHom is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.coe_rtensor_hom LinearMap.coe_rTensorHomₓ'. -/
 @[simp]
 theorem coe_rTensorHom : (rTensorHom M : (N →ₗ[R] P) → N ⊗[R] M →ₗ[R] P ⊗[R] M) = rTensor M :=
@@ -1713,10 +1494,7 @@ theorem coe_rTensorHom : (rTensorHom M : (N →ₗ[R] P) → N ⊗[R] M →ₗ[R
 #align linear_map.coe_rtensor_hom LinearMap.coe_rTensorHom
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_add LinearMap.lTensor_addₓ'. -/
 @[simp]
 theorem lTensor_add (f g : N →ₗ[R] P) : (f + g).lTensor M = f.lTensor M + g.lTensor M :=
@@ -1724,10 +1502,7 @@ theorem lTensor_add (f g : N →ₗ[R] P) : (f + g).lTensor M = f.lTensor M + g.
 #align linear_map.ltensor_add LinearMap.lTensor_add
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_add LinearMap.rTensor_addₓ'. -/
 @[simp]
 theorem rTensor_add (f g : N →ₗ[R] P) : (f + g).rTensor M = f.rTensor M + g.rTensor M :=
@@ -1735,10 +1510,7 @@ theorem rTensor_add (f g : N →ₗ[R] P) : (f + g).rTensor M = f.rTensor M + g.
 #align linear_map.rtensor_add LinearMap.rTensor_add
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_zero LinearMap.lTensor_zeroₓ'. -/
 @[simp]
 theorem lTensor_zero : lTensor M (0 : N →ₗ[R] P) = 0 :=
@@ -1746,10 +1518,7 @@ theorem lTensor_zero : lTensor M (0 : N →ₗ[R] P) = 0 :=
 #align linear_map.ltensor_zero LinearMap.lTensor_zero
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_zero LinearMap.rTensor_zeroₓ'. -/
 @[simp]
 theorem rTensor_zero : rTensor M (0 : N →ₗ[R] P) = 0 :=
@@ -1757,10 +1526,7 @@ theorem rTensor_zero : rTensor M (0 : N →ₗ[R] P) = 0 :=
 #align linear_map.rtensor_zero LinearMap.rTensor_zero
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_smul LinearMap.lTensor_smulₓ'. -/
 @[simp]
 theorem lTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).lTensor M = r • f.lTensor M :=
@@ -1768,10 +1534,7 @@ theorem lTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).lTensor M = r • f
 #align linear_map.ltensor_smul LinearMap.lTensor_smul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_smul LinearMap.rTensor_smulₓ'. -/
 @[simp]
 theorem rTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).rTensor M = r • f.rTensor M :=
@@ -1779,10 +1542,7 @@ theorem rTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).rTensor M = r • f
 #align linear_map.rtensor_smul LinearMap.rTensor_smul
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp LinearMap.lTensor_compₓ'. -/
 theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) :=
   by
@@ -1791,20 +1551,14 @@ theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) :
 #align linear_map.ltensor_comp LinearMap.lTensor_comp
 
 /- warning: linear_map.ltensor_comp_apply -> LinearMap.lTensor_comp_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_apply LinearMap.lTensor_comp_applyₓ'. -/
 theorem lTensor_comp_apply (x : M ⊗[R] N) :
     (g.comp f).lTensor M x = (g.lTensor M) ((f.lTensor M) x) := by rw [ltensor_comp, coe_comp]
 #align linear_map.ltensor_comp_apply LinearMap.lTensor_comp_apply
 
 /- warning: linear_map.rtensor_comp -> LinearMap.rTensor_comp is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp LinearMap.rTensor_compₓ'. -/
 theorem rTensor_comp : (g.comp f).rTensor M = (g.rTensor M).comp (f.rTensor M) :=
   by
@@ -1813,30 +1567,21 @@ theorem rTensor_comp : (g.comp f).rTensor M = (g.rTensor M).comp (f.rTensor M) :
 #align linear_map.rtensor_comp LinearMap.rTensor_comp
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_apply LinearMap.rTensor_comp_applyₓ'. -/
 theorem rTensor_comp_apply (x : N ⊗[R] M) :
     (g.comp f).rTensor M x = (g.rTensor M) ((f.rTensor M) x) := by rw [rtensor_comp, coe_comp]
 #align linear_map.rtensor_comp_apply LinearMap.rTensor_comp_apply
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_mul LinearMap.lTensor_mulₓ'. -/
 theorem lTensor_mul (f g : Module.End R N) : (f * g).lTensor M = f.lTensor M * g.lTensor M :=
   lTensor_comp M f g
 #align linear_map.ltensor_mul LinearMap.lTensor_mul
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_mul LinearMap.rTensor_mulₓ'. -/
 theorem rTensor_mul (f g : Module.End R N) : (f * g).rTensor M = f.rTensor M * g.rTensor M :=
   rTensor_comp M f g
@@ -1856,10 +1601,7 @@ theorem lTensor_id : (id : N →ₗ[R] N).lTensor M = id :=
 #align linear_map.ltensor_id LinearMap.lTensor_id
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_id_apply LinearMap.lTensor_id_applyₓ'. -/
 -- `simp` can prove this.
 theorem lTensor_id_apply (x : M ⊗[R] N) : (LinearMap.id : N →ₗ[R] N).lTensor M x = x := by
@@ -1878,10 +1620,7 @@ theorem rTensor_id : (id : N →ₗ[R] N).rTensor M = id :=
 #align linear_map.rtensor_id LinearMap.rTensor_id
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_id_apply LinearMap.rTensor_id_applyₓ'. -/
 -- `simp` can prove this.
 theorem rTensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rTensor M x = x := by
@@ -1891,10 +1630,7 @@ theorem rTensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rTens
 variable {N}
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_rtensor LinearMap.lTensor_comp_rTensorₓ'. -/
 @[simp]
 theorem lTensor_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
@@ -1903,10 +1639,7 @@ theorem lTensor_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
 #align linear_map.ltensor_comp_rtensor LinearMap.lTensor_comp_rTensor
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_ltensor LinearMap.rTensor_comp_lTensorₓ'. -/
 @[simp]
 theorem rTensor_comp_lTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
@@ -1915,10 +1648,7 @@ theorem rTensor_comp_lTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
 #align linear_map.rtensor_comp_ltensor LinearMap.rTensor_comp_lTensor
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.map_comp_rtensor LinearMap.map_comp_rTensorₓ'. -/
 @[simp]
 theorem map_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (f' : S →ₗ[R] M) :
@@ -1927,10 +1657,7 @@ theorem map_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (f' : S →ₗ[
 #align linear_map.map_comp_rtensor LinearMap.map_comp_rTensor
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.map_comp_ltensor LinearMap.map_comp_lTensorₓ'. -/
 @[simp]
 theorem map_comp_lTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (g' : S →ₗ[R] N) :
@@ -1939,10 +1666,7 @@ theorem map_comp_lTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (g' : S →ₗ[
 #align linear_map.map_comp_ltensor LinearMap.map_comp_lTensor
 
 /- warning: linear_map.rtensor_comp_map -> LinearMap.rTensor_comp_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_map LinearMap.rTensor_comp_mapₓ'. -/
 @[simp]
 theorem rTensor_comp_map (f' : P →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
@@ -1951,10 +1675,7 @@ theorem rTensor_comp_map (f' : P →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[
 #align linear_map.rtensor_comp_map LinearMap.rTensor_comp_map
 
 /- warning: linear_map.ltensor_comp_map -> LinearMap.lTensor_comp_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_map LinearMap.lTensor_comp_mapₓ'. -/
 @[simp]
 theorem lTensor_comp_map (g' : Q →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
@@ -1965,10 +1686,7 @@ theorem lTensor_comp_map (g' : Q →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[
 variable {M}
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_pow LinearMap.rTensor_powₓ'. -/
 @[simp]
 theorem rTensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rTensor N ^ n = (f ^ n).rTensor N :=
@@ -1978,10 +1696,7 @@ theorem rTensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rTensor N ^ n = (f ^ n).rT
 #align linear_map.rtensor_pow LinearMap.rTensor_pow
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_pow LinearMap.lTensor_powₓ'. -/
 @[simp]
 theorem lTensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.lTensor M ^ n = (f ^ n).lTensor M :=
@@ -2026,10 +1741,7 @@ def Neg.aux : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
 variable {R}
 
 /- warning: tensor_product.neg.aux_of -> TensorProduct.Neg.aux_of is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.neg.aux_of TensorProduct.Neg.aux_ofₓ'. -/
 theorem Neg.aux_of (m : M) (n : N) : Neg.aux R (FreeAddMonoid.of (m, n)) = (-m) ⊗ₜ[R] n :=
   rfl
@@ -2167,10 +1879,7 @@ end TensorProduct
 namespace LinearMap
 
 /- warning: linear_map.ltensor_sub -> LinearMap.lTensor_sub is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_sub LinearMap.lTensor_subₓ'. -/
 @[simp]
 theorem lTensor_sub (f g : N →ₗ[R] P) : (f - g).lTensor M = f.lTensor M - g.lTensor M := by
@@ -2178,10 +1887,7 @@ theorem lTensor_sub (f g : N →ₗ[R] P) : (f - g).lTensor M = f.lTensor M - g.
 #align linear_map.ltensor_sub LinearMap.lTensor_sub
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_sub LinearMap.rTensor_subₓ'. -/
 @[simp]
 theorem rTensor_sub (f g : N →ₗ[R] P) : (f - g).rTensor M = f.rTensor M - g.rTensor M := by
@@ -2189,10 +1895,7 @@ theorem rTensor_sub (f g : N →ₗ[R] P) : (f - g).rTensor M = f.rTensor M - g.
 #align linear_map.rtensor_sub LinearMap.rTensor_sub
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_neg LinearMap.lTensor_negₓ'. -/
 @[simp]
 theorem lTensor_neg (f : N →ₗ[R] P) : (-f).lTensor M = -f.lTensor M := by
@@ -2200,10 +1903,7 @@ theorem lTensor_neg (f : N →ₗ[R] P) : (-f).lTensor M = -f.lTensor M := by
 #align linear_map.ltensor_neg LinearMap.lTensor_neg
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_neg LinearMap.rTensor_negₓ'. -/
 @[simp]
 theorem rTensor_neg (f : N →ₗ[R] P) : (-f).rTensor M = -f.rTensor M := by

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

@@ -543,7 +543,7 @@ variable {R M N}
 lean 3 declaration is
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 but is expected to have type
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u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u1, u1, u2, 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))) N (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u3 u2} R R M (LinearMap.{u1, u1, u2, 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))) N (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u2, max u3 u2} R R N (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, max u3 u2} R R R N (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (smulCommClass_self.{u1, max u3 u2} R (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, max u3 u2} R (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddCommMonoid.toAddMonoid.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) (Module.toMulActionWithZero.{u1, max u3 u2} R (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.mk.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) m) n) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u3}} {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (m : M) (n : N), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) n) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u1, u1, u2, 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))) N (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M 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u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u1, u1, u2, 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))) N (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u3 u2} R R M (LinearMap.{u1, u1, u2, 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))) N (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u2, max u3 u2} R R N (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, max u3 u2} R R R N 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_inst_1)) (AddMonoid.toZero.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddCommMonoid.toAddMonoid.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) (Module.toMulActionWithZero.{u1, max u3 u2} R (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.mk.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) m) n) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)
 Case conversion may be inaccurate. Consider using '#align tensor_product.mk_apply TensorProduct.mk_applyₓ'. -/
 @[simp]
 theorem mk_apply (m : M) (n : N) : mk R M N m n = m ⊗ₜ n :=
@@ -677,7 +677,7 @@ def liftAux : M ⊗[R] N →+ P :=
 lean 3 declaration is
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 but is expected to have type
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u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u1 u4} R R M (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) f m) n)
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u2}} {N : Type.{u1}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_11 : Module.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6] (f : LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11))))) (m : M) (n : N), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) (TensorProduct.tmul.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), max (succ u2) (succ u1), succ u4} (AddMonoidHom.{max u1 u2, u4} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) _x) (AddHomClass.toFunLike.{max (max u2 u1) u4, max u2 u1, u4} (AddMonoidHom.{max u1 u2, u4} (TensorProduct.{u3, u2, u1} R _inst_1 M 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P _inst_5 _inst_6 _inst_10 _inst_11) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), succ u2, max (succ u1) (succ u4)} (LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u1 u4} R R M (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift_aux_tmul TensorProduct.liftAux_tmulₓ'. -/
 theorem liftAux_tmul (m n) : liftAux f (m ⊗ₜ n) = f m n :=
   rfl
@@ -716,7 +716,7 @@ variable {f}
 lean 3 declaration is
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 but is expected to have type
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(fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u1, u4} R R (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (TensorProduct.lift.{u3, u2, u1, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x y)) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) 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_inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) f x) y)
 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.tmul TensorProduct.lift.tmulₓ'. -/
 @[simp]
 theorem lift.tmul (x y) : lift f (x ⊗ₜ y) = f x y :=
@@ -727,7 +727,7 @@ theorem lift.tmul (x y) : lift f (x ⊗ₜ y) = f x y :=
 lean 3 declaration is
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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 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (TensorProduct.lift.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x y)) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (fun (_x : LinearMap.{u1, 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 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u2}} {N : Type.{u1}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_11 : Module.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6] {f : LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11))))} (x : M) (y : N), Eq.{succ u4} ((fun 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_inst_10) P (AddZeroClass.toAdd.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)))) (AddZeroClass.toAdd.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (AddHom.addHomClass.{max u2 u1, u4} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (AddZeroClass.toAdd.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) f x) y)
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u2}} {N : Type.{u1}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_11 : Module.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6] {f : LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11))))} (x : M) (y : N), Eq.{succ u4} ((fun 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.tmul' TensorProduct.lift.tmul'ₓ'. -/
 @[simp]
 theorem lift.tmul' (x y) : (lift f).1 (x ⊗ₜ y) = f x y :=
@@ -738,7 +738,7 @@ theorem lift.tmul' (x y) : (lift f).1 (x ⊗ₜ y) = f x y :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align tensor_product.ext' TensorProduct.ext'ₓ'. -/
 theorem ext' {g h : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x ⊗ₜ y)) : g = h :=
   LinearMap.ext fun z =>
@@ -750,7 +750,7 @@ theorem ext' {g h : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.unique TensorProduct.lift.uniqueₓ'. -/
 theorem lift.unique {g : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = f x y) : g = lift f :=
   ext' fun m n => by rw [H, lift.tmul]
@@ -823,7 +823,7 @@ variable {R M N P}
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.uncurry_apply TensorProduct.uncurry_applyₓ'. -/
 @[simp]
 theorem uncurry_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
@@ -848,7 +848,7 @@ def lift.equiv : (M →ₗ[R] N →ₗ[R] P) ≃ₗ[R] M ⊗ N →ₗ[R] P :=
 lean 3 declaration is
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 but is expected to have type
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P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R 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(SMulHomClass.toFunLike.{max (max u3 u1) u2, u4, max (max u3 u1) u2, max (max u3 u1) u2} (LinearEquiv.{u4, u4, max (max u2 u1) u3, max u2 u1 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))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N 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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P 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_inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (SMulZeroClass.toSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toZero.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} 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(LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) 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_inst_10) _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u2} R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u2} R R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (SemilinearMapClass.distribMulActionHomClass.{u4, max (max u3 u1) u2, max (max u3 u1) u2, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, 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_inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, max u1 u2} R R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u2} R R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (fun (_x : LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) => LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u4, max (max u3 u1) u2, max (max u3 u1) u2} (LinearEquiv.{u4, u4, max (max u2 u1) u3, max u2 u1 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))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u2} R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, max u1 u2} R R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) 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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P 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_inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (SMulZeroClass.toSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toZero.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, max u1 u2} R R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R 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_inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.equiv_apply TensorProduct.lift.equiv_applyₓ'. -/
 @[simp]
 theorem lift.equiv_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
@@ -860,7 +860,7 @@ theorem lift.equiv_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
 lean 3 declaration is
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(AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, 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_inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, 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_inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u2, max u3 u1} R R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 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(CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.equiv_symm_apply TensorProduct.lift.equiv_symm_applyₓ'. -/
 @[simp]
 theorem lift.equiv_symm_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) :
@@ -886,7 +886,7 @@ variable {R M N P}
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.lcurry_apply TensorProduct.lcurry_applyₓ'. -/
 @[simp]
 theorem lcurry_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) : lcurry R M N P f m n = f (m ⊗ₜ n) :=
@@ -909,7 +909,7 @@ def curry (f : M ⊗ N →ₗ[R] P) : M →ₗ[R] N →ₗ[R] P :=
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.curry_apply TensorProduct.curry_applyₓ'. -/
 @[simp]
 theorem curry_apply (f : M ⊗ N →ₗ[R] P) (m : M) (n : N) : curry f m n = f (m ⊗ₜ n) :=
@@ -930,7 +930,7 @@ theorem curry_injective : Function.Injective (curry : (M ⊗[R] N →ₗ[R] P) 
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.ext_threefold TensorProduct.ext_threefoldₓ'. -/
 theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
     (H : ∀ x y z, g (x ⊗ₜ y ⊗ₜ z) = h (x ⊗ₜ y ⊗ₜ z)) : g = h :=
@@ -943,7 +943,7 @@ theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.ext_fourfold TensorProduct.ext_fourfoldₓ'. -/
 -- We'll need this one for checking the pentagon identity!
 theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
@@ -957,7 +957,7 @@ theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
 lean 3 declaration is
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(TensorProduct.addCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) S (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (TensorProduct.addCommMonoid.{u6, max u2 u3, max u4 u5} R _inst_1 (TensorProduct.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) _inst_8 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, max u2 u3, max u4 u5} R _inst_1 (TensorProduct.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) _inst_13 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) ψ (TensorProduct.tmul.{u6, max u2 u3, max u4 u5} R _inst_1 (TensorProduct.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.tmul.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 w x) (TensorProduct.tmul.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12 y z)))) -> (Eq.{max (max (max (max (succ u2) (succ u3)) (succ u4)) (succ u5)) (succ u1)} (LinearMap.{u6, u6, max (max u5 u4) u3 u2, u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (TensorProduct.{u6, max u3 u2, max u5 u4} R _inst_1 (TensorProduct.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) S (TensorProduct.addCommMonoid.{u6, max u2 u3, max u4 u5} R _inst_1 (TensorProduct.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) _inst_8 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, max u2 u3, max u4 u5} R _inst_1 (TensorProduct.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) _inst_13) φ ψ)
 Case conversion may be inaccurate. Consider using '#align tensor_product.ext_fourfold' TensorProduct.ext_fourfold'ₓ'. -/
 /-- Two linear maps (M ⊗ N) ⊗ (P ⊗ Q) → S which agree on all elements of the
 form (m ⊗ₜ n) ⊗ₜ (p ⊗ₜ q) are equal. -/
@@ -995,7 +995,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (m : M) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (LinearEquiv.{u1, u1, max u1 u2, 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))) (TensorProduct.lid._proof_1.{u1} R _inst_1) (TensorProduct.lid._proof_2.{u1} R _inst_1) (TensorProduct.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) M (TensorProduct.addCommMonoid.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _inst_4 (TensorProduct.module.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _inst_9) (fun (_x : LinearEquiv.{u1, u1, max u1 u2, 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))) (TensorProduct.lid._proof_1.{u1} R _inst_1) (TensorProduct.lid._proof_2.{u1} R _inst_1) (TensorProduct.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) M (TensorProduct.addCommMonoid.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _inst_4 (TensorProduct.module.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _inst_9) => (TensorProduct.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) -> M) (LinearEquiv.hasCoeToFun.{u1, u1, max u1 u2, u2} R R (TensorProduct.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _inst_4 (TensorProduct.module.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _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))) (TensorProduct.lid._proof_1.{u1} R _inst_1) (TensorProduct.lid._proof_2.{u1} R _inst_1)) (TensorProduct.lid.{u1, u2} R _inst_1 M _inst_4 _inst_9) (TensorProduct.tmul.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9 r m)) (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} 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.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_9)))) r m)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (m : M) (r : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) => M) (TensorProduct.tmul.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9 r m)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearEquiv.{u1, u1, max u2 u1, 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, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) M (TensorProduct.addCommMonoid.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _inst_4 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _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))))))) (TensorProduct.lid.{u1, u2} R _inst_1 M _inst_4 _inst_9) 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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (m : M) (r : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) => M) (TensorProduct.tmul.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9 r m)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearEquiv.{u1, 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lid_tmul TensorProduct.lid_tmulₓ'. -/
 @[simp]
 theorem lid_tmul (m : M) (r : R) : (TensorProduct.lid R M : R ⊗ M → M) (r ⊗ₜ m) = r • m :=
@@ -1008,7 +1008,7 @@ theorem lid_tmul (m : M) (r : R) : (TensorProduct.lid R M : R ⊗ M → M) (r 
 lean 3 declaration is
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R _inst_1) M (TensorProduct.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _inst_4 (TensorProduct.addCommMonoid.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _inst_9 (TensorProduct.module.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9)) (fun (_x : 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(Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (TensorProduct.addCommMonoid.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _inst_9 (TensorProduct.module.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _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))) (TensorProduct.lid._proof_2.{u1} R _inst_1) (TensorProduct.lid._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u1 u2, u2} R R (TensorProduct.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _inst_4 (TensorProduct.module.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9) _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))) (TensorProduct.lid._proof_1.{u1} R _inst_1) (TensorProduct.lid._proof_2.{u1} R _inst_1) (TensorProduct.lid.{u1, u2} R _inst_1 M _inst_4 _inst_9)) m) (TensorProduct.tmul.{u1, u1, u2} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_4 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_9 (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) m)
 but is expected to have type
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_inst_4 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_9) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u2, u2, u1} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_4 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_9) (TensorProduct.addCommMonoid.{u2, u2, u1} R _inst_1 R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_4 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_9)) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u2, u1} R _inst_1 R M 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lid_symm_apply TensorProduct.lid_symm_applyₓ'. -/
 @[simp]
 theorem lid_symm_apply (m : M) : (TensorProduct.lid R M).symm m = 1 ⊗ₜ m :=
@@ -1036,7 +1036,7 @@ protected def comm : M ⊗ N ≃ₗ[R] N ⊗ M :=
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) (N : Type.{u3}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (m : M) (n : N), Eq.{succ (max u3 u2)} (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (coeFn.{max (succ (max u2 u3)) (succ (max u3 u2)), max (succ (max u2 u3)) (succ (max u3 u2))} (LinearEquiv.{u1, u1, max u2 u3, 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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.comm._proof_1.{u1} R _inst_1) (TensorProduct.comm._proof_2.{u1} R _inst_1) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (fun (_x : LinearEquiv.{u1, u1, max u2 u3, 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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.comm._proof_1.{u1} R _inst_1) (TensorProduct.comm._proof_2.{u1} R _inst_1) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) => (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u3, max u3 u2} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _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))) (TensorProduct.comm._proof_1.{u1} R _inst_1) (TensorProduct.comm._proof_2.{u1} R _inst_1)) (TensorProduct.comm.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)
 but is expected to have type
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u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _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 u3 u2, max u3 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _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))))))) (TensorProduct.comm.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)
 Case conversion may be inaccurate. Consider using '#align tensor_product.comm_tmul TensorProduct.comm_tmulₓ'. -/
 @[simp]
 theorem comm_tmul (m : M) (n : N) : (TensorProduct.comm R M N) (m ⊗ₜ n) = n ⊗ₜ m :=
@@ -1047,7 +1047,7 @@ theorem comm_tmul (m : M) (n : N) : (TensorProduct.comm R M N) (m ⊗ₜ n) = n
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) (N : Type.{u3}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (m : M) (n : N), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (coeFn.{max (succ (max u3 u2)) (succ (max u2 u3)), max (succ (max u3 u2)) (succ (max u2 u3))} (LinearEquiv.{u1, u1, max u3 u2, 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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.comm._proof_2.{u1} R _inst_1) (TensorProduct.comm._proof_1.{u1} R _inst_1) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (fun (_x : LinearEquiv.{u1, u1, max u3 u2, 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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.comm._proof_2.{u1} R _inst_1) (TensorProduct.comm._proof_1.{u1} R _inst_1) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) => (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) -> (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (LinearEquiv.hasCoeToFun.{u1, u1, max u3 u2, max u2 u3} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (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.comm._proof_2.{u1} R _inst_1) (TensorProduct.comm._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u2 u3, max u3 u2} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _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))) (TensorProduct.comm._proof_1.{u1} R _inst_1) (TensorProduct.comm._proof_2.{u1} R _inst_1) (TensorProduct.comm.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (M : Type.{u3}) (N : Type.{u2}) [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (m : M) (n : N), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearEquiv.{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))) (RingHom.id.{u1} R 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(x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, max u3 u2, max u3 u2} (LinearEquiv.{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))) (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 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) 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 Case conversion may be inaccurate. Consider using '#align tensor_product.comm_symm_tmul TensorProduct.comm_symm_tmulₓ'. -/
 @[simp]
 theorem comm_symm_tmul (m : M) (n : N) : (TensorProduct.comm R M N).symm (n ⊗ₜ m) = m ⊗ₜ n :=
@@ -1078,7 +1078,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (m : M) (r : R), Eq.{succ u2} M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearEquiv.{u1, u1, max u2 u1, 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))) (TensorProduct.rid._proof_1.{u1} R _inst_1) (TensorProduct.rid._proof_2.{u1} R _inst_1) (TensorProduct.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} 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(CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_9)))) r m)
 but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_9) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, u2, max u1 u2} R (TensorProduct.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1))) _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 u1 u2, u2} R R (TensorProduct.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_4 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _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))))))) (TensorProduct.rid.{u1, u2} R _inst_1 M _inst_4 _inst_9) 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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (m : M) (r : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => M) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) m r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearEquiv.{u1, 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_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, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (TensorProduct.addCommMonoid.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_4 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_9) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, u2, max u1 u2} R (TensorProduct.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_4 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _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))))))) (TensorProduct.rid.{u1, u2} R _inst_1 M _inst_4 _inst_9) 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 Case conversion may be inaccurate. Consider using '#align tensor_product.rid_tmul TensorProduct.rid_tmulₓ'. -/
 @[simp]
 theorem rid_tmul (m : M) (r : R) : (TensorProduct.rid R M) (m ⊗ₜ r) = r • m :=
@@ -1091,7 +1091,7 @@ theorem rid_tmul (m : M) (r : R) : (TensorProduct.rid R M) (m ⊗ₜ r) = r •
 lean 3 declaration is
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(Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_9 (TensorProduct.module.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> (TensorProduct.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (TensorProduct.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (TensorProduct.addCommMonoid.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_9 (TensorProduct.module.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (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.rid._proof_2.{u1} R _inst_1) (TensorProduct.rid._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u2 u1, u2} R R (TensorProduct.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_4 (TensorProduct.module.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _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))) (TensorProduct.rid._proof_1.{u1} R _inst_1) (TensorProduct.rid._proof_2.{u1} R _inst_1) (TensorProduct.rid.{u1, u2} R _inst_1 M _inst_4 _inst_9)) m) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) m (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R 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 but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_9 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) _inst_9 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (TensorProduct.rid.{u2, u1} R _inst_1 M _inst_4 _inst_9)) m) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 M R _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_9 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) m (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align tensor_product.rid_symm_apply TensorProduct.rid_symm_applyₓ'. -/
 @[simp]
 theorem rid_symm_apply (m : M) : (TensorProduct.rid R M).symm m = m ⊗ₜ 1 :=
@@ -1128,7 +1128,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (m : M) (n : N) (p : P), Eq.{succ (max u2 u3 u4)} (TensorProduct.{u1, u2, max u3 u4} R _inst_1 M (TensorProduct.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_9 (TensorProduct.module.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11)) (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 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 but is expected to have type
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_inst_6 _inst_10 _inst_11)) (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, u4, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11) (TensorProduct.tmul.{u1, max u4 u3, u2} R _inst_1 (TensorProduct.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (TensorProduct.tmul.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n) p)) (TensorProduct.tmul.{u1, u4, max u2 u3} R _inst_1 M (TensorProduct.{u1, u3, u2} R 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 Case conversion may be inaccurate. Consider using '#align tensor_product.assoc_tmul TensorProduct.assoc_tmulₓ'. -/
 @[simp]
 theorem assoc_tmul (m : M) (n : N) (p : P) :
@@ -1140,7 +1140,7 @@ theorem assoc_tmul (m : M) (n : N) (p : P) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (m : M) (n : N) (p : P), Eq.{succ (max (max u2 u3) u4)} (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (coeFn.{max (succ (max u2 u3 u4)) (succ (max (max u2 u3) u4)), max (succ (max u2 u3 u4)) (succ (max (max u2 u3) u4))} (LinearEquiv.{u1, u1, max u2 u3 u4, max (max u2 u3) u4} R R 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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, u4, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11)) (TensorProduct.tmul.{u1, u4, max u3 u2} R _inst_1 M (TensorProduct.{u1, u3, u2} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_9 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) m (TensorProduct.tmul.{u1, u3, u2} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11 n p))) (TensorProduct.tmul.{u1, max u3 u4, u2} R _inst_1 (TensorProduct.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (TensorProduct.tmul.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n) p)
 Case conversion may be inaccurate. Consider using '#align tensor_product.assoc_symm_tmul TensorProduct.assoc_symm_tmulₓ'. -/
 @[simp]
 theorem assoc_symm_tmul (m : M) (n : N) (p : P) :
@@ -1163,7 +1163,7 @@ def map (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : M ⊗ N →ₗ[R] P ⊗ Q :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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max u4 u5} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.map.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12 (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (fun (_x : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u1, u3, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) 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 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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_inst_10 _inst_12) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => Q) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) g n))
+  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u4 u2, max u3 u1} R R (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (TensorProduct.addCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (TensorProduct.map.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g) (TensorProduct.tmul.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u5, u3, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => P) m) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => Q) n) _inst_6 _inst_7 _inst_11 _inst_12 (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) f m) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => Q) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) g n))
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_tmul TensorProduct.map_tmulₓ'. -/
 @[simp]
 theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f g (m ⊗ₜ n) = f m ⊗ₜ g n :=
@@ -1174,7 +1174,7 @@ theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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_inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (setOf.{max u4 u5} (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (fun (t : TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) => Exists.{succ u2} M (fun (m : M) => Exists.{succ u3} N (fun (n : N) => Eq.{succ (max u4 u5)} (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.tmul.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12 (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (fun (_x : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12) (fun (_x : LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12) => N -> Q) (LinearMap.hasCoeToFun.{u1, u1, u3, u5} R R N Q (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) g n)) t)))))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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 Case conversion may be inaccurate. Consider using '#align tensor_product.map_range_eq_span_tmul TensorProduct.map_range_eq_span_tmulₓ'. -/
 theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (map f g).range = Submodule.span R { t | ∃ m n, f m ⊗ₜ g n = t } :=
@@ -1374,7 +1374,7 @@ variable {R M N P Q}
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align tensor_product.map_bilinear_apply TensorProduct.mapBilinear_applyₓ'. -/
 @[simp]
 theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear R M N P Q f g = map f g :=
@@ -1385,7 +1385,7 @@ theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {P : Type.{u3}} {Q : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u4} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_11 : Module.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u4} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (p : P) (f : LinearMap.{u1, u1, 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 Q _inst_4 _inst_7 _inst_9 _inst_12) (m : M), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.lTensorHomToHomLTensor_applyₓ'. -/
 @[simp]
 theorem lTensorHomToHomLTensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
@@ -1397,7 +1397,7 @@ theorem lTensorHomToHomLTensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {P : Type.{u3}} {Q : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u4} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_11 : Module.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u4} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : 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))) M P _inst_4 _inst_6 _inst_9 _inst_11) (q : Q) (m : M), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) 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 but is expected to have type
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_inst_1)))) f m) q)
 Case conversion may be inaccurate. Consider using '#align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rTensorHomToHomRTensor_applyₓ'. -/
 @[simp]
 theorem rTensorHomToHomRTensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
@@ -1409,7 +1409,7 @@ theorem rTensorHomToHomRTensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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 but is expected to have type
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(TensorProduct.homTensorHomMap.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12) (TensorProduct.tmul.{u5, max u4 u3, max u2 u1} R _inst_1 (LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12) (LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u5, u4, u3} R R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_11 (smulCommClass_self.{u5, u3} R P (CommSemiring.toCommMonoid.{u5} R _inst_1) (MulActionWithZero.toMulAction.{u5, u3} R P (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_6)) (Module.toMulActionWithZero.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u5, u2, u1} R R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_12 (smulCommClass_self.{u5, u1} R Q (CommSemiring.toCommMonoid.{u5} R _inst_1) (MulActionWithZero.toMulAction.{u5, u1} R Q (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (AddMonoid.toZero.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q _inst_7)) (Module.toMulActionWithZero.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_12)))) f g)) (TensorProduct.map.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)
 Case conversion may be inaccurate. Consider using '#align tensor_product.hom_tensor_hom_map_apply TensorProduct.homTensorHomMap_applyₓ'. -/
 @[simp]
 theorem homTensorHomMap_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
@@ -1437,7 +1437,7 @@ def congr (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) : M ⊗ N ≃ₗ[R] P ⊗ Q :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : LinearEquiv.{u1, u1, 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)) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearEquiv.{u1, u1, u3, 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)) N Q _inst_5 _inst_7 _inst_10 _inst_12) (m : M) (n : N), Eq.{succ (max u4 u5)} (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (coeFn.{max (succ (max u2 u3)) (succ (max u4 u5)), max (succ (max u2 u3)) (succ (max u4 u5))} (LinearEquiv.{u1, u1, max u2 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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.congr._proof_5.{u1} R _inst_1) (TensorProduct.congr._proof_6.{u1} R _inst_1) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (fun (_x : LinearEquiv.{u1, u1, max u2 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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.congr._proof_5.{u1} R _inst_1) (TensorProduct.congr._proof_6.{u1} R _inst_1) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) => (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u3, max u4 u5} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (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.congr._proof_5.{u1} R _inst_1) (TensorProduct.congr._proof_6.{u1} R _inst_1)) (TensorProduct.congr.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12 (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearEquiv.{u1, u1, 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)) M P _inst_4 _inst_6 _inst_9 _inst_11) (fun (_x : LinearEquiv.{u1, u1, 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)) M P _inst_4 _inst_6 _inst_9 _inst_11) => M -> P) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (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 m) (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearEquiv.{u1, u1, u3, 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)) N Q _inst_5 _inst_7 _inst_10 _inst_12) (fun (_x : LinearEquiv.{u1, u1, u3, 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)) N Q _inst_5 _inst_7 _inst_10 _inst_12) => N -> Q) (LinearEquiv.hasCoeToFun.{u1, u1, u3, u5} R R N Q (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (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))) g n))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearEquiv.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearEquiv.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) N Q _inst_5 _inst_7 _inst_10 _inst_12) (m : M) (n : N), Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.tmul.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), max (succ u4) 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(CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) N Q _inst_5 _inst_7 _inst_10 _inst_12) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (SemilinearEquivClass.instSemilinearMapClass.{u5, u5, u2, u1, max u2 u1} R R N Q (LinearEquiv.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) N Q _inst_5 _inst_7 _inst_10 _inst_12) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))))) g n))
+  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearEquiv.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearEquiv.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) N Q _inst_5 _inst_7 _inst_10 _inst_12) (m : M) (n : N), Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.tmul.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), max (succ u4) 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(DistribSMul.toSMulZeroClass.{u5, u2} R N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (DistribMulAction.toDistribSMul.{u5, u2} R N (MonoidWithZero.toMonoid.{u5} R (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} N _inst_5) (Module.toDistribMulAction.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_10)))) (SMulZeroClass.toSMul.{u5, u1} R Q (AddMonoid.toZero.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q _inst_7)) (DistribSMul.toSMulZeroClass.{u5, u1} R Q (AddMonoid.toAddZeroClass.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q _inst_7)) (DistribMulAction.toDistribSMul.{u5, u1} R Q (MonoidWithZero.toMonoid.{u5} R (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} Q _inst_7) (Module.toDistribMulAction.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_12)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u5, u2, u1} (LinearEquiv.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) N Q _inst_5 _inst_7 _inst_10 _inst_12) R N Q (MonoidWithZero.toMonoid.{u5} R (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} N _inst_5) (AddCommMonoid.toAddMonoid.{u1} Q _inst_7) (Module.toDistribMulAction.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_10) (Module.toDistribMulAction.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_12) (SemilinearMapClass.distribMulActionHomClass.{u5, u2, u1, max u2 u1} R N Q (LinearEquiv.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) N Q _inst_5 _inst_7 _inst_10 _inst_12) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (SemilinearEquivClass.instSemilinearMapClass.{u5, u5, u2, u1, max u2 u1} R R N Q (LinearEquiv.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) N Q _inst_5 _inst_7 _inst_10 _inst_12) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))))) g n))
 Case conversion may be inaccurate. Consider using '#align tensor_product.congr_tmul TensorProduct.congr_tmulₓ'. -/
 @[simp]
 theorem congr_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (m : M) (n : N) :
@@ -1449,7 +1449,7 @@ theorem congr_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (m : M) (n : N) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : LinearEquiv.{u1, u1, 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)) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearEquiv.{u1, u1, u3, 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)) N Q _inst_5 _inst_7 _inst_10 _inst_12) (p : P) (q : Q), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (coeFn.{max (succ (max u4 u5)) (succ (max u2 u3)), max (succ (max u4 u5)) (succ (max u2 u3))} (LinearEquiv.{u1, u1, max u4 u5, 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 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_inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (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.congr._proof_6.{u1} R _inst_1) (TensorProduct.congr._proof_5.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u2 u3, max u4 u5} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) 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 but is expected to have type
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_inst_12 _inst_10) R Q N (MonoidWithZero.toMonoid.{u5} R (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} Q _inst_7) (AddCommMonoid.toAddMonoid.{u2} N _inst_5) (Module.toDistribMulAction.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_12) (Module.toDistribMulAction.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u5, u1, u2, max u2 u1} R Q N (LinearEquiv.{u5, u5, u1, u2} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) Q N _inst_7 _inst_5 _inst_12 _inst_10) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_5 _inst_12 _inst_10 (SemilinearEquivClass.instSemilinearMapClass.{u5, u5, u1, u2, max u2 u1} R R Q N (LinearEquiv.{u5, u5, u1, u2} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) Q N _inst_7 _inst_5 _inst_12 _inst_10) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_5 _inst_12 _inst_10 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u5, u5, u1, u2} R R Q N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_5 _inst_12 _inst_10 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))))) (LinearEquiv.symm.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) g) q))
+  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearEquiv.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R 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u5, u3, u4} (LinearEquiv.{u5, u5, u3, u4} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) P M _inst_6 _inst_4 _inst_11 _inst_9) R P M (SMulZeroClass.toSMul.{u5, u3} R P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_6)) (DistribSMul.toSMulZeroClass.{u5, u3} R P (AddMonoid.toAddZeroClass.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_6)) (DistribMulAction.toDistribSMul.{u5, u3} R P (MonoidWithZero.toMonoid.{u5} R (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} P _inst_6) (Module.toDistribMulAction.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6 _inst_11)))) (SMulZeroClass.toSMul.{u5, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (DistribSMul.toSMulZeroClass.{u5, u4} R M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (DistribMulAction.toDistribSMul.{u5, u4} R M (MonoidWithZero.toMonoid.{u5} R (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} M _inst_4) (Module.toDistribMulAction.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_9)))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u5, u3, u4} (LinearEquiv.{u5, u5, u3, u4} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) P M _inst_6 _inst_4 _inst_11 _inst_9) R P M (MonoidWithZero.toMonoid.{u5} R (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} P _inst_6) (AddCommMonoid.toAddMonoid.{u4} M _inst_4) (Module.toDistribMulAction.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6 _inst_11) (Module.toDistribMulAction.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_9) (SemilinearMapClass.distribMulActionHomClass.{u5, u3, u4, max u4 u3} R P M (LinearEquiv.{u5, u5, u3, u4} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6 _inst_4 _inst_11 _inst_9 (SemilinearEquivClass.instSemilinearMapClass.{u5, u5, u3, u4, max u4 u3} R R P M (LinearEquiv.{u5, u5, u3, u4} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6 _inst_4 _inst_11 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u5, u5, u3, u4} R R P M (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6 _inst_4 _inst_11 _inst_9 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))))) (LinearEquiv.symm.{u5, u5, u4, u3} R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) f) p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearEquiv.{u5, u5, u1, u2} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) Q N _inst_7 _inst_5 _inst_12 _inst_10) Q (fun (_x : Q) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Q) => N) _x) (SMulHomClass.toFunLike.{max u2 u1, u5, u1, u2} (LinearEquiv.{u5, u5, u1, u2} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) Q N _inst_7 _inst_5 _inst_12 _inst_10) R Q N (SMulZeroClass.toSMul.{u5, u1} R Q (AddMonoid.toZero.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q _inst_7)) (DistribSMul.toSMulZeroClass.{u5, u1} R Q (AddMonoid.toAddZeroClass.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q _inst_7)) (DistribMulAction.toDistribSMul.{u5, u1} R Q (MonoidWithZero.toMonoid.{u5} R (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} Q _inst_7) (Module.toDistribMulAction.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_12)))) (SMulZeroClass.toSMul.{u5, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (DistribSMul.toSMulZeroClass.{u5, u2} R N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (DistribMulAction.toDistribSMul.{u5, u2} R N (MonoidWithZero.toMonoid.{u5} R (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} N _inst_5) (Module.toDistribMulAction.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_10)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u5, u1, u2} (LinearEquiv.{u5, u5, u1, u2} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) Q N _inst_7 _inst_5 _inst_12 _inst_10) R Q N (MonoidWithZero.toMonoid.{u5} R (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} Q _inst_7) (AddCommMonoid.toAddMonoid.{u2} N _inst_5) (Module.toDistribMulAction.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_12) (Module.toDistribMulAction.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u5, u1, u2, max u2 u1} R Q N (LinearEquiv.{u5, u5, u1, u2} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) Q N _inst_7 _inst_5 _inst_12 _inst_10) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_5 _inst_12 _inst_10 (SemilinearEquivClass.instSemilinearMapClass.{u5, u5, u1, u2, max u2 u1} R R Q N (LinearEquiv.{u5, u5, u1, u2} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) Q N _inst_7 _inst_5 _inst_12 _inst_10) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_5 _inst_12 _inst_10 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u5, u5, u1, u2} R R Q N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_5 _inst_12 _inst_10 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))))) (LinearEquiv.symm.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (RingHomInvPair.ids.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) g) q))
 Case conversion may be inaccurate. Consider using '#align tensor_product.congr_symm_tmul TensorProduct.congr_symm_tmulₓ'. -/
 @[simp]
 theorem congr_symm_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (p : P) (q : Q) :
@@ -1479,7 +1479,7 @@ variable {M N P Q}
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (m : M) (n : N) (p : P), Eq.{succ (max u3 u2 u4)} (TensorProduct.{u1, u3, max u2 u4} R _inst_1 N (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) _inst_10 (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (coeFn.{max (succ (max u2 u3 u4)) (succ (max u3 u2 u4)), max (succ (max u2 u3 u4)) (succ (max u3 u2 u4))} (LinearEquiv.{u1, u1, max u2 u3 u4, max u3 u2 u4} R R 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align tensor_product.left_comm_tmul TensorProduct.leftComm_tmulₓ'. -/
 @[simp]
 theorem leftComm_tmul (m : M) (n : N) (p : P) : leftComm R M N P (m ⊗ₜ (n ⊗ₜ p)) = n ⊗ₜ (m ⊗ₜ p) :=
@@ -1490,7 +1490,7 @@ theorem leftComm_tmul (m : M) (n : N) (p : P) : leftComm R M N P (m ⊗ₜ (n 
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (m : M) (n : N) (p : P), Eq.{succ (max u2 u3 u4)} (TensorProduct.{u1, u2, max u3 u4} R _inst_1 M (TensorProduct.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_9 (TensorProduct.module.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11)) (coeFn.{max (succ (max u3 u2 u4)) (succ (max u2 u3 u4)), max (succ (max u3 u2 u4)) (succ (max u2 u3 u4))} (LinearEquiv.{u1, u1, max u3 u2 u4, max u2 u3 u4} R R 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align tensor_product.left_comm_symm_tmul TensorProduct.leftComm_symm_tmulₓ'. -/
 @[simp]
 theorem leftComm_symm_tmul (m : M) (n : N) (p : P) :
@@ -1529,7 +1529,7 @@ variable {M N P Q}
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (m : M) (n : N) (p : P) (q : Q), Eq.{succ (max (max u2 u4) u3 u5)} (TensorProduct.{u1, max u2 u4, max u3 u5} R _inst_1 (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.{u1, u3, u5} R _inst_1 N Q _inst_5 _inst_7 _inst_10 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u3, u5} R _inst_1 N Q 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 Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_comm_tmul TensorProduct.tensorTensorTensorComm_tmulₓ'. -/
 @[simp]
 theorem tensorTensorTensorComm_tmul (m : M) (n : N) (p : P) (q : Q) :
@@ -1576,7 +1576,7 @@ variable {M N P Q}
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (m : M) (n : N) (p : P) (q : Q), Eq.{succ (max (max u2 u3 u4) u5)} (TensorProduct.{u1, max u2 u3 u4, u5} R _inst_1 (TensorProduct.{u1, u2, max u3 u4} R _inst_1 M (TensorProduct.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_9 (TensorProduct.module.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11)) Q (TensorProduct.addCommMonoid.{u1, u2, max u3 u4} R _inst_1 M (TensorProduct.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_9 (TensorProduct.module.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11)) _inst_7 (TensorProduct.module.{u1, u2, max u3 u4} R _inst_1 M (TensorProduct.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_9 (TensorProduct.module.{u1, u3, u4} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11)) _inst_12) (coeFn.{max (succ (max (max u2 u3) u4 u5)) (succ (max (max u2 u3 u4) u5)), max (succ (max (max u2 u3) u4 u5)) (succ (max (max u2 u3 u4) u5))} (LinearEquiv.{u1, u1, max (max u2 u3) u4 u5, max (max u2 u3 u4) u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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N P _inst_5 _inst_6 _inst_10 _inst_11) m (TensorProduct.tmul.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11 n p)) q)
 Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_assoc_tmul TensorProduct.tensorTensorTensorAssoc_tmulₓ'. -/
 @[simp]
 theorem tensorTensorTensorAssoc_tmul (m : M) (n : N) (p : P) (q : Q) :
@@ -1588,7 +1588,7 @@ theorem tensorTensorTensorAssoc_tmul (m : M) (n : N) (p : P) (q : Q) :
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (m : M) (n : N) (p : P) (q : Q), Eq.{succ (max (max u2 u3) u4 u5)} (TensorProduct.{u1, max u2 u3, max u4 u5} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q 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_inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12)) (TensorProduct.tmul.{u1, max (max u5 u4) u3, u2} R _inst_1 (TensorProduct.{u1, u5, max u3 u4} R _inst_1 M (TensorProduct.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_9 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11)) Q (TensorProduct.addCommMonoid.{u1, u5, max u4 u3} R _inst_1 M (TensorProduct.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_9 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11)) _inst_7 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u5, max u4 u3} R _inst_1 M (TensorProduct.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_9 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11)) _inst_12 (TensorProduct.tmul.{u1, u5, max u4 u3} R _inst_1 M (TensorProduct.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_9 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11) m (TensorProduct.tmul.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11 n p)) q)) (TensorProduct.tmul.{u1, max u4 u5, max u2 u3} R _inst_1 (TensorProduct.{u1, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.tmul.{u1, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12 p q))
 Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_assoc_symm_tmul TensorProduct.tensorTensorTensorAssoc_symm_tmulₓ'. -/
 @[simp]
 theorem tensorTensorTensorAssoc_symm_tmul (m : M) (n : N) (p : P) (q : Q) :
@@ -1630,7 +1630,7 @@ variable (g : P →ₗ[R] Q) (f : N →ₗ[R] P)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{succ (max u2 u4)} (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (coeFn.{max (succ (max u2 u3)) (succ (max u2 u4)), max (succ (max u2 u3)) (succ (max u2 u4))} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (fun (_x : LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) => (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, max u2 u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.lTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11 m (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f n))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u1 u4, max u3 u4} 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))) (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.lTensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u2, u4, u3} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) n) _inst_4 _inst_6 _inst_9 _inst_11 m (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u1 u4, max u3 u4} 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))) (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.lTensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u2, u4, u3} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) n) _inst_4 _inst_6 _inst_9 _inst_11 m (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n))
 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_tmul LinearMap.lTensor_tmulₓ'. -/
 @[simp]
 theorem lTensor_tmul (m : M) (n : N) : f.lTensor M (m ⊗ₜ n) = m ⊗ₜ f n :=
@@ -1641,7 +1641,7 @@ theorem lTensor_tmul (m : M) (n : N) : f.lTensor M (m ⊗ₜ n) = m ⊗ₜ f n :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{succ (max u4 u2)} (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (coeFn.{max (succ (max u3 u2)) (succ (max u4 u2)), max (succ (max u3 u2)) (succ (max u4 u2))} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (fun (_x : LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) => (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) -> (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u2, max u4 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.rTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (TensorProduct.tmul.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f n) m)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u4 u1, max u4 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))) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.rTensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (TensorProduct.tmul.{u2, u3, u4} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) n) M _inst_6 _inst_4 _inst_11 _inst_9 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n) m)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u4 u1, max u4 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))) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.rTensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (TensorProduct.tmul.{u2, u3, u4} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) n) M _inst_6 _inst_4 _inst_11 _inst_9 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n) m)
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_tmul LinearMap.rTensor_tmulₓ'. -/
 @[simp]
 theorem rTensor_tmul (m : M) (n : N) : f.rTensor M (n ⊗ₜ m) = f n ⊗ₜ m :=
@@ -1694,7 +1694,7 @@ def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], Eq.{max (max (succ u3) (succ u4)) (succ (max u2 u3)) (succ (max u2 u4))} ((fun (_x : LinearMap.{u1, u1, max u3 u4, max (max u2 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))) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align linear_map.coe_ltensor_hom LinearMap.coe_lTensorHomₓ'. -/
 @[simp]
 theorem coe_lTensorHom : (lTensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R] M ⊗[R] P) = lTensor M :=
@@ -1705,7 +1705,7 @@ theorem coe_lTensorHom : (lTensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R
 lean 3 declaration is
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 but is expected to have type
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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.rTensorHom.{u1, u4, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11)) (LinearMap.rTensor.{u1, u4, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11)
 Case conversion may be inaccurate. Consider using '#align linear_map.coe_rtensor_hom LinearMap.coe_rTensorHomₓ'. -/
 @[simp]
 theorem coe_rTensorHom : (rTensorHom M : (N →ₗ[R] P) → N ⊗[R] M →ₗ[R] P ⊗[R] M) = rTensor M :=
@@ -1794,7 +1794,7 @@ theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) :
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_apply LinearMap.lTensor_comp_applyₓ'. -/
 theorem lTensor_comp_apply (x : M ⊗[R] N) :
     (g.comp f).lTensor M x = (g.lTensor M) ((f.lTensor M) x) := by rw [ltensor_comp, coe_comp]
@@ -1816,7 +1816,7 @@ theorem rTensor_comp : (g.comp f).rTensor M = (g.rTensor M).comp (f.rTensor M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (g : 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))) P Q _inst_6 _inst_7 _inst_11 _inst_12) (f : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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+  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] (M : Type.{u3}) {N : Type.{u4}} {P : Type.{u1}} {Q : Type.{u2}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_6 : AddCommMonoid.{u1} P] [_inst_7 : AddCommMonoid.{u2} Q] [_inst_9 : Module.{u5, u3} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u4} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u1} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u2} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (g : LinearMap.{u5, u5, u1, u2} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) P Q _inst_6 _inst_7 _inst_11 _inst_12) (f : LinearMap.{u5, u5, u4, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_apply LinearMap.rTensor_comp_applyₓ'. -/
 theorem rTensor_comp_apply (x : N ⊗[R] M) :
     (g.comp f).rTensor M x = (g.rTensor M) ((f.rTensor M) x) := by rw [rtensor_comp, coe_comp]
@@ -1859,7 +1859,7 @@ theorem lTensor_id : (id : N →ₗ[R] N).lTensor M = id :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) (N : Type.{u3}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (x : TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (fun (_x : 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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) => (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, max u2 u3} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.lTensor.{u1, u2, u3, u3} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)) x) x
 but is expected to have type
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+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Type.{u2}) (N : Type.{u1}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (x : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) x) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u1, max u2 u1} R R (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.lTensor.{u3, u2, u1, u1} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10)) x) x
 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_id_apply LinearMap.lTensor_id_applyₓ'. -/
 -- `simp` can prove this.
 theorem lTensor_id_apply (x : M ⊗[R] N) : (LinearMap.id : N →ₗ[R] N).lTensor M x = x := by
@@ -1881,7 +1881,7 @@ theorem rTensor_id : (id : N →ₗ[R] N).rTensor M = id :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) (N : Type.{u3}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (x : TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9), Eq.{succ (max u3 u2)} (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (coeFn.{succ (max u3 u2), succ (max u3 u2)} (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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (fun (_x : 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) => (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) -> (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u2, max u3 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.rTensor.{u1, u2, u3, u3} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)) x) x
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Type.{u1}) (N : Type.{u2}) [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (x : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) x) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u1 u2, max u1 u2} R R (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.rTensor.{u3, u1, u2, u2} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10)) x) x
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Type.{u1}) (N : Type.{u2}) [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (x : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) x) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u1 u2, max u1 u2} R R (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.rTensor.{u3, u1, u2, u2} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10)) x) x
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_id_apply LinearMap.rTensor_id_applyₓ'. -/
 -- `simp` can prove this.
 theorem rTensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rTensor M x = x := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -1346,18 +1346,18 @@ def mapBilinear : (M →ₗ[R] P) →ₗ[R] (N →ₗ[R] Q) →ₗ[R] M ⊗[R] N
   LinearMap.mk₂ R map map_add_left map_smul_left map_add_right map_smul_right
 #align tensor_product.map_bilinear TensorProduct.mapBilinear
 
-#print TensorProduct.ltensorHomToHomLtensor /-
+#print TensorProduct.lTensorHomToHomLTensor /-
 /-- The canonical linear map from `P ⊗[R] (M →ₗ[R] Q)` to `(M →ₗ[R] P ⊗[R] Q)` -/
-def ltensorHomToHomLtensor : P ⊗[R] (M →ₗ[R] Q) →ₗ[R] M →ₗ[R] P ⊗[R] Q :=
+def lTensorHomToHomLTensor : P ⊗[R] (M →ₗ[R] Q) →ₗ[R] M →ₗ[R] P ⊗[R] Q :=
   TensorProduct.lift (llcomp R M Q _ ∘ₗ mk R P Q)
-#align tensor_product.ltensor_hom_to_hom_ltensor TensorProduct.ltensorHomToHomLtensor
+#align tensor_product.ltensor_hom_to_hom_ltensor TensorProduct.lTensorHomToHomLTensor
 -/
 
-#print TensorProduct.rtensorHomToHomRtensor /-
+#print TensorProduct.rTensorHomToHomRTensor /-
 /-- The canonical linear map from `(M →ₗ[R] P) ⊗[R] Q` to `(M →ₗ[R] P ⊗[R] Q)` -/
-def rtensorHomToHomRtensor : (M →ₗ[R] P) ⊗[R] Q →ₗ[R] M →ₗ[R] P ⊗[R] Q :=
+def rTensorHomToHomRTensor : (M →ₗ[R] P) ⊗[R] Q →ₗ[R] M →ₗ[R] P ⊗[R] Q :=
   TensorProduct.lift (llcomp R M P _ ∘ₗ (mk R P Q).flip).flip
-#align tensor_product.rtensor_hom_to_hom_rtensor TensorProduct.rtensorHomToHomRtensor
+#align tensor_product.rtensor_hom_to_hom_rtensor TensorProduct.rTensorHomToHomRTensor
 -/
 
 #print TensorProduct.homTensorHomMap /-
@@ -1381,29 +1381,29 @@ theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear
   rfl
 #align tensor_product.map_bilinear_apply TensorProduct.mapBilinear_apply
 
-/- warning: tensor_product.ltensor_hom_to_hom_ltensor_apply -> TensorProduct.ltensorHomToHomLtensor_apply is a dubious translation:
+/- warning: tensor_product.ltensor_hom_to_hom_ltensor_apply -> TensorProduct.lTensorHomToHomLTensor_apply is a dubious translation:
 lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.lTensorHomToHomLTensor_applyₓ'. -/
 @[simp]
-theorem ltensorHomToHomLtensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
-    ltensorHomToHomLtensor R M P Q (p ⊗ₜ f) m = p ⊗ₜ f m :=
+theorem lTensorHomToHomLTensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
+    lTensorHomToHomLTensor R M P Q (p ⊗ₜ f) m = p ⊗ₜ f m :=
   rfl
-#align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.ltensorHomToHomLtensor_apply
+#align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.lTensorHomToHomLTensor_apply
 
-/- warning: tensor_product.rtensor_hom_to_hom_rtensor_apply -> TensorProduct.rtensorHomToHomRtensor_apply is a dubious translation:
+/- warning: tensor_product.rtensor_hom_to_hom_rtensor_apply -> TensorProduct.rTensorHomToHomRTensor_apply is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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_inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u4, u2, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12))) (Module.toMulActionWithZero.{u4, max u2 u1} R (TensorProduct.{u4, u2, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (TensorProduct.rTensorHomToHomRTensor.{u4, u3, u2, u1} R _inst_1 M P Q _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12) (TensorProduct.tmul.{u4, max u3 u2, u1} R _inst_1 (LinearMap.{u4, u4, u3, u2} 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))) M P _inst_4 _inst_6 _inst_9 _inst_11) Q (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_7 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) _inst_12 f q)) m) (TensorProduct.tmul.{u4, u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => P) m) Q _inst_6 _inst_7 _inst_11 _inst_12 (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} 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))) M P _inst_4 _inst_6 _inst_9 _inst_11) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) q)
+Case conversion may be inaccurate. Consider using '#align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rTensorHomToHomRTensor_applyₓ'. -/
 @[simp]
-theorem rtensorHomToHomRtensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
-    rtensorHomToHomRtensor R M P Q (f ⊗ₜ q) m = f m ⊗ₜ q :=
+theorem rTensorHomToHomRTensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
+    rTensorHomToHomRTensor R M P Q (f ⊗ₜ q) m = f m ⊗ₜ q :=
   rfl
-#align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rtensorHomToHomRtensor_apply
+#align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rTensorHomToHomRTensor_apply
 
 /- warning: tensor_product.hom_tensor_hom_map_apply -> TensorProduct.homTensorHomMap_apply is a dubious translation:
 lean 3 declaration is
@@ -1602,66 +1602,66 @@ namespace LinearMap
 
 variable {R} (M) {N P Q}
 
-/- warning: linear_map.ltensor -> LinearMap.ltensor is a dubious translation:
+/- warning: linear_map.ltensor -> LinearMap.lTensor is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) -> (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) -> (LinearMap.{u1, u1, max u3 u2, max u4 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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11))
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor LinearMap.ltensorₓ'. -/
+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor LinearMap.lTensorₓ'. -/
 /-- `ltensor M f : M ⊗ N →ₗ M ⊗ P` is the natural linear map induced by `f : N →ₗ P`. -/
-def ltensor (f : N →ₗ[R] P) : M ⊗ N →ₗ[R] M ⊗ P :=
+def lTensor (f : N →ₗ[R] P) : M ⊗ N →ₗ[R] M ⊗ P :=
   TensorProduct.map id f
-#align linear_map.ltensor LinearMap.ltensor
+#align linear_map.ltensor LinearMap.lTensor
 
-/- warning: linear_map.rtensor -> LinearMap.rtensor is a dubious translation:
+/- warning: linear_map.rtensor -> LinearMap.rTensor is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) -> (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) -> (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9))
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor LinearMap.rtensorₓ'. -/
+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor LinearMap.rTensorₓ'. -/
 /-- `rtensor f M : N₁ ⊗ M →ₗ N₂ ⊗ M` is the natural linear map induced by `f : N₁ →ₗ N₂`. -/
-def rtensor (f : N →ₗ[R] P) : N ⊗ M →ₗ[R] P ⊗ M :=
+def rTensor (f : N →ₗ[R] P) : N ⊗ M →ₗ[R] P ⊗ M :=
   TensorProduct.map f id
-#align linear_map.rtensor LinearMap.rtensor
+#align linear_map.rtensor LinearMap.rTensor
 
 variable (g : P →ₗ[R] Q) (f : N →ₗ[R] P)
 
-/- warning: linear_map.ltensor_tmul -> LinearMap.ltensor_tmul is a dubious translation:
+/- warning: linear_map.ltensor_tmul -> LinearMap.lTensor_tmul is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{succ (max u2 u4)} (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (coeFn.{max (succ (max u2 u3)) (succ (max u2 u4)), max (succ (max u2 u3)) (succ (max u2 u4))} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (fun (_x : LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) => (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, max u2 u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.lTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11 m (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f n))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_tmul LinearMap.ltensor_tmulₓ'. -/
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_tmul LinearMap.lTensor_tmulₓ'. -/
 @[simp]
-theorem ltensor_tmul (m : M) (n : N) : f.ltensor M (m ⊗ₜ n) = m ⊗ₜ f n :=
+theorem lTensor_tmul (m : M) (n : N) : f.lTensor M (m ⊗ₜ n) = m ⊗ₜ f n :=
   rfl
-#align linear_map.ltensor_tmul LinearMap.ltensor_tmul
+#align linear_map.ltensor_tmul LinearMap.lTensor_tmul
 
-/- warning: linear_map.rtensor_tmul -> LinearMap.rtensor_tmul is a dubious translation:
+/- warning: linear_map.rtensor_tmul -> LinearMap.rTensor_tmul is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{succ (max u4 u2)} (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (coeFn.{max (succ (max u3 u2)) (succ (max u4 u2)), max (succ (max u3 u2)) (succ (max u4 u2))} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (fun (_x : LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) => (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) -> (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u2, max u4 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.rTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (TensorProduct.tmul.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f n) m)
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_tmul LinearMap.rtensor_tmulₓ'. -/
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u4 u1, max u4 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))) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.rTensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (TensorProduct.tmul.{u2, u3, u4} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) n) M _inst_6 _inst_4 _inst_11 _inst_9 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n) m)
+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_tmul LinearMap.rTensor_tmulₓ'. -/
 @[simp]
-theorem rtensor_tmul (m : M) (n : N) : f.rtensor M (n ⊗ₜ m) = f n ⊗ₜ m :=
+theorem rTensor_tmul (m : M) (n : N) : f.rTensor M (n ⊗ₜ m) = f n ⊗ₜ m :=
   rfl
-#align linear_map.rtensor_tmul LinearMap.rtensor_tmul
+#align linear_map.rtensor_tmul LinearMap.rTensor_tmul
 
 open TensorProduct
 
 attribute [local ext] TensorProduct.ext
 
-/- warning: linear_map.ltensor_hom -> LinearMap.ltensorHom is a dubious translation:
+/- warning: linear_map.ltensor_hom -> LinearMap.lTensorHom is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], LinearMap.{u1, u1, max u3 u4, max (max u2 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))) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, max u2 u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_11 (LinearMap.lTensorHom._proof_1.{u1, u4} R _inst_1 P _inst_6 _inst_11)) (LinearMap.module.{u1, u1, u1, max u2 u3, max u2 u4} R R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (LinearMap.lTensorHom._proof_2.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], LinearMap.{u1, u1, max u4 u3, max (max u4 u2) 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))) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.{u1, u1, max u3 u2, max u4 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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, max u2 u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, max u2 u4} R R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (smulCommClass_self.{u1, max u2 u4} R (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, max u2 u4} R (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{max u2 u4} (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (AddCommMonoid.toAddMonoid.{max u2 u4} (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11))) (Module.toMulActionWithZero.{u1, max u2 u4} R (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)))))
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_hom LinearMap.ltensorHomₓ'. -/
+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_hom LinearMap.lTensorHomₓ'. -/
 /-- `ltensor_hom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
-def ltensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
+def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
     where
-  toFun := ltensor M
+  toFun := lTensor M
   map_add' f g := by
     ext (x y)
     simp only [compr₂_apply, mk_apply, add_apply, ltensor_tmul, tmul_add]
@@ -1669,18 +1669,18 @@ def ltensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
     dsimp
     ext (x y)
     simp only [compr₂_apply, mk_apply, tmul_smul, smul_apply, ltensor_tmul]
-#align linear_map.ltensor_hom LinearMap.ltensorHom
+#align linear_map.ltensor_hom LinearMap.lTensorHom
 
-/- warning: linear_map.rtensor_hom -> LinearMap.rtensorHom is a dubious translation:
+/- warning: linear_map.rtensor_hom -> LinearMap.rTensorHom is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], LinearMap.{u1, u1, max u3 u4, max (max u3 u2) u4 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))) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u3 u2, max u4 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_11 (LinearMap.rtensorHom._proof_1.{u1, u4} R _inst_1 P _inst_6 _inst_11)) (LinearMap.module.{u1, u1, u1, max u3 u2, max u4 u2} R R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (LinearMap.rtensorHom._proof_2.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], LinearMap.{u1, u1, max u3 u4, max (max u3 u2) u4 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))) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u3 u2, max u4 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_11 (LinearMap.rTensorHom._proof_1.{u1, u4} R _inst_1 P _inst_6 _inst_11)) (LinearMap.module.{u1, u1, u1, max u3 u2, max u4 u2} R R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (LinearMap.rTensorHom._proof_2.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], LinearMap.{u1, u1, max u4 u3, max (max u2 u4) 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))) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, max u2 u4} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, max u2 u4} R R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (smulCommClass_self.{u1, max u2 u4} R (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, max u2 u4} R (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{max u2 u4} (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (AddCommMonoid.toAddMonoid.{max u2 u4} (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9))) (Module.toMulActionWithZero.{u1, max u2 u4} R (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)))))
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_hom LinearMap.rtensorHomₓ'. -/
+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_hom LinearMap.rTensorHomₓ'. -/
 /-- `rtensor_hom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
-def rtensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
+def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
     where
-  toFun f := f.rtensor M
+  toFun f := f.rTensor M
   map_add' f g := by
     ext (x y)
     simp only [compr₂_apply, mk_apply, add_apply, rtensor_tmul, add_tmul]
@@ -1688,307 +1688,307 @@ def rtensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
     dsimp
     ext (x y)
     simp only [compr₂_apply, mk_apply, smul_tmul, tmul_smul, smul_apply, rtensor_tmul]
-#align linear_map.rtensor_hom LinearMap.rtensorHom
+#align linear_map.rtensor_hom LinearMap.rTensorHom
 
-/- warning: linear_map.coe_ltensor_hom -> LinearMap.coe_ltensorHom is a dubious translation:
+/- warning: linear_map.coe_ltensor_hom -> LinearMap.coe_lTensorHom is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_map.coe_ltensor_hom LinearMap.coe_lTensorHomₓ'. -/
 @[simp]
-theorem coe_ltensorHom : (ltensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R] M ⊗[R] P) = ltensor M :=
+theorem coe_lTensorHom : (lTensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R] M ⊗[R] P) = lTensor M :=
   rfl
-#align linear_map.coe_ltensor_hom LinearMap.coe_ltensorHom
+#align linear_map.coe_ltensor_hom LinearMap.coe_lTensorHom
 
-/- warning: linear_map.coe_rtensor_hom -> LinearMap.coe_rtensorHom is a dubious translation:
+/- warning: linear_map.coe_rtensor_hom -> LinearMap.coe_rTensorHom is a dubious translation:
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 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.coe_rtensor_hom LinearMap.coe_rtensorHomₓ'. -/
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+Case conversion may be inaccurate. Consider using '#align linear_map.coe_rtensor_hom LinearMap.coe_rTensorHomₓ'. -/
 @[simp]
-theorem coe_rtensorHom : (rtensorHom M : (N →ₗ[R] P) → N ⊗[R] M →ₗ[R] P ⊗[R] M) = rtensor M :=
+theorem coe_rTensorHom : (rTensorHom M : (N →ₗ[R] P) → N ⊗[R] M →ₗ[R] P ⊗[R] M) = rTensor M :=
   rfl
-#align linear_map.coe_rtensor_hom LinearMap.coe_rtensorHom
+#align linear_map.coe_rtensor_hom LinearMap.coe_rTensorHom
 
-/- warning: linear_map.ltensor_add -> LinearMap.ltensor_add is a dubious translation:
+/- warning: linear_map.ltensor_add -> LinearMap.lTensor_add is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (g : 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (succ (max u2 u3)) (succ (max u2 u4))} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.lTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 (HAdd.hAdd.{max u3 u4, max u3 u4, max u3 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (instHAdd.{max u3 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.hasAdd.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) f g)) (HAdd.hAdd.{max (max u2 u3) u2 u4, max (max u2 u3) u2 u4, max (max u2 u3) u2 u4} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) 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_inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (instHAdd.{max (max u2 u3) u2 u4} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.hasAdd.{u1, u1, max u2 u3, max u2 u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.lTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (LinearMap.lTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 g))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] (M : Type.{u1}) {N : Type.{u3}} {P : Type.{u2}} [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u2} P] [_inst_9 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_11 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6] (f : LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (g : LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (max (succ u1) (succ u3)) (succ 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(CommSemiring.toSemiring.{u4} R _inst_1))) (TensorProduct.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.instAddLinearMap.{u4, u4, max u1 u3, max u1 u2} R R (TensorProduct.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.ltensor.{u4, u1, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (LinearMap.ltensor.{u4, u1, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 g))
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_add LinearMap.ltensor_addₓ'. -/
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_add LinearMap.lTensor_addₓ'. -/
 @[simp]
-theorem ltensor_add (f g : N →ₗ[R] P) : (f + g).ltensor M = f.ltensor M + g.ltensor M :=
-  (ltensorHom M).map_add f g
-#align linear_map.ltensor_add LinearMap.ltensor_add
+theorem lTensor_add (f g : N →ₗ[R] P) : (f + g).lTensor M = f.lTensor M + g.lTensor M :=
+  (lTensorHom M).map_add f g
+#align linear_map.ltensor_add LinearMap.lTensor_add
 
-/- warning: linear_map.rtensor_add -> LinearMap.rtensor_add is a dubious translation:
+/- warning: linear_map.rtensor_add -> LinearMap.rTensor_add is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (g : 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (succ (max u3 u2)) (succ (max u4 u2))} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.rTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 (HAdd.hAdd.{max u3 u4, max u3 u4, max u3 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (instHAdd.{max u3 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.hasAdd.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) f g)) (HAdd.hAdd.{max (max u3 u2) u4 u2, max (max u3 u2) u4 u2, max (max u3 u2) u4 u2} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) 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_inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (instHAdd.{max (max u3 u2) u4 u2} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.hasAdd.{u1, u1, max u3 u2, max u4 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.rTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (LinearMap.rTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 g))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] (M : Type.{u1}) {N : Type.{u3}} {P : Type.{u2}} [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u2} P] [_inst_9 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_11 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6] (f : LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (g : LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (max (succ u1) (succ u3)) (succ 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(CommSemiring.toSemiring.{u4} R _inst_1))) (TensorProduct.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.instAddLinearMap.{u4, u4, max u1 u3, max u1 u2} R R (TensorProduct.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.rtensor.{u4, u1, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (LinearMap.rtensor.{u4, u1, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 g))
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_add LinearMap.rtensor_addₓ'. -/
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] (M : Type.{u1}) {N : Type.{u3}} {P : Type.{u2}} [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u2} P] [_inst_9 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_11 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6] (f : LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (g : LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (max (succ u1) (succ u3)) (succ 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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_add LinearMap.rTensor_addₓ'. -/
 @[simp]
-theorem rtensor_add (f g : N →ₗ[R] P) : (f + g).rtensor M = f.rtensor M + g.rtensor M :=
-  (rtensorHom M).map_add f g
-#align linear_map.rtensor_add LinearMap.rtensor_add
+theorem rTensor_add (f g : N →ₗ[R] P) : (f + g).rTensor M = f.rTensor M + g.rTensor M :=
+  (rTensorHom M).map_add f g
+#align linear_map.rtensor_add LinearMap.rTensor_add
 
-/- warning: linear_map.ltensor_zero -> LinearMap.ltensor_zero is a dubious translation:
+/- warning: linear_map.ltensor_zero -> LinearMap.lTensor_zero is a dubious translation:
 lean 3 declaration is
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(CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u4}) {N : Type.{u3}} {P : Type.{u2}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u2} P] [_inst_9 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u1, u1, max u3 u4, 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))) (TensorProduct.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.ltensor.{u1, u4, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 (OfNat.ofNat.{max u3 u2} (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) 0 (Zero.toOfNat0.{max u3 u2} (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.instZeroLinearMap.{u1, u1, u3, u2} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (OfNat.ofNat.{max (max u4 u3) u2} (LinearMap.{u1, u1, max u3 u4, 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))) (TensorProduct.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) 0 (Zero.toOfNat0.{max (max u4 u3) u2} (LinearMap.{u1, u1, max u3 u4, 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))) (TensorProduct.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.instZeroLinearMap.{u1, u1, max u4 u3, max u4 u2} R R (TensorProduct.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_zero LinearMap.ltensor_zeroₓ'. -/
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u4}) {N : Type.{u3}} {P : Type.{u2}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u2} P] [_inst_9 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u1, u1, max u3 u4, 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))) (TensorProduct.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.lTensor.{u1, u4, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 (OfNat.ofNat.{max u3 u2} (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) 0 (Zero.toOfNat0.{max u3 u2} (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.instZeroLinearMap.{u1, u1, u3, u2} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (OfNat.ofNat.{max (max u4 u3) u2} (LinearMap.{u1, u1, max u3 u4, 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))) (TensorProduct.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) 0 (Zero.toOfNat0.{max (max u4 u3) u2} (LinearMap.{u1, u1, max u3 u4, 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))) (TensorProduct.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.instZeroLinearMap.{u1, u1, max u4 u3, max u4 u2} R R (TensorProduct.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_zero LinearMap.lTensor_zeroₓ'. -/
 @[simp]
-theorem ltensor_zero : ltensor M (0 : N →ₗ[R] P) = 0 :=
-  (ltensorHom M).map_zero
-#align linear_map.ltensor_zero LinearMap.ltensor_zero
+theorem lTensor_zero : lTensor M (0 : N →ₗ[R] P) = 0 :=
+  (lTensorHom M).map_zero
+#align linear_map.ltensor_zero LinearMap.lTensor_zero
 
-/- warning: linear_map.rtensor_zero -> LinearMap.rtensor_zero is a dubious translation:
+/- warning: linear_map.rtensor_zero -> LinearMap.rTensor_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], Eq.{max (succ (max u3 u2)) (succ (max u4 u2))} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.rtensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 (OfNat.ofNat.{max u3 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) 0 (OfNat.mk.{max u3 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) 0 (Zero.zero.{max u3 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.hasZero.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (OfNat.ofNat.{max (max u3 u2) u4 u2} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) 0 (OfNat.mk.{max (max u3 u2) u4 u2} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) 0 (Zero.zero.{max (max u3 u2) u4 u2} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.hasZero.{u1, u1, max u3 u2, max u4 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], Eq.{max (succ (max u3 u2)) (succ (max u4 u2))} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.rTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 (OfNat.ofNat.{max u3 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) 0 (OfNat.mk.{max u3 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) 0 (Zero.zero.{max u3 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.hasZero.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (OfNat.ofNat.{max (max u3 u2) u4 u2} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) 0 (OfNat.mk.{max (max u3 u2) u4 u2} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) 0 (Zero.zero.{max (max u3 u2) u4 u2} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.hasZero.{u1, u1, max u3 u2, max u4 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_zero LinearMap.rtensor_zeroₓ'. -/
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_zero LinearMap.rTensor_zeroₓ'. -/
 @[simp]
-theorem rtensor_zero : rtensor M (0 : N →ₗ[R] P) = 0 :=
-  (rtensorHom M).map_zero
-#align linear_map.rtensor_zero LinearMap.rtensor_zero
+theorem rTensor_zero : rTensor M (0 : N →ₗ[R] P) = 0 :=
+  (rTensorHom M).map_zero
+#align linear_map.rtensor_zero LinearMap.rTensor_zero
 
-/- warning: linear_map.ltensor_smul -> LinearMap.ltensor_smul is a dubious translation:
+/- warning: linear_map.ltensor_smul -> LinearMap.lTensor_smul is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (r : R) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (succ (max u2 u3)) (succ (max u2 u4))} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.lTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.hasSmul.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)))) r f)) (SMul.smul.{u1, max (max u2 u3) u2 u4} R (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.hasSmul.{u1, u1, u1, max u2 u3, max u2 u4} R R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _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))) (TensorProduct.distribMulAction.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (smulCommClass_self.{u1, max u2 u4} R (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, max u2 u4} R (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u2 u4} (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (AddMonoid.toAddZeroClass.{max u2 u4} (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (AddCommMonoid.toAddMonoid.{max u2 u4} (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)))) (Module.toMulActionWithZero.{u1, max u2 u4} R (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11))))) r (LinearMap.lTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] (M : Type.{u1}) {N : Type.{u3}} {P : Type.{u2}} [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u2} P] [_inst_9 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_11 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6] (r : R) (f : LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u3 u1, max u2 u1} 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, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.ltensor.{u4, u1, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 (HSMul.hSMul.{u4, max u3 u2, max u3 u2} R (LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (instHSMul.{u4, max u3 u2} R (LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.instSMulLinearMap.{u4, u4, u4, u3, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) r f)) (HSMul.hSMul.{u4, max (max u1 u3) u2, max (max u1 u3) u2} R (LinearMap.{u4, u4, max u3 u1, max u2 u1} 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, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.{u4, u4, max u3 u1, max u2 u1} 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, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (instHSMul.{u4, max (max u1 u3) u2} R (LinearMap.{u4, u4, max u3 u1, max u2 u1} 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, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.instSMulLinearMap.{u4, u4, u4, max u1 u3, max u1 u2} R R R (TensorProduct.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (TensorProduct.instDistribMulActionTensorProductToMonoidToMonoidWithZeroToSemiringToAddMonoidAddCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (smulCommClass_self.{u4, max u1 u2} R (TensorProduct.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, max u1 u2} R (TensorProduct.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{max u1 u2} (TensorProduct.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (AddCommMonoid.toAddMonoid.{max u1 u2} (TensorProduct.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11))) (Module.toMulActionWithZero.{u4, max u1 u2} R (TensorProduct.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u2} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)))))) r (LinearMap.ltensor.{u4, u1, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f))
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_smul LinearMap.ltensor_smulₓ'. -/
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] (M : Type.{u1}) {N : Type.{u3}} {P : Type.{u2}} [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u2} P] [_inst_9 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_11 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6] (r : R) (f : LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u3 u1, max u2 u1} 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))) 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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_smul LinearMap.lTensor_smulₓ'. -/
 @[simp]
-theorem ltensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).ltensor M = r • f.ltensor M :=
-  (ltensorHom M).map_smul r f
-#align linear_map.ltensor_smul LinearMap.ltensor_smul
+theorem lTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).lTensor M = r • f.lTensor M :=
+  (lTensorHom M).map_smul r f
+#align linear_map.ltensor_smul LinearMap.lTensor_smul
 
-/- warning: linear_map.rtensor_smul -> LinearMap.rtensor_smul is a dubious translation:
+/- warning: linear_map.rtensor_smul -> LinearMap.rTensor_smul is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (r : R) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (succ (max u3 u2)) (succ (max u4 u2))} (LinearMap.{u1, u1, max u3 u2, max u4 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))) 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(CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)))) r f)) (SMul.smul.{u1, max (max u3 u2) u4 u2} R (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.hasSmul.{u1, u1, u1, max u3 u2, max u4 u2} R R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _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))) (TensorProduct.distribMulAction.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (smulCommClass_self.{u1, max u4 u2} R (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, max u4 u2} R (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u4 u2} (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (AddMonoid.toAddZeroClass.{max u4 u2} (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (AddCommMonoid.toAddMonoid.{max u4 u2} (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)))) (Module.toMulActionWithZero.{u1, max u4 u2} R (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9))))) r (LinearMap.rTensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] (M : Type.{u1}) {N : Type.{u3}} {P : Type.{u2}} [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u2} P] [_inst_9 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_11 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6] (r : R) (f : LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u1 u3, max u1 u2} 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, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.rtensor.{u4, u1, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 (HSMul.hSMul.{u4, max u3 u2, max u3 u2} R (LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (instHSMul.{u4, max u3 u2} R (LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.instSMulLinearMap.{u4, u4, u4, u3, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) r f)) (HSMul.hSMul.{u4, max (max u1 u3) u2, max (max u1 u3) u2} R (LinearMap.{u4, u4, max u1 u3, max u1 u2} 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, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.{u4, u4, max u1 u3, max u1 u2} 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, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (instHSMul.{u4, max (max u1 u3) u2} R (LinearMap.{u4, u4, max u1 u3, max u1 u2} 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, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.instSMulLinearMap.{u4, u4, u4, max u1 u3, max u1 u2} R R R (TensorProduct.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (TensorProduct.instDistribMulActionTensorProductToMonoidToMonoidWithZeroToSemiringToAddMonoidAddCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (smulCommClass_self.{u4, max u1 u2} R (TensorProduct.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, max u1 u2} R (TensorProduct.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{max u1 u2} (TensorProduct.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (AddCommMonoid.toAddMonoid.{max u1 u2} (TensorProduct.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9))) (Module.toMulActionWithZero.{u4, max u1 u2} R (TensorProduct.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)))))) r (LinearMap.rtensor.{u4, u1, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f))
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_smul LinearMap.rtensor_smulₓ'. -/
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] (M : Type.{u1}) {N : Type.{u3}} {P : Type.{u2}} [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u2} P] [_inst_9 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_11 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6] (r : R) (f : LinearMap.{u4, u4, u3, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u1 u3, max u1 u2} 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))) 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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_smul LinearMap.rTensor_smulₓ'. -/
 @[simp]
-theorem rtensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).rtensor M = r • f.rtensor M :=
-  (rtensorHom M).map_smul r f
-#align linear_map.rtensor_smul LinearMap.rtensor_smul
+theorem rTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).rTensor M = r • f.rTensor M :=
+  (rTensorHom M).map_smul r f
+#align linear_map.rtensor_smul LinearMap.rTensor_smul
 
-/- warning: linear_map.ltensor_comp -> LinearMap.ltensor_comp is a dubious translation:
+/- warning: linear_map.ltensor_comp -> LinearMap.lTensor_comp is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u5}) {N : Type.{u4}} {P : Type.{u1}} {Q : Type.{u3}} [_inst_4 : AddCommMonoid.{u5} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_6 : AddCommMonoid.{u1} P] [_inst_7 : AddCommMonoid.{u3} Q] [_inst_9 : Module.{u2, u5} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u1} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] [_inst_12 : Module.{u2, u3} R Q (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7] (g : 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))) P Q _inst_6 _inst_7 _inst_11 _inst_12) (f : LinearMap.{u2, u2, u4, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (LinearMap.{u2, u2, max u4 u5, max u3 u5} 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))) (TensorProduct.{u2, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u5, u3} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.addCommMonoid.{u2, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u5, u3} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u5, u3} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12)) (LinearMap.ltensor.{u2, u5, u4, u3} R _inst_1 M N Q _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 (LinearMap.comp.{u2, u2, u2, u4, u1, u3} R R R N P Q (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_7 _inst_10 _inst_11 _inst_12 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} 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)))) g f)) (LinearMap.comp.{u2, u2, u2, max u5 u4, max u5 u1, max u5 u3} R R R (TensorProduct.{u2, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u5, u1} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.{u2, u5, u3} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u5, u1} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u2, u5, u3} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u5, u1} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u5, u3} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} 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)))) (LinearMap.ltensor.{u2, u5, u1, u3} R _inst_1 M P Q _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12 g) (LinearMap.ltensor.{u2, u5, u4, u1} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f))
-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp LinearMap.ltensor_compₓ'. -/
-theorem ltensor_comp : (g.comp f).ltensor M = (g.ltensor M).comp (f.ltensor M) :=
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u5}) {N : Type.{u4}} {P : Type.{u1}} {Q : Type.{u3}} [_inst_4 : AddCommMonoid.{u5} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_6 : AddCommMonoid.{u1} P] [_inst_7 : AddCommMonoid.{u3} Q] [_inst_9 : Module.{u2, u5} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u1} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] [_inst_12 : Module.{u2, u3} R Q (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7] (g : 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))) P Q _inst_6 _inst_7 _inst_11 _inst_12) (f : LinearMap.{u2, u2, u4, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (LinearMap.{u2, u2, max u4 u5, max u3 u5} 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))) (TensorProduct.{u2, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u5, u3} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.addCommMonoid.{u2, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u5, u3} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u5, u3} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12)) (LinearMap.lTensor.{u2, u5, u4, u3} R _inst_1 M N Q _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 (LinearMap.comp.{u2, u2, u2, u4, u1, u3} R R R N P Q (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_7 _inst_10 _inst_11 _inst_12 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} 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)))) g f)) (LinearMap.comp.{u2, u2, u2, max u5 u4, max u5 u1, max u5 u3} R R R (TensorProduct.{u2, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u5, u1} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.{u2, u5, u3} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u5, u1} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u2, u5, u3} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u5, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u5, u1} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u5, u3} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} 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)))) (LinearMap.lTensor.{u2, u5, u1, u3} R _inst_1 M P Q _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12 g) (LinearMap.lTensor.{u2, u5, u4, u1} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f))
+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp LinearMap.lTensor_compₓ'. -/
+theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) :=
   by
   ext (m n)
   simp only [compr₂_apply, mk_apply, comp_apply, ltensor_tmul]
-#align linear_map.ltensor_comp LinearMap.ltensor_comp
+#align linear_map.ltensor_comp LinearMap.lTensor_comp
 
-/- warning: linear_map.ltensor_comp_apply -> LinearMap.ltensor_comp_apply is a dubious translation:
+/- warning: linear_map.ltensor_comp_apply -> LinearMap.lTensor_comp_apply is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_apply LinearMap.ltensor_comp_applyₓ'. -/
-theorem ltensor_comp_apply (x : M ⊗[R] N) :
-    (g.comp f).ltensor M x = (g.ltensor M) ((f.ltensor M) x) := by rw [ltensor_comp, coe_comp]
-#align linear_map.ltensor_comp_apply LinearMap.ltensor_comp_apply
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_apply LinearMap.lTensor_comp_applyₓ'. -/
+theorem lTensor_comp_apply (x : M ⊗[R] N) :
+    (g.comp f).lTensor M x = (g.lTensor M) ((f.lTensor M) x) := by rw [ltensor_comp, coe_comp]
+#align linear_map.ltensor_comp_apply LinearMap.lTensor_comp_apply
 
-/- warning: linear_map.rtensor_comp -> LinearMap.rtensor_comp is a dubious translation:
+/- warning: linear_map.rtensor_comp -> LinearMap.rTensor_comp is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u5}) {N : Type.{u4}} {P : Type.{u1}} {Q : Type.{u3}} [_inst_4 : AddCommMonoid.{u5} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_6 : AddCommMonoid.{u1} P] [_inst_7 : AddCommMonoid.{u3} Q] [_inst_9 : Module.{u2, u5} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u1} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] [_inst_12 : Module.{u2, u3} R Q (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7] (g : 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))) P Q _inst_6 _inst_7 _inst_11 _inst_12) (f : LinearMap.{u2, u2, u4, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (LinearMap.{u2, u2, max u5 u4, max u5 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))) (TensorProduct.{u2, u4, u5} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u5} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (TensorProduct.addCommMonoid.{u2, u4, u5} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u5} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u5} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u5} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9)) (LinearMap.rtensor.{u2, u5, u4, u3} R _inst_1 M N Q _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 (LinearMap.comp.{u2, u2, u2, u4, u1, u3} R R R N P Q (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_7 _inst_10 _inst_11 _inst_12 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} 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)))) g f)) (LinearMap.comp.{u2, u2, u2, max u5 u4, max u5 u1, max u5 u3} R R R (TensorProduct.{u2, u4, u5} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u1, u5} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.{u2, u3, u5} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u4, u5} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u1, u5} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u5} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u5} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u5} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u5} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} 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)))) (LinearMap.rtensor.{u2, u5, u1, u3} R _inst_1 M P Q _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12 g) (LinearMap.rtensor.{u2, u5, u4, u1} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f))
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp LinearMap.rtensor_compₓ'. -/
-theorem rtensor_comp : (g.comp f).rtensor M = (g.rtensor M).comp (f.rtensor M) :=
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u5}) {N : Type.{u4}} {P : Type.{u1}} {Q : Type.{u3}} [_inst_4 : AddCommMonoid.{u5} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_6 : AddCommMonoid.{u1} P] [_inst_7 : AddCommMonoid.{u3} Q] [_inst_9 : Module.{u2, u5} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u1} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] [_inst_12 : Module.{u2, u3} R Q (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7] (g : 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))) P Q _inst_6 _inst_7 _inst_11 _inst_12) (f : LinearMap.{u2, u2, u4, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (LinearMap.{u2, u2, max u5 u4, max u5 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))) (TensorProduct.{u2, u4, u5} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u5} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (TensorProduct.addCommMonoid.{u2, u4, u5} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u5} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u5} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u5} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9)) (LinearMap.rTensor.{u2, u5, u4, u3} R _inst_1 M N Q _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 (LinearMap.comp.{u2, u2, u2, u4, u1, u3} R R R N P Q (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_7 _inst_10 _inst_11 _inst_12 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} 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)))) g f)) (LinearMap.comp.{u2, u2, u2, max u5 u4, max u5 u1, max u5 u3} R R R (TensorProduct.{u2, u4, u5} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u1, u5} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.{u2, u3, u5} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u4, u5} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u1, u5} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u5} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u5} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u5} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u5} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} 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)))) (LinearMap.rTensor.{u2, u5, u1, u3} R _inst_1 M P Q _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12 g) (LinearMap.rTensor.{u2, u5, u4, u1} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f))
+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp LinearMap.rTensor_compₓ'. -/
+theorem rTensor_comp : (g.comp f).rTensor M = (g.rTensor M).comp (f.rTensor M) :=
   by
   ext (m n)
   simp only [compr₂_apply, mk_apply, comp_apply, rtensor_tmul]
-#align linear_map.rtensor_comp LinearMap.rtensor_comp
+#align linear_map.rtensor_comp LinearMap.rTensor_comp
 
-/- warning: linear_map.rtensor_comp_apply -> LinearMap.rtensor_comp_apply is a dubious translation:
+/- warning: linear_map.rtensor_comp_apply -> LinearMap.rTensor_comp_apply is a dubious translation:
 lean 3 declaration is
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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_5 _inst_6 _inst_10 _inst_11) (x : TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9), Eq.{succ (max u5 u2)} (TensorProduct.{u1, u5, u2} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (coeFn.{max (succ (max u3 u2)) (succ (max u5 u2)), max (succ (max u3 u2)) (succ (max u5 u2))} (LinearMap.{u1, u1, max u3 u2, max u5 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u5, u2} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u5, u2} R _inst_1 Q M _inst_7 _inst_4 _inst_12 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M 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 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_apply LinearMap.rtensor_comp_applyₓ'. -/
-theorem rtensor_comp_apply (x : N ⊗[R] M) :
-    (g.comp f).rtensor M x = (g.rtensor M) ((f.rtensor M) x) := by rw [rtensor_comp, coe_comp]
-#align linear_map.rtensor_comp_apply LinearMap.rtensor_comp_apply
+  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] (M : Type.{u3}) {N : Type.{u4}} {P : Type.{u1}} {Q : Type.{u2}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_6 : AddCommMonoid.{u1} P] [_inst_7 : AddCommMonoid.{u2} Q] [_inst_9 : Module.{u5, u3} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u4} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u1} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u2} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (g : LinearMap.{u5, u5, u1, u2} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) P Q _inst_6 _inst_7 _inst_11 _inst_12) (f : LinearMap.{u5, u5, u4, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_apply LinearMap.rTensor_comp_applyₓ'. -/
+theorem rTensor_comp_apply (x : N ⊗[R] M) :
+    (g.comp f).rTensor M x = (g.rTensor M) ((f.rTensor M) x) := by rw [rtensor_comp, coe_comp]
+#align linear_map.rtensor_comp_apply LinearMap.rTensor_comp_apply
 
-/- warning: linear_map.ltensor_mul -> LinearMap.ltensor_mul is a dubious translation:
+/- warning: linear_map.ltensor_mul -> LinearMap.lTensor_mul is a dubious translation:
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_inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (instHMul.{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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (LinearMap.module.End.hasMul.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) (LinearMap.lTensor.{u1, u2, u3, u3} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 f) (LinearMap.lTensor.{u1, u2, u3, u3} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 g))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_mul LinearMap.ltensor_mulₓ'. -/
-theorem ltensor_mul (f g : Module.End R N) : (f * g).ltensor M = f.ltensor M * g.ltensor M :=
-  ltensor_comp M f g
-#align linear_map.ltensor_mul LinearMap.ltensor_mul
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Type.{u1}) {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (f : Module.End.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10) (g : Module.End.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10), Eq.{max (succ u1) (succ u2)} (LinearMap.{u3, u3, max u2 u1, max u2 u1} 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))) (TensorProduct.{u3, u1, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u1, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u1, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_mul LinearMap.lTensor_mulₓ'. -/
+theorem lTensor_mul (f g : Module.End R N) : (f * g).lTensor M = f.lTensor M * g.lTensor M :=
+  lTensor_comp M f g
+#align linear_map.ltensor_mul LinearMap.lTensor_mul
 
-/- warning: linear_map.rtensor_mul -> LinearMap.rtensor_mul is a dubious translation:
+/- warning: linear_map.rtensor_mul -> LinearMap.rTensor_mul is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_mul LinearMap.rtensor_mulₓ'. -/
-theorem rtensor_mul (f g : Module.End R N) : (f * g).rtensor M = f.rtensor M * g.rtensor M :=
-  rtensor_comp M f g
-#align linear_map.rtensor_mul LinearMap.rtensor_mul
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Type.{u1}) {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (f : Module.End.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10) (g : Module.End.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10), Eq.{max (succ u1) (succ u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (LinearMap.rTensor.{u3, u1, u2, u2} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (HMul.hMul.{u2, u2, u2} (Module.End.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10) (Module.End.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10) (Module.End.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10) (instHMul.{u2} (Module.End.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10) (LinearMap.instMulEnd.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10)) f g)) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) 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_inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (instHMul.{max u1 u2} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (LinearMap.instMulEnd.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9))) (LinearMap.rTensor.{u3, u1, u2, u2} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 f) (LinearMap.rTensor.{u3, u1, u2, u2} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 g))
+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_mul LinearMap.rTensor_mulₓ'. -/
+theorem rTensor_mul (f g : Module.End R N) : (f * g).rTensor M = f.rTensor M * g.rTensor M :=
+  rTensor_comp M f g
+#align linear_map.rtensor_mul LinearMap.rTensor_mul
 
 variable (N)
 
-/- warning: linear_map.ltensor_id -> LinearMap.ltensor_id is a dubious translation:
+/- warning: linear_map.ltensor_id -> LinearMap.lTensor_id is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) (N : Type.{u3}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5], Eq.{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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (LinearMap.lTensor.{u1, u2, u3, u3} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)) (LinearMap.id.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_id LinearMap.ltensor_idₓ'. -/
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u3}) (N : Type.{u2}) [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5], Eq.{max (succ u3) (succ u2)} (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, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (LinearMap.lTensor.{u1, u3, u2, u2} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)) (LinearMap.id.{u1, max u3 u2} R (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))
+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_id LinearMap.lTensor_idₓ'. -/
 @[simp]
-theorem ltensor_id : (id : N →ₗ[R] N).ltensor M = id :=
+theorem lTensor_id : (id : N →ₗ[R] N).lTensor M = id :=
   map_id
-#align linear_map.ltensor_id LinearMap.ltensor_id
+#align linear_map.ltensor_id LinearMap.lTensor_id
 
-/- warning: linear_map.ltensor_id_apply -> LinearMap.ltensor_id_apply is a dubious translation:
+/- warning: linear_map.ltensor_id_apply -> LinearMap.lTensor_id_apply is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) (N : Type.{u3}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (x : TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (fun (_x : 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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) => (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, max u2 u3} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.lTensor.{u1, u2, u3, u3} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)) x) x
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_id_apply LinearMap.ltensor_id_applyₓ'. -/
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Type.{u2}) (N : Type.{u1}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (x : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) x) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u1, max u2 u1} R R (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.lTensor.{u3, u2, u1, u1} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10)) x) x
+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_id_apply LinearMap.lTensor_id_applyₓ'. -/
 -- `simp` can prove this.
-theorem ltensor_id_apply (x : M ⊗[R] N) : (LinearMap.id : N →ₗ[R] N).ltensor M x = x := by
+theorem lTensor_id_apply (x : M ⊗[R] N) : (LinearMap.id : N →ₗ[R] N).lTensor M x = x := by
   rw [ltensor_id, id_coe, id.def]
-#align linear_map.ltensor_id_apply LinearMap.ltensor_id_apply
+#align linear_map.ltensor_id_apply LinearMap.lTensor_id_apply
 
-/- warning: linear_map.rtensor_id -> LinearMap.rtensor_id is a dubious translation:
+/- warning: linear_map.rtensor_id -> LinearMap.rTensor_id is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) (N : Type.{u3}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5], Eq.{succ (max u3 u2)} (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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (LinearMap.rTensor.{u1, u2, u3, u3} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)) (LinearMap.id.{u1, max u3 u2} R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_id LinearMap.rtensor_idₓ'. -/
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u3}) (N : Type.{u2}) [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5], Eq.{max (succ u3) (succ u2)} (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 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (LinearMap.rTensor.{u1, u3, u2, u2} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)) (LinearMap.id.{u1, max u3 u2} R (TensorProduct.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9))
+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_id LinearMap.rTensor_idₓ'. -/
 @[simp]
-theorem rtensor_id : (id : N →ₗ[R] N).rtensor M = id :=
+theorem rTensor_id : (id : N →ₗ[R] N).rTensor M = id :=
   map_id
-#align linear_map.rtensor_id LinearMap.rtensor_id
+#align linear_map.rtensor_id LinearMap.rTensor_id
 
-/- warning: linear_map.rtensor_id_apply -> LinearMap.rtensor_id_apply is a dubious translation:
+/- warning: linear_map.rtensor_id_apply -> LinearMap.rTensor_id_apply is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_id_apply LinearMap.rtensor_id_applyₓ'. -/
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_id_apply LinearMap.rTensor_id_applyₓ'. -/
 -- `simp` can prove this.
-theorem rtensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rtensor M x = x := by
+theorem rTensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rTensor M x = x := by
   rw [rtensor_id, id_coe, id.def]
-#align linear_map.rtensor_id_apply LinearMap.rtensor_id_apply
+#align linear_map.rtensor_id_apply LinearMap.rTensor_id_apply
 
 variable {N}
 
-/- warning: linear_map.ltensor_comp_rtensor -> LinearMap.ltensor_comp_rtensor is a dubious translation:
+/- warning: linear_map.ltensor_comp_rtensor -> LinearMap.lTensor_comp_rTensor is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_rtensor LinearMap.ltensor_comp_rtensorₓ'. -/
+  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] (M : Type.{u4}) {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12), Eq.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1)} (LinearMap.{u5, u5, max u4 u2, max u3 u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (LinearMap.comp.{u5, u5, u5, max u4 u2, max u2 u3, max u3 u1} R R R (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u5, u3, u2} R _inst_1 P N _inst_6 _inst_5 _inst_11 _inst_10) (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (TensorProduct.addCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u5, u3, u2} R _inst_1 P N _inst_6 _inst_5 _inst_11 _inst_10) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u2} R _inst_1 P N _inst_6 _inst_5 _inst_11 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomCompTriple.ids.{u5, u5} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (LinearMap.lTensor.{u5, u3, u2, u1} R _inst_1 P N Q _inst_6 _inst_5 _inst_7 _inst_11 _inst_10 _inst_12 g) (LinearMap.rTensor.{u5, u2, u4, u3} R _inst_1 N M P _inst_5 _inst_4 _inst_6 _inst_10 _inst_9 _inst_11 f)) (TensorProduct.map.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)
+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_rtensor LinearMap.lTensor_comp_rTensorₓ'. -/
 @[simp]
-theorem ltensor_comp_rtensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
-    (g.ltensor P).comp (f.rtensor N) = map f g := by
+theorem lTensor_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
+    (g.lTensor P).comp (f.rTensor N) = map f g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
-#align linear_map.ltensor_comp_rtensor LinearMap.ltensor_comp_rtensor
+#align linear_map.ltensor_comp_rtensor LinearMap.lTensor_comp_rTensor
 
-/- warning: linear_map.rtensor_comp_ltensor -> LinearMap.rtensor_comp_ltensor is a dubious translation:
+/- warning: linear_map.rtensor_comp_ltensor -> LinearMap.rTensor_comp_lTensor is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12), Eq.{max (succ (max u2 u3)) (succ (max u4 u5))} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (LinearMap.comp.{u1, u1, u1, max u2 u3, max u2 u5, max u4 u5} R R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u5} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u5} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u5} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} 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)))) (LinearMap.rTensor.{u1, u5, u2, u4} R _inst_1 Q M P _inst_7 _inst_4 _inst_6 _inst_12 _inst_9 _inst_11 f) (LinearMap.lTensor.{u1, u2, u3, u5} R _inst_1 M N Q _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 g)) (TensorProduct.map.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] (M : Type.{u4}) {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12), Eq.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1)} (LinearMap.{u5, u5, max u4 u2, max u3 u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (LinearMap.comp.{u5, u5, u5, max u4 u2, max u4 u1, max u3 u1} R R R (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u5, u4, u1} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (TensorProduct.addCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u5, u4, u1} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u4, u1} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomCompTriple.ids.{u5, u5} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (LinearMap.rtensor.{u5, u1, u4, u3} R _inst_1 Q M P _inst_7 _inst_4 _inst_6 _inst_12 _inst_9 _inst_11 f) (LinearMap.ltensor.{u5, u4, u2, u1} R _inst_1 M N Q _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 g)) (TensorProduct.map.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_ltensor LinearMap.rtensor_comp_ltensorₓ'. -/
+  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] (M : Type.{u4}) {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12), Eq.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1)} (LinearMap.{u5, u5, max u4 u2, max u3 u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (LinearMap.comp.{u5, u5, u5, max u4 u2, max u4 u1, max u3 u1} R R R (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u5, u4, u1} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (TensorProduct.addCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u5, u4, u1} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u4, u1} R _inst_1 M Q _inst_4 _inst_7 _inst_9 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHomCompTriple.ids.{u5, u5} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (LinearMap.rTensor.{u5, u1, u4, u3} R _inst_1 Q M P _inst_7 _inst_4 _inst_6 _inst_12 _inst_9 _inst_11 f) (LinearMap.lTensor.{u5, u4, u2, u1} R _inst_1 M N Q _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 g)) (TensorProduct.map.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)
+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_ltensor LinearMap.rTensor_comp_lTensorₓ'. -/
 @[simp]
-theorem rtensor_comp_ltensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
-    (f.rtensor Q).comp (g.ltensor M) = map f g := by
+theorem rTensor_comp_lTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
+    (f.rTensor Q).comp (g.lTensor M) = map f g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
-#align linear_map.rtensor_comp_ltensor LinearMap.rtensor_comp_ltensor
+#align linear_map.rtensor_comp_ltensor LinearMap.rTensor_comp_lTensor
 
-/- warning: linear_map.map_comp_rtensor -> LinearMap.map_comp_rtensor is a dubious translation:
+/- warning: linear_map.map_comp_rtensor -> LinearMap.map_comp_rTensor is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} {S : Type.{u6}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_8 : AddCommMonoid.{u6} S] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] [_inst_13 : Module.{u1, u6} R S (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12) (f' : LinearMap.{u1, u1, u6, 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))) S M _inst_8 _inst_4 _inst_13 _inst_9), Eq.{max (succ (max u6 u3)) (succ (max u4 u5))} (LinearMap.{u1, u1, max u6 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))) (TensorProduct.{u1, u6, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u6, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u6, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (LinearMap.comp.{u1, u1, u1, max u6 u3, max u2 u3, max u4 u5} R R R (TensorProduct.{u1, u6, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u6, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u6, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} 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.map.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g) (LinearMap.rtensor.{u1, u3, u6, u2} R _inst_1 N S M _inst_5 _inst_8 _inst_4 _inst_10 _inst_13 _inst_9 f')) (TensorProduct.map.{u1, u6, u3, u4, u5} R _inst_1 S N P Q _inst_8 _inst_5 _inst_6 _inst_7 _inst_13 _inst_10 _inst_11 _inst_12 (LinearMap.comp.{u1, u1, u1, u6, u2, u4} R R R S M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_4 _inst_6 _inst_13 _inst_9 _inst_11 (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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} 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)))) f f') g)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} {S : Type.{u6}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_8 : AddCommMonoid.{u6} S] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] [_inst_13 : Module.{u1, u6} R S (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12) (f' : LinearMap.{u1, u1, u6, 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))) S M _inst_8 _inst_4 _inst_13 _inst_9), Eq.{max (succ (max u6 u3)) (succ (max u4 u5))} (LinearMap.{u1, u1, max u6 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))) (TensorProduct.{u1, u6, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u6, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u6, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (LinearMap.comp.{u1, u1, u1, max u6 u3, max u2 u3, max u4 u5} R R R (TensorProduct.{u1, u6, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u6, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u6, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} 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.map.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g) (LinearMap.rTensor.{u1, u3, u6, u2} R _inst_1 N S M _inst_5 _inst_8 _inst_4 _inst_10 _inst_13 _inst_9 f')) (TensorProduct.map.{u1, u6, u3, u4, u5} R _inst_1 S N P Q _inst_8 _inst_5 _inst_6 _inst_7 _inst_13 _inst_10 _inst_11 _inst_12 (LinearMap.comp.{u1, u1, u1, u6, u2, u4} R R R S M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_4 _inst_6 _inst_13 _inst_9 _inst_11 (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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} 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)))) f f') g)
 but is expected to have type
-  forall {R : Type.{u6}} [_inst_1 : CommSemiring.{u6} R] (M : Type.{u5}) {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u2}} {S : Type.{u1}} [_inst_4 : AddCommMonoid.{u5} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u2} Q] [_inst_8 : AddCommMonoid.{u1} S] [_inst_9 : Module.{u6, u5} R M (CommSemiring.toSemiring.{u6} R _inst_1) _inst_4] [_inst_10 : Module.{u6, u3} R N (CommSemiring.toSemiring.{u6} R _inst_1) _inst_5] [_inst_11 : Module.{u6, u4} R P (CommSemiring.toSemiring.{u6} R _inst_1) _inst_6] [_inst_12 : Module.{u6, u2} R Q (CommSemiring.toSemiring.{u6} R _inst_1) _inst_7] [_inst_13 : Module.{u6, u1} R S (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] (f : LinearMap.{u6, u6, u5, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u6, u6, u3, u2} R 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_inst_10) (TensorProduct.addCommMonoid.{u6, u4, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u1, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (LinearMap.comp.{u6, u6, u6, max u1 u3, max u5 u3, max u4 u2} R R R (TensorProduct.{u6, u1, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.{u6, u5, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u4, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (TensorProduct.addCommMonoid.{u6, u1, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.addCommMonoid.{u6, u5, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u1, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u5, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomCompTriple.ids.{u6, u6} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (TensorProduct.map.{u6, u5, u3, u4, u2} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g) (LinearMap.rtensor.{u6, u3, u1, u5} R _inst_1 N S M _inst_5 _inst_8 _inst_4 _inst_10 _inst_13 _inst_9 f')) (TensorProduct.map.{u6, u1, u3, u4, u2} R _inst_1 S N P Q _inst_8 _inst_5 _inst_6 _inst_7 _inst_13 _inst_10 _inst_11 _inst_12 (LinearMap.comp.{u6, u6, u6, u1, u5, u4} R R R S M P (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_4 _inst_6 _inst_13 _inst_9 _inst_11 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomCompTriple.ids.{u6, u6} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) f f') g)
-Case conversion may be inaccurate. Consider using '#align linear_map.map_comp_rtensor LinearMap.map_comp_rtensorₓ'. -/
+  forall {R : Type.{u6}} [_inst_1 : CommSemiring.{u6} R] (M : Type.{u5}) {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u2}} {S : Type.{u1}} [_inst_4 : AddCommMonoid.{u5} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u2} Q] [_inst_8 : AddCommMonoid.{u1} S] [_inst_9 : Module.{u6, u5} R M (CommSemiring.toSemiring.{u6} R _inst_1) _inst_4] [_inst_10 : Module.{u6, u3} R N (CommSemiring.toSemiring.{u6} R _inst_1) _inst_5] [_inst_11 : Module.{u6, u4} R P (CommSemiring.toSemiring.{u6} R _inst_1) _inst_6] [_inst_12 : Module.{u6, u2} R Q (CommSemiring.toSemiring.{u6} R _inst_1) _inst_7] [_inst_13 : Module.{u6, u1} R S (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] (f : LinearMap.{u6, u6, u5, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u6, u6, u3, u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12) (f' : LinearMap.{u6, u6, u1, u5} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) S M _inst_8 _inst_4 _inst_13 _inst_9), Eq.{max (max (max (succ u3) (succ u4)) (succ u2)) (succ u1)} (LinearMap.{u6, u6, max u1 u3, max u4 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (TensorProduct.{u6, u1, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.{u6, u4, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u6, u1, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u1, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (LinearMap.comp.{u6, u6, u6, max u1 u3, max u5 u3, max u4 u2} R R R (TensorProduct.{u6, u1, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.{u6, u5, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u4, u2} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (TensorProduct.addCommMonoid.{u6, u1, u3} R _inst_1 S N _inst_8 _inst_5 _inst_13 _inst_10) (TensorProduct.addCommMonoid.{u6, u5, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u2} R 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(CommSemiring.toSemiring.{u6} R _inst_1)))) f f') g)
+Case conversion may be inaccurate. Consider using '#align linear_map.map_comp_rtensor LinearMap.map_comp_rTensorₓ'. -/
 @[simp]
-theorem map_comp_rtensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (f' : S →ₗ[R] M) :
-    (map f g).comp (f'.rtensor _) = map (f.comp f') g := by
+theorem map_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (f' : S →ₗ[R] M) :
+    (map f g).comp (f'.rTensor _) = map (f.comp f') g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
-#align linear_map.map_comp_rtensor LinearMap.map_comp_rtensor
+#align linear_map.map_comp_rtensor LinearMap.map_comp_rTensor
 
-/- warning: linear_map.map_comp_ltensor -> LinearMap.map_comp_ltensor is a dubious translation:
+/- warning: linear_map.map_comp_ltensor -> LinearMap.map_comp_lTensor is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} {S : Type.{u6}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_8 : AddCommMonoid.{u6} S] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] [_inst_13 : Module.{u1, u6} R S (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12) (g' : LinearMap.{u1, u1, u6, 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))) S N _inst_8 _inst_5 _inst_13 _inst_10), Eq.{max (succ (max u2 u6)) (succ (max u4 u5))} (LinearMap.{u1, u1, max u2 u6, 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))) (TensorProduct.{u1, u2, u6} R _inst_1 M S _inst_4 _inst_8 _inst_9 _inst_13) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u6} R _inst_1 M S _inst_4 _inst_8 _inst_9 _inst_13) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u6} R _inst_1 M S _inst_4 _inst_8 _inst_9 _inst_13) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (LinearMap.comp.{u1, u1, u1, max u2 u6, max u2 u3, max u4 u5} R R R (TensorProduct.{u1, u2, u6} R _inst_1 M S _inst_4 _inst_8 _inst_9 _inst_13) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u6} R _inst_1 M S _inst_4 _inst_8 _inst_9 _inst_13) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u6} R _inst_1 M S _inst_4 _inst_8 _inst_9 _inst_13) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} 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.map.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g) (LinearMap.lTensor.{u1, u2, u6, u3} R _inst_1 M S N _inst_4 _inst_8 _inst_5 _inst_9 _inst_13 _inst_10 g')) (TensorProduct.map.{u1, u2, u6, u4, u5} R _inst_1 M S P Q _inst_4 _inst_8 _inst_6 _inst_7 _inst_9 _inst_13 _inst_11 _inst_12 f (LinearMap.comp.{u1, u1, u1, u6, u3, u5} R R R S N Q (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_5 _inst_7 _inst_13 _inst_10 _inst_12 (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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} 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)))) g g'))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.map_comp_ltensor LinearMap.map_comp_ltensorₓ'. -/
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+Case conversion may be inaccurate. Consider using '#align linear_map.map_comp_ltensor LinearMap.map_comp_lTensorₓ'. -/
 @[simp]
-theorem map_comp_ltensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (g' : S →ₗ[R] N) :
-    (map f g).comp (g'.ltensor _) = map f (g.comp g') := by
+theorem map_comp_lTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (g' : S →ₗ[R] N) :
+    (map f g).comp (g'.lTensor _) = map f (g.comp g') := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
-#align linear_map.map_comp_ltensor LinearMap.map_comp_ltensor
+#align linear_map.map_comp_ltensor LinearMap.map_comp_lTensor
 
-/- warning: linear_map.rtensor_comp_map -> LinearMap.rtensor_comp_map is a dubious translation:
+/- warning: linear_map.rtensor_comp_map -> LinearMap.rTensor_comp_map is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} {S : Type.{u6}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_8 : AddCommMonoid.{u6} S] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] [_inst_13 : Module.{u1, u6} R S (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] (f' : LinearMap.{u1, u1, u4, u6} 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))) P S _inst_6 _inst_8 _inst_11 _inst_13) (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12), Eq.{max (succ (max u2 u3)) (succ (max u6 u5))} (LinearMap.{u1, u1, max u2 u3, max u6 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u6, u5} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u6, u5} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u6, u5} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12)) (LinearMap.comp.{u1, u1, u1, max u2 u3, max u4 u5, max u6 u5} R R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.{u1, u6, u5} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u6, u5} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u6, u5} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} 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)))) (LinearMap.rTensor.{u1, u5, u4, u6} R _inst_1 Q P S _inst_7 _inst_6 _inst_8 _inst_12 _inst_11 _inst_13 f') (TensorProduct.map.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)) (TensorProduct.map.{u1, u2, u3, u6, u5} R _inst_1 M N S Q _inst_4 _inst_5 _inst_8 _inst_7 _inst_9 _inst_10 _inst_13 _inst_12 (LinearMap.comp.{u1, u1, u1, u2, u4, u6} R R R M P S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _inst_8 _inst_9 _inst_11 _inst_13 (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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} 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)))) f' f) g)
 but is expected to have type
-  forall {R : Type.{u6}} [_inst_1 : CommSemiring.{u6} R] (M : Type.{u3}) {N : Type.{u2}} {P : Type.{u5}} {Q : Type.{u1}} {S : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u5} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_8 : AddCommMonoid.{u4} S] [_inst_9 : Module.{u6, u3} R M (CommSemiring.toSemiring.{u6} R _inst_1) _inst_4] [_inst_10 : Module.{u6, u2} R N (CommSemiring.toSemiring.{u6} R _inst_1) _inst_5] [_inst_11 : Module.{u6, u5} R P (CommSemiring.toSemiring.{u6} R _inst_1) _inst_6] [_inst_12 : Module.{u6, u1} R Q (CommSemiring.toSemiring.{u6} R _inst_1) _inst_7] [_inst_13 : Module.{u6, u4} R S (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] (f' : LinearMap.{u6, u6, u5, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) P S _inst_6 _inst_8 _inst_11 _inst_13) (f : LinearMap.{u6, u6, u3, u5} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u6, u6, u2, u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12), Eq.{max (max (max (succ u3) (succ u2)) (succ u1)) (succ u4)} (LinearMap.{u6, u6, max u2 u3, max u4 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (TensorProduct.{u6, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u4, u1} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (TensorProduct.addCommMonoid.{u6, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u1} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u1} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12)) (LinearMap.comp.{u6, u6, u6, max u2 u3, max u5 u1, max u4 u1} R R R (TensorProduct.{u6, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u5, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.{u6, u4, u1} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (TensorProduct.addCommMonoid.{u6, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u5, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u6, u4, u1} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u5, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u1} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomCompTriple.ids.{u6, u6} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearMap.rtensor.{u6, u1, u5, u4} R _inst_1 Q P S _inst_7 _inst_6 _inst_8 _inst_12 _inst_11 _inst_13 f') (TensorProduct.map.{u6, u3, u2, u5, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)) (TensorProduct.map.{u6, u3, u2, u4, u1} R _inst_1 M N S Q _inst_4 _inst_5 _inst_8 _inst_7 _inst_9 _inst_10 _inst_13 _inst_12 (LinearMap.comp.{u6, u6, u6, u3, u5, u4} R R R M P S (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_4 _inst_6 _inst_8 _inst_9 _inst_11 _inst_13 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomCompTriple.ids.{u6, u6} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) f' f) g)
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_map LinearMap.rtensor_comp_mapₓ'. -/
+  forall {R : Type.{u6}} [_inst_1 : CommSemiring.{u6} R] (M : Type.{u3}) {N : Type.{u2}} {P : Type.{u5}} {Q : Type.{u1}} {S : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u5} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_8 : AddCommMonoid.{u4} S] [_inst_9 : Module.{u6, u3} R M (CommSemiring.toSemiring.{u6} R _inst_1) _inst_4] [_inst_10 : Module.{u6, u2} R N (CommSemiring.toSemiring.{u6} R _inst_1) _inst_5] [_inst_11 : Module.{u6, u5} R P (CommSemiring.toSemiring.{u6} R _inst_1) _inst_6] [_inst_12 : Module.{u6, u1} R Q (CommSemiring.toSemiring.{u6} R _inst_1) _inst_7] [_inst_13 : Module.{u6, u4} R S (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] (f' : LinearMap.{u6, u6, u5, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) P S _inst_6 _inst_8 _inst_11 _inst_13) (f : LinearMap.{u6, u6, u3, u5} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u6, u6, u2, u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12), Eq.{max (max (max (succ u3) (succ u2)) (succ u1)) (succ u4)} (LinearMap.{u6, u6, max u2 u3, max u4 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (TensorProduct.{u6, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u4, u1} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (TensorProduct.addCommMonoid.{u6, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u1} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u1} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12)) (LinearMap.comp.{u6, u6, u6, max u2 u3, max u5 u1, max u4 u1} R R R (TensorProduct.{u6, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u5, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.{u6, u4, u1} R _inst_1 S Q _inst_8 _inst_7 _inst_13 _inst_12) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (TensorProduct.addCommMonoid.{u6, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u5, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u6, u4, u1} R 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_inst_8 _inst_12 _inst_11 _inst_13 f') (TensorProduct.map.{u6, u3, u2, u5, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)) (TensorProduct.map.{u6, u3, u2, u4, u1} R _inst_1 M N S Q _inst_4 _inst_5 _inst_8 _inst_7 _inst_9 _inst_10 _inst_13 _inst_12 (LinearMap.comp.{u6, u6, u6, u3, u5, u4} R R R M P S (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_4 _inst_6 _inst_8 _inst_9 _inst_11 _inst_13 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomCompTriple.ids.{u6, u6} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) f' f) g)
+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_map LinearMap.rTensor_comp_mapₓ'. -/
 @[simp]
-theorem rtensor_comp_map (f' : P →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
-    (f'.rtensor _).comp (map f g) = map (f'.comp f) g := by
+theorem rTensor_comp_map (f' : P →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
+    (f'.rTensor _).comp (map f g) = map (f'.comp f) g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
-#align linear_map.rtensor_comp_map LinearMap.rtensor_comp_map
+#align linear_map.rtensor_comp_map LinearMap.rTensor_comp_map
 
-/- warning: linear_map.ltensor_comp_map -> LinearMap.ltensor_comp_map is a dubious translation:
+/- warning: linear_map.ltensor_comp_map -> LinearMap.lTensor_comp_map is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} {S : Type.{u6}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_8 : AddCommMonoid.{u6} S] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] [_inst_13 : Module.{u1, u6} R S (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] (g' : LinearMap.{u1, u1, u5, u6} 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))) Q S _inst_7 _inst_8 _inst_12 _inst_13) (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12), Eq.{max (succ (max u2 u3)) (succ (max u4 u6))} (LinearMap.{u1, u1, max u2 u3, max u4 u6} 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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u6} R _inst_1 P S _inst_6 _inst_8 _inst_11 _inst_13) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u6} R _inst_1 P S _inst_6 _inst_8 _inst_11 _inst_13) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u6} R _inst_1 P S _inst_6 _inst_8 _inst_11 _inst_13)) (LinearMap.comp.{u1, u1, u1, max u2 u3, max u4 u5, max u4 u6} R R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.{u1, u4, u6} R _inst_1 P S _inst_6 _inst_8 _inst_11 _inst_13) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u4, u6} R _inst_1 P S _inst_6 _inst_8 _inst_11 _inst_13) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u4, u6} R _inst_1 P S _inst_6 _inst_8 _inst_11 _inst_13) (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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} 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)))) (LinearMap.lTensor.{u1, u4, u5, u6} R _inst_1 P Q S _inst_6 _inst_7 _inst_8 _inst_11 _inst_12 _inst_13 g') (TensorProduct.map.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)) (TensorProduct.map.{u1, u2, u3, u4, u6} R _inst_1 M N P S _inst_4 _inst_5 _inst_6 _inst_8 _inst_9 _inst_10 _inst_11 _inst_13 f (LinearMap.comp.{u1, u1, u1, u3, u5, u6} R R R N Q S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_7 _inst_8 _inst_10 _inst_12 _inst_13 (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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} 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)))) g' g))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_map LinearMap.ltensor_comp_mapₓ'. -/
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_map LinearMap.lTensor_comp_mapₓ'. -/
 @[simp]
-theorem ltensor_comp_map (g' : Q →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
-    (g'.ltensor _).comp (map f g) = map f (g'.comp g) := by
+theorem lTensor_comp_map (g' : Q →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
+    (g'.lTensor _).comp (map f g) = map f (g'.comp g) := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
-#align linear_map.ltensor_comp_map LinearMap.ltensor_comp_map
+#align linear_map.ltensor_comp_map LinearMap.lTensor_comp_map
 
 variable {M}
 
-/- warning: linear_map.rtensor_pow -> LinearMap.rtensor_pow is a dubious translation:
+/- warning: linear_map.rtensor_pow -> LinearMap.rTensor_pow is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (f : LinearMap.{u1, u1, u2, 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 M _inst_4 _inst_4 _inst_9 _inst_9) (n : Nat), Eq.{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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (HPow.hPow.{max u2 u3, 0, 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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) Nat (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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (instHPow.{max u2 u3, 0} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) 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_inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (Module.End.monoid.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)))) (LinearMap.rTensor.{u1, u3, u2, u2} R _inst_1 N M M _inst_5 _inst_4 _inst_4 _inst_10 _inst_9 _inst_9 f) n) (LinearMap.rTensor.{u1, u3, u2, u2} R _inst_1 N M M _inst_5 _inst_4 _inst_4 _inst_10 _inst_9 _inst_9 (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) 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 but is expected to have type
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(TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 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(TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (instHPow.{max u2 u1, 0} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) Nat (Monoid.Pow.{max u2 u1} (LinearMap.{u3, 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(CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M M _inst_4 _inst_4 _inst_9 _inst_9) Nat (Monoid.Pow.{u2} (LinearMap.{u3, u3, u2, u2} 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_4 _inst_4 _inst_9 _inst_9) (Module.End.monoid.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 _inst_9))) f n))
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_pow LinearMap.rtensor_powₓ'. -/
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u2}} {N : Type.{u1}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (f : LinearMap.{u3, u3, u2, u2} 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_4 _inst_4 _inst_9 _inst_9) (n : Nat), Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_pow LinearMap.rTensor_powₓ'. -/
 @[simp]
-theorem rtensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rtensor N ^ n = (f ^ n).rtensor N :=
+theorem rTensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rTensor N ^ n = (f ^ n).rTensor N :=
   by
   have h := TensorProduct.map_pow f (id : N →ₗ[R] N) n
   rwa [id_pow] at h
-#align linear_map.rtensor_pow LinearMap.rtensor_pow
+#align linear_map.rtensor_pow LinearMap.rTensor_pow
 
-/- warning: linear_map.ltensor_pow -> LinearMap.ltensor_pow is a dubious translation:
+/- warning: linear_map.ltensor_pow -> LinearMap.lTensor_pow is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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(TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u1, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (instHPow.{max u1 u2, 0} (LinearMap.{u3, u3, max u2 u1, max u2 u1} 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))) (TensorProduct.{u3, u1, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u1, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u1, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u1, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u1, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u1, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) Nat (Monoid.Pow.{max u1 u2} (LinearMap.{u3, 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-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_pow LinearMap.ltensor_powₓ'. -/
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u1}} {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (f : LinearMap.{u3, u3, u2, u2} 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))) N N _inst_5 _inst_5 _inst_10 _inst_10) (n : Nat), Eq.{max (succ u1) (succ u2)} (LinearMap.{u3, u3, max u2 u1, max u2 u1} 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))) (TensorProduct.{u3, u1, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u1, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_pow LinearMap.lTensor_powₓ'. -/
 @[simp]
-theorem ltensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.ltensor M ^ n = (f ^ n).ltensor M :=
+theorem lTensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.lTensor M ^ n = (f ^ n).lTensor M :=
   by
   have h := TensorProduct.map_pow (id : M →ₗ[R] M) f n
   rwa [id_pow] at h
-#align linear_map.ltensor_pow LinearMap.ltensor_pow
+#align linear_map.ltensor_pow LinearMap.lTensor_pow
 
 end LinearMap
 
@@ -2166,49 +2166,49 @@ end TensorProduct
 
 namespace LinearMap
 
-/- warning: linear_map.ltensor_sub -> LinearMap.ltensor_sub is a dubious translation:
+/- warning: linear_map.ltensor_sub -> LinearMap.lTensor_sub is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : AddCommGroup.{u4} P] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] [_inst_9 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4)] (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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_8 _inst_9) (g : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R 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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : AddCommGroup.{u4} P] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] [_inst_9 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4)] (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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_8 _inst_9) (g : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R 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 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_sub LinearMap.ltensor_subₓ'. -/
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Type.{u1}} {N : Type.{u3}} {P : Type.{u2}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : AddCommGroup.{u2} P] [_inst_7 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] [_inst_9 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4)] (f : LinearMap.{u4, u4, u3, u2} 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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_8 _inst_9) (g : LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R 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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_sub LinearMap.lTensor_subₓ'. -/
 @[simp]
-theorem ltensor_sub (f g : N →ₗ[R] P) : (f - g).ltensor M = f.ltensor M - g.ltensor M := by
+theorem lTensor_sub (f g : N →ₗ[R] P) : (f - g).lTensor M = f.lTensor M - g.lTensor M := by
   simp only [← coe_ltensor_hom, map_sub]
-#align linear_map.ltensor_sub LinearMap.ltensor_sub
+#align linear_map.ltensor_sub LinearMap.lTensor_sub
 
-/- warning: linear_map.rtensor_sub -> LinearMap.rtensor_sub is a dubious translation:
+/- warning: linear_map.rtensor_sub -> LinearMap.rTensor_sub is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : AddCommGroup.{u4} P] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] [_inst_9 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4)] (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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_8 _inst_9) (g : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R 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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : AddCommGroup.{u4} P] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] [_inst_9 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4)] (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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_8 _inst_9) (g : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R 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 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_8 _inst_9 f) (LinearMap.rtensor.{u4, u1, u3, u2} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_8 _inst_9 g))
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_sub LinearMap.rtensor_subₓ'. -/
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Type.{u1}} {N : Type.{u3}} {P : Type.{u2}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : AddCommGroup.{u2} P] [_inst_7 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] [_inst_9 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4)] (f : LinearMap.{u4, u4, u3, u2} 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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_8 _inst_9) (g : LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R 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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_sub LinearMap.rTensor_subₓ'. -/
 @[simp]
-theorem rtensor_sub (f g : N →ₗ[R] P) : (f - g).rtensor M = f.rtensor M - g.rtensor M := by
+theorem rTensor_sub (f g : N →ₗ[R] P) : (f - g).rTensor M = f.rTensor M - g.rTensor M := by
   simp only [← coe_rtensor_hom, map_sub]
-#align linear_map.rtensor_sub LinearMap.rtensor_sub
+#align linear_map.rtensor_sub LinearMap.rTensor_sub
 
-/- warning: linear_map.ltensor_neg -> LinearMap.ltensor_neg is a dubious translation:
+/- warning: linear_map.ltensor_neg -> LinearMap.lTensor_neg is a dubious translation:
 lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_9)) (LinearMap.hasNeg.{u1, u1, max u2 u3, max u2 u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (TensorProduct.{u1, u2, u4} R _inst_1 M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (TensorProduct.addCommGroup.{u1, u2, u4} R _inst_1 M P _inst_2 _inst_4 _inst_7 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.ltensor.{u1, u2, u3, u4} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_8 _inst_9 f))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : AddCommGroup.{u4} P] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] [_inst_9 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4)] (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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_8 _inst_9), Eq.{max (succ (max u2 u3)) (succ (max u2 u4))} (LinearMap.{u1, u1, max u2 u3, max u2 u4} R R 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u4} R _inst_1 M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_9)) (LinearMap.lTensor.{u1, u2, u3, u4} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_8 _inst_9 (Neg.neg.{max u3 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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_8 _inst_9) (LinearMap.hasNeg.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_4 _inst_8 _inst_9 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f)) (Neg.neg.{max 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(AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_9)) (LinearMap.hasNeg.{u1, u1, max u2 u3, max u2 u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (TensorProduct.{u1, u2, u4} R _inst_1 M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (TensorProduct.addCommGroup.{u1, u2, u4} R _inst_1 M P _inst_2 _inst_4 _inst_7 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.lTensor.{u1, u2, u3, u4} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_8 _inst_9 f))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Type.{u1}} {N : Type.{u3}} {P : Type.{u2}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : AddCommGroup.{u2} P] [_inst_7 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] [_inst_9 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4)] (f : LinearMap.{u4, u4, u3, u2} 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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_8 _inst_9), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u3 u1, max u2 u1} R R 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_inst_8) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u2} R _inst_1 M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_9)) (LinearMap.ltensor.{u4, u1, u3, u2} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_8 _inst_9 (Neg.neg.{max u3 u2} (LinearMap.{u4, u4, u3, u2} 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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_8 _inst_9) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u4, u3, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_4 _inst_8 _inst_9 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f)) (Neg.neg.{max (max u1 u3) u2} (LinearMap.{u4, u4, max u3 u1, max u2 u1} 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, u1, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (TensorProduct.{u4, u1, u2} R _inst_1 M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_9) (TensorProduct.addCommMonoid.{u4, u1, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (TensorProduct.addCommMonoid.{u4, u1, u2} R _inst_1 M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u1, u2} R _inst_1 M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_9)) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u4, max u1 u3, max u1 u2} R R (TensorProduct.{u4, u1, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (TensorProduct.{u4, u1, u2} R _inst_1 M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_9) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u1, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N 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-Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_neg LinearMap.ltensor_negₓ'. -/
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_neg LinearMap.lTensor_negₓ'. -/
 @[simp]
-theorem ltensor_neg (f : N →ₗ[R] P) : (-f).ltensor M = -f.ltensor M := by
+theorem lTensor_neg (f : N →ₗ[R] P) : (-f).lTensor M = -f.lTensor M := by
   simp only [← coe_ltensor_hom, map_neg]
-#align linear_map.ltensor_neg LinearMap.ltensor_neg
+#align linear_map.ltensor_neg LinearMap.lTensor_neg
 
-/- warning: linear_map.rtensor_neg -> LinearMap.rtensor_neg is a dubious translation:
+/- warning: linear_map.rtensor_neg -> LinearMap.rTensor_neg is a dubious translation:
 lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_8 _inst_7) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 _inst_7)) (LinearMap.hasNeg.{u1, u1, max u3 u2, max u4 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_8 _inst_7) (TensorProduct.{u1, u4, u2} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_8 _inst_7) (TensorProduct.addCommGroup.{u1, u4, u2} R _inst_1 P M _inst_4 _inst_2 _inst_9 _inst_7) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_8 _inst_7) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 _inst_7) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.rTensor.{u1, u2, u3, u4} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_8 _inst_9 f))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Type.{u1}} {N : Type.{u3}} {P : Type.{u2}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : AddCommGroup.{u2} P] [_inst_7 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] [_inst_9 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4)] (f : LinearMap.{u4, u4, u3, u2} 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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_8 _inst_9), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u1 u3, max u1 u2} 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, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7)) (LinearMap.rtensor.{u4, u1, u3, u2} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_8 _inst_9 (Neg.neg.{max u3 u2} (LinearMap.{u4, u4, u3, u2} 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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_8 _inst_9) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u4, u3, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_4 _inst_8 _inst_9 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f)) (Neg.neg.{max (max u1 u3) u2} (LinearMap.{u4, u4, max u1 u3, max u1 u2} 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, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7)) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u4, max u1 u3, max u1 u2} R R (TensorProduct.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.addCommGroup.{u4, u2, u1} R _inst_1 P M _inst_4 _inst_2 _inst_9 _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.rtensor.{u4, u1, u3, u2} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_8 _inst_9 f))
-Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_neg LinearMap.rtensor_negₓ'. -/
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Type.{u1}} {N : Type.{u3}} {P : Type.{u2}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : AddCommGroup.{u2} P] [_inst_7 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] [_inst_9 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4)] (f : LinearMap.{u4, u4, u3, u2} 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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_8 _inst_9), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u1 u3, max u1 u2} 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, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7)) (LinearMap.rTensor.{u4, u1, u3, u2} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_8 _inst_9 (Neg.neg.{max u3 u2} (LinearMap.{u4, u4, u3, u2} 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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_8 _inst_9) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u4, u3, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_4 _inst_8 _inst_9 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f)) (Neg.neg.{max (max u1 u3) u2} (LinearMap.{u4, u4, max u1 u3, max u1 u2} 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, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.addCommMonoid.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7)) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u4, max u1 u3, max u1 u2} R R (TensorProduct.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.addCommGroup.{u4, u2, u1} R _inst_1 P M _inst_4 _inst_2 _inst_9 _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_8 _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.rTensor.{u4, u1, u3, u2} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_8 _inst_9 f))
+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_neg LinearMap.rTensor_negₓ'. -/
 @[simp]
-theorem rtensor_neg (f : N →ₗ[R] P) : (-f).rtensor M = -f.rtensor M := by
+theorem rTensor_neg (f : N →ₗ[R] P) : (-f).rTensor M = -f.rTensor M := by
   simp only [← coe_rtensor_hom, map_neg]
-#align linear_map.rtensor_neg LinearMap.rtensor_neg
+#align linear_map.rtensor_neg LinearMap.rTensor_neg
 
 end LinearMap
 

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

@@ -543,7 +543,7 @@ variable {R M N}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (m : M) (n : N), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, 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))) N (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) 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 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u3}} {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (m : M) (n : N), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) n) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u1, u1, u2, 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))) N (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R N (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u3, max u2 u3} R R 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u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u1, u1, u2, 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))) N (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u3 u2} R R M (LinearMap.{u1, u1, u2, 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))) N (TensorProduct.{u1, u3, u2} R _inst_1 M N 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_inst_1)) (AddMonoid.toZero.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddCommMonoid.toAddMonoid.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) (Module.toMulActionWithZero.{u1, max u3 u2} R (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.mk.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) m) n) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)
 Case conversion may be inaccurate. Consider using '#align tensor_product.mk_apply TensorProduct.mk_applyₓ'. -/
 @[simp]
 theorem mk_apply (m : M) (n : N) : mk R M N m n = m ⊗ₜ n :=
@@ -677,7 +677,7 @@ def liftAux : M ⊗[R] N →+ P :=
 lean 3 declaration is
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 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u2}} {N : Type.{u1}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_11 : Module.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6] (f : LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P 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_inst_10) P (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (AddMonoidHom.addMonoidHomClass.{max u2 u1, u4} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))))) (TensorProduct.liftAux.{u3, u2, u1, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), succ u2, max (succ u1) (succ u4)} (LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u1 u4} R R M (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) f m) n)
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u2}} {N : Type.{u1}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_11 : Module.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6] (f : LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift_aux_tmul TensorProduct.liftAux_tmulₓ'. -/
 theorem liftAux_tmul (m n) : liftAux f (m ⊗ₜ n) = f m n :=
   rfl
@@ -716,7 +716,7 @@ variable {f}
 lean 3 declaration is
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 but is expected to have type
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(CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u1 u4} R R M (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) f x) y)
 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.tmul TensorProduct.lift.tmulₓ'. -/
 @[simp]
 theorem lift.tmul (x y) : lift f (x ⊗ₜ y) = f x y :=
@@ -727,7 +727,7 @@ theorem lift.tmul (x y) : lift f (x ⊗ₜ y) = f x y :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] {f : LinearMap.{u1, u1, u2, max 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 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11))))} (x : M) (y : N), Eq.{succ u4} P (LinearMap.toFun.{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 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (TensorProduct.lift.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x y)) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max 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 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11))))) (fun (_x : LinearMap.{u1, u1, u2, max 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 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11))))) => M -> (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))) N P _inst_5 _inst_6 _inst_10 _inst_11)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x) y)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u2}} {N : Type.{u1}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_11 : Module.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6] {f : LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.tmul' TensorProduct.lift.tmul'ₓ'. -/
 @[simp]
 theorem lift.tmul' (x y) : (lift f).1 (x ⊗ₜ y) = f x y :=
@@ -738,7 +738,7 @@ theorem lift.tmul' (x y) : (lift f).1 (x ⊗ₜ y) = f x y :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align tensor_product.ext' TensorProduct.ext'ₓ'. -/
 theorem ext' {g h : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x ⊗ₜ y)) : g = h :=
   LinearMap.ext fun z =>
@@ -750,7 +750,7 @@ theorem ext' {g h : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.unique TensorProduct.lift.uniqueₓ'. -/
 theorem lift.unique {g : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = f x y) : g = lift f :=
   ext' fun m n => by rw [H, lift.tmul]
@@ -823,7 +823,7 @@ variable {R M N P}
 lean 3 declaration is
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 but is expected to have type
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R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P 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 Case conversion may be inaccurate. Consider using '#align tensor_product.uncurry_apply TensorProduct.uncurry_applyₓ'. -/
 @[simp]
 theorem uncurry_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
@@ -848,7 +848,7 @@ def lift.equiv : (M →ₗ[R] N →ₗ[R] P) ≃ₗ[R] M ⊗ N →ₗ[R] P :=
 lean 3 declaration is
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 but is expected to have type
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_inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) 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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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toZero.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) 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_inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) 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_inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R 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R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, max u1 u2} R R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) 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R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u4, u4, u4, u4, u1, u2} R R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) 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(TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (SemilinearMapClass.distribMulActionHomClass.{u4, max (max u3 u1) u2, max (max u3 u1) u2, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P 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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u2} R R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (fun (_x : LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) => LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u4, max (max u3 u1) u2, max (max u3 u1) u2} (LinearEquiv.{u4, u4, max (max u2 u1) u3, max u2 u1 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))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u2} R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, max u1 u2} R R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u4, u4, u4, u4, u1, u2} R R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P 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_inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (SMulZeroClass.toSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toZero.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 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(LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) 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_inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) 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(CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R 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_inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R 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R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, max u1 u2} R R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) 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R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u4, u4, u4, u4, u1, u2} R R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.equiv_apply TensorProduct.lift.equiv_applyₓ'. -/
 @[simp]
 theorem lift.equiv_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
@@ -860,7 +860,7 @@ theorem lift.equiv_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
 lean 3 declaration is
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 but is expected to have type
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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u2, max u3 u1} R R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 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(RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) 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u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u2, max u3 u1} R R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u4, u4, u4, u4, u3, u1} R R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P 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(RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) 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R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u4, u4, u4, u4, u3, u1} R R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R 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(CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.equiv_symm_apply TensorProduct.lift.equiv_symm_applyₓ'. -/
 @[simp]
 theorem lift.equiv_symm_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) :
@@ -886,7 +886,7 @@ variable {R M N P}
 lean 3 declaration is
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(CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u4, u4, u4, u4, u3, u1} R R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (TensorProduct.lcurry.{u4, u2, u3, u1} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11) f) m) n) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R (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, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f (TensorProduct.tmul.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n))
 Case conversion may be inaccurate. Consider using '#align tensor_product.lcurry_apply TensorProduct.lcurry_applyₓ'. -/
 @[simp]
 theorem lcurry_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) : lcurry R M N P f m n = f (m ⊗ₜ n) :=
@@ -909,7 +909,7 @@ def curry (f : M ⊗ N →ₗ[R] P) : M →ₗ[R] N →ₗ[R] P :=
 lean 3 declaration is
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_inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_11 (TensorProduct.curry._proof_1.{u1, u4} R _inst_1 P _inst_6 _inst_11)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.curry.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) m) n) (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 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (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 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) => (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> P) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 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 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u1}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u1} P] [_inst_9 : Module.{u4, u2} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_11 : Module.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6] (f : LinearMap.{u4, u4, max u3 u2, u1} 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, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (m : M) (n : N), 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_inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (TensorProduct.curry.{u4, u2, u3, u1} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) m) n) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R (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, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f (TensorProduct.tmul.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n))
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u1}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u1} P] [_inst_9 : Module.{u4, u2} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_11 : Module.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6] (f : LinearMap.{u4, u4, max u3 u2, u1} 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, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (m : M) (n : N), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) n) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u2, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u2, max u1 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) 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_inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P 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_inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (TensorProduct.curry.{u4, u2, u3, u1} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) m) n) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R (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, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f (TensorProduct.tmul.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n))
 Case conversion may be inaccurate. Consider using '#align tensor_product.curry_apply TensorProduct.curry_applyₓ'. -/
 @[simp]
 theorem curry_apply (f : M ⊗ N →ₗ[R] P) (m : M) (n : N) : curry f m n = f (m ⊗ₜ n) :=
@@ -930,7 +930,7 @@ theorem curry_injective : Function.Injective (curry : (M ⊗[R] N →ₗ[R] P) 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] {g : LinearMap.{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))) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 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 Case conversion may be inaccurate. Consider using '#align tensor_product.ext_threefold TensorProduct.ext_threefoldₓ'. -/
 theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
     (H : ∀ x y z, g (x ⊗ₜ y ⊗ₜ z) = h (x ⊗ₜ y ⊗ₜ z)) : g = h :=
@@ -943,7 +943,7 @@ theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} {S : Type.{u6}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_8 : AddCommMonoid.{u6} S] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] [_inst_13 : Module.{u1, u6} R S (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] {g : LinearMap.{u1, u1, max (max (max u2 u3) u4) u5, u6} 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, max (max u2 u3) u4, u5} R 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 Case conversion may be inaccurate. Consider using '#align tensor_product.ext_fourfold TensorProduct.ext_fourfoldₓ'. -/
 -- We'll need this one for checking the pentagon identity!
 theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
@@ -957,7 +957,7 @@ theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.ext_fourfold' TensorProduct.ext_fourfold'ₓ'. -/
 /-- Two linear maps (M ⊗ N) ⊗ (P ⊗ Q) → S which agree on all elements of the
 form (m ⊗ₜ n) ⊗ₜ (p ⊗ₜ q) are equal. -/
@@ -1163,7 +1163,7 @@ def map (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : M ⊗ N →ₗ[R] P ⊗ Q :=
 lean 3 declaration is
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(coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (fun (_x : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u1, u3, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) 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 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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_inst_10 _inst_12) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => Q) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) g n))
+  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12) (m : M) (n : N), Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.tmul.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (LinearMap.{u5, u5, max u2 u4, max u1 u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u4 u2, max u3 u1} R R (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (TensorProduct.addCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (TensorProduct.map.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g) (TensorProduct.tmul.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u5, u3, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => P) m) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => Q) n) _inst_6 _inst_7 _inst_11 _inst_12 (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) f m) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => Q) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) g n))
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_tmul TensorProduct.map_tmulₓ'. -/
 @[simp]
 theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f g (m ⊗ₜ n) = f m ⊗ₜ g n :=
@@ -1174,7 +1174,7 @@ theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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max u4 u5} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.map.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)) (Submodule.span.{u1, max u4 u5} R (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (setOf.{max u4 u5} (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (fun (t : TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) => Exists.{succ u2} M (fun (m : M) => Exists.{succ u3} N (fun (n : N) => Eq.{succ (max u4 u5)} (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.tmul.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12 (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (fun (_x : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12) (fun (_x : LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12) => N -> Q) (LinearMap.hasCoeToFun.{u1, u1, u3, u5} R R N Q (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) g n)) t)))))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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 Case conversion may be inaccurate. Consider using '#align tensor_product.map_range_eq_span_tmul TensorProduct.map_range_eq_span_tmulₓ'. -/
 theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (map f g).range = Submodule.span R { t | ∃ m n, f m ⊗ₜ g n = t } :=
@@ -1374,7 +1374,7 @@ variable {R M N P Q}
 lean 3 declaration is
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 but is expected to have type
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(TensorProduct.mapBilinear.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12) f) g) (TensorProduct.map.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_bilinear_apply TensorProduct.mapBilinear_applyₓ'. -/
 @[simp]
 theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear R M N P Q f g = map f g :=
@@ -1385,7 +1385,7 @@ theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.ltensorHomToHomLtensor_applyₓ'. -/
 @[simp]
 theorem ltensorHomToHomLtensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
@@ -1397,7 +1397,7 @@ theorem ltensorHomToHomLtensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {P : Type.{u3}} {Q : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u4} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_11 : Module.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u4} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : 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))) M P _inst_4 _inst_6 _inst_9 _inst_11) (q : Q) (m : M), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) 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+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Type.{u3}} {P : Type.{u2}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_6 : AddCommMonoid.{u2} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_11 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6] [_inst_12 : Module.{u4, u1} R Q (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (f : LinearMap.{u4, u4, u3, u2} 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))) M P _inst_4 _inst_6 _inst_9 _inst_11) (q : Q) (m : M), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => TensorProduct.{u4, u2, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) m) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, max (succ u2) (succ u1)} ((fun 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(AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) _inst_12 f q)) m) (TensorProduct.tmul.{u4, u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => P) m) Q _inst_6 _inst_7 _inst_11 _inst_12 (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} 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))) M P _inst_4 _inst_6 _inst_9 _inst_11) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) q)
 Case conversion may be inaccurate. Consider using '#align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rtensorHomToHomRtensor_applyₓ'. -/
 @[simp]
 theorem rtensorHomToHomRtensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
@@ -1409,7 +1409,7 @@ theorem rtensorHomToHomRtensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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_inst_12) (TensorProduct.tmul.{u1, max u2 u4, max u3 u5} R _inst_1 (LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12) (LinearMap.addCommMonoid.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u5} R R N Q (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u4} R R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _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 (TensorProduct.homTensorHomMap._proof_1.{u1, u4} R _inst_1 P _inst_6 _inst_11)) (LinearMap.module.{u1, u1, u1, u3, u5} R R R N Q (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_12 (TensorProduct.homTensorHomMap._proof_2.{u1, u5} R _inst_1 Q _inst_7 _inst_12)) f g)) (TensorProduct.map.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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(Module.toMulActionWithZero.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u5, u2, u1} R R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_12 (smulCommClass_self.{u5, u1} R Q (CommSemiring.toCommMonoid.{u5} R _inst_1) (MulActionWithZero.toMulAction.{u5, u1} R Q (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (AddMonoid.toZero.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q _inst_7)) (Module.toMulActionWithZero.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_12))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u5, max u4 u2, max u3 u1} R R R (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u5, u3, u1} 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(MulActionWithZero.toMulAction.{u5, max u3 u1} R (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (AddMonoid.toZero.{max u3 u1} (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (AddCommMonoid.toAddMonoid.{max u3 u1} (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12))) (Module.toMulActionWithZero.{u5, max u3 u1} R (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u5} R _inst_1) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12))))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (TensorProduct.homTensorHomMap.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12) (TensorProduct.tmul.{u5, max u4 u3, max u2 u1} R _inst_1 (LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12) (LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u5, u4, u3} R R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_11 (smulCommClass_self.{u5, u3} R P (CommSemiring.toCommMonoid.{u5} R _inst_1) (MulActionWithZero.toMulAction.{u5, u3} R P (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_6)) (Module.toMulActionWithZero.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u5, u2, u1} R R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_12 (smulCommClass_self.{u5, u1} R Q (CommSemiring.toCommMonoid.{u5} R _inst_1) (MulActionWithZero.toMulAction.{u5, u1} R Q (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (AddMonoid.toZero.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q _inst_7)) (Module.toMulActionWithZero.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_12)))) f g)) (TensorProduct.map.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)
 Case conversion may be inaccurate. Consider using '#align tensor_product.hom_tensor_hom_map_apply TensorProduct.homTensorHomMap_applyₓ'. -/
 @[simp]
 theorem homTensorHomMap_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
@@ -1630,7 +1630,7 @@ variable (g : P →ₗ[R] Q) (f : N →ₗ[R] P)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{succ (max u2 u4)} (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (coeFn.{max (succ (max u2 u3)) (succ (max u2 u4)), max (succ (max u2 u3)) (succ (max u2 u4))} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (fun (_x : LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) => (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, max u2 u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.ltensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11 m (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f n))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u1 u4, max u3 u4} 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))) (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.ltensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u2, u4, u3} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) n) _inst_4 _inst_6 _inst_9 _inst_11 m (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u1 u4, max u3 u4} 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))) (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.ltensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u2, u4, u3} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) n) _inst_4 _inst_6 _inst_9 _inst_11 m (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n))
 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_tmul LinearMap.ltensor_tmulₓ'. -/
 @[simp]
 theorem ltensor_tmul (m : M) (n : N) : f.ltensor M (m ⊗ₜ n) = m ⊗ₜ f n :=
@@ -1641,7 +1641,7 @@ theorem ltensor_tmul (m : M) (n : N) : f.ltensor M (m ⊗ₜ n) = m ⊗ₜ f n :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{succ (max u4 u2)} (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (coeFn.{max (succ (max u3 u2)) (succ (max u4 u2)), max (succ (max u3 u2)) (succ (max u4 u2))} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (fun (_x : LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) => (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) -> (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u2, max u4 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.rtensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (TensorProduct.tmul.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f n) m)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u4 u1, max u4 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))) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.rtensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (TensorProduct.tmul.{u2, u3, u4} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) n) M _inst_6 _inst_4 _inst_11 _inst_9 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n) m)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u4 u1, max u4 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))) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.rtensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (TensorProduct.tmul.{u2, u3, u4} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) n) M _inst_6 _inst_4 _inst_11 _inst_9 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n) m)
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_tmul LinearMap.rtensor_tmulₓ'. -/
 @[simp]
 theorem rtensor_tmul (m : M) (n : N) : f.rtensor M (n ⊗ₜ m) = f n ⊗ₜ m :=
@@ -1694,7 +1694,7 @@ def rtensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], Eq.{max (max (succ u3) (succ u4)) (succ (max u2 u3)) (succ (max u2 u4))} ((fun (_x : LinearMap.{u1, u1, max u3 u4, max (max u2 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))) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align linear_map.coe_ltensor_hom LinearMap.coe_ltensorHomₓ'. -/
 @[simp]
 theorem coe_ltensorHom : (ltensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R] M ⊗[R] P) = ltensor M :=
@@ -1705,7 +1705,7 @@ theorem coe_ltensorHom : (ltensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R
 lean 3 declaration is
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 but is expected to have type
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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.rtensorHom.{u1, u4, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11)) (LinearMap.rtensor.{u1, u4, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11)
 Case conversion may be inaccurate. Consider using '#align linear_map.coe_rtensor_hom LinearMap.coe_rtensorHomₓ'. -/
 @[simp]
 theorem coe_rtensorHom : (rtensorHom M : (N →ₗ[R] P) → N ⊗[R] M →ₗ[R] P ⊗[R] M) = rtensor M :=
@@ -1794,7 +1794,7 @@ theorem ltensor_comp : (g.comp f).ltensor M = (g.ltensor M).comp (f.ltensor M) :
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_apply LinearMap.ltensor_comp_applyₓ'. -/
 theorem ltensor_comp_apply (x : M ⊗[R] N) :
     (g.comp f).ltensor M x = (g.ltensor M) ((f.ltensor M) x) := by rw [ltensor_comp, coe_comp]
@@ -1816,7 +1816,7 @@ theorem rtensor_comp : (g.comp f).rtensor M = (g.rtensor M).comp (f.rtensor M) :
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_apply LinearMap.rtensor_comp_applyₓ'. -/
 theorem rtensor_comp_apply (x : N ⊗[R] M) :
     (g.comp f).rtensor M x = (g.rtensor M) ((f.rtensor M) x) := by rw [rtensor_comp, coe_comp]
@@ -1859,7 +1859,7 @@ theorem ltensor_id : (id : N →ₗ[R] N).ltensor M = id :=
 lean 3 declaration is
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 but is expected to have type
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+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Type.{u2}) (N : Type.{u1}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (x : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) x) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u1, max u2 u1} R R (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.ltensor.{u3, u2, u1, u1} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10)) x) x
 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_id_apply LinearMap.ltensor_id_applyₓ'. -/
 -- `simp` can prove this.
 theorem ltensor_id_apply (x : M ⊗[R] N) : (LinearMap.id : N →ₗ[R] N).ltensor M x = x := by
@@ -1881,7 +1881,7 @@ theorem rtensor_id : (id : N →ₗ[R] N).rtensor M = id :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) (N : Type.{u3}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (x : TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9), Eq.{succ (max u3 u2)} (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (coeFn.{succ (max u3 u2), succ (max u3 u2)} (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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (fun (_x : 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) => (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) -> (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u2, max u3 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.rtensor.{u1, u2, u3, u3} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)) x) x
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Type.{u1}) (N : Type.{u2}) [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (x : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) x) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u1 u2, max u1 u2} R R (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.rtensor.{u3, u1, u2, u2} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10)) x) x
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Type.{u1}) (N : Type.{u2}) [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (x : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) x) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u1 u2, max u1 u2} R R (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.rtensor.{u3, u1, u2, u2} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10)) x) x
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_id_apply LinearMap.rtensor_id_applyₓ'. -/
 -- `simp` can prove this.
 theorem rtensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rtensor M x = x := by

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

@@ -2135,7 +2135,7 @@ theorem sub_tmul (m₁ m₂ : M) (n : N) : (m₁ - m₂) ⊗ₜ n = m₁ ⊗ₜ[
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)], TensorProduct.CompatibleSMul.{u1, 0, u2, u3} R _inst_1 Int Int.monoid M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8 (Module.toDistribMulAction.{0, u2} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.intModule.{u2} M _inst_2)) (Module.toDistribMulAction.{0, u3} Int N Int.semiring (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.intModule.{u3} N _inst_3))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)], TensorProduct.CompatibleSMul.{u1, 0, u2, u3} R _inst_1 Int Int.instMonoidInt M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8 (Module.toDistribMulAction.{0, u2} Int M (Ring.toSemiring.{0} Int (CommRing.toRing.{0} Int Int.instCommRingInt)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.intModule.{u2} M _inst_2)) (Module.toDistribMulAction.{0, u3} Int N (Ring.toSemiring.{0} Int (CommRing.toRing.{0} Int Int.instCommRingInt)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.intModule.{u3} N _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)], TensorProduct.CompatibleSMul.{u1, 0, u2, u3} R _inst_1 Int Int.instMonoidInt M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8 (Module.toDistribMulAction.{0, u2} Int M (CommSemiring.toSemiring.{0} Int (CommRing.toCommSemiring.{0} Int Int.instCommRingInt)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.intModule.{u2} M _inst_2)) (Module.toDistribMulAction.{0, u3} Int N (CommSemiring.toSemiring.{0} Int (CommRing.toCommSemiring.{0} Int Int.instCommRingInt)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.intModule.{u3} N _inst_3))
 Case conversion may be inaccurate. Consider using '#align tensor_product.compatible_smul.int TensorProduct.CompatibleSMul.intₓ'. -/
 /-- While the tensor product will automatically inherit a ℤ-module structure from
 `add_comm_group.int_module`, that structure won't be compatible with lemmas like `tmul_smul` unless

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

@@ -1195,7 +1195,7 @@ theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {P : Type.{u2}} {Q : Type.{u3}} [_inst_6 : AddCommMonoid.{u2} P] [_inst_7 : AddCommMonoid.{u3} Q] [_inst_11 : Module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (p : Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) (q : Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12), 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 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) P (Submodule.setLike.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)) p) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) Q (Submodule.setLike.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12)) q) (Submodule.addCommMonoid.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.addCommMonoid.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q) (Submodule.module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.module.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q)) (TensorProduct.{u1, u2, u3} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) P (Submodule.setLike.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)) p) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) Q (Submodule.setLike.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12)) q) (Submodule.addCommMonoid.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.addCommMonoid.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q) (Submodule.module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.module.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) P (Submodule.setLike.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)) p) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) Q (Submodule.setLike.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12)) q) (Submodule.addCommMonoid.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.addCommMonoid.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q) (Submodule.module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.module.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q)) (TensorProduct.module.{u1, u2, u3} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {P : Type.{u2}} {Q : Type.{u3}} [_inst_6 : AddCommMonoid.{u2} P] [_inst_7 : AddCommMonoid.{u3} Q] [_inst_11 : Module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (p : Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) (q : Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12), 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 (Subtype.{succ u2} P (fun (x : P) => Membership.mem.{u2, u2} P (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) P (Submodule.instSetLikeSubmodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)) x p)) (Subtype.{succ u3} Q (fun (x : Q) => Membership.mem.{u3, u3} Q (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) Q (Submodule.instSetLikeSubmodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12)) x q)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q)) (TensorProduct.{u1, u2, u3} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 (Subtype.{succ u2} P (fun (x : P) => Membership.mem.{u2, u2} P (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) P (Submodule.instSetLikeSubmodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)) x p)) (Subtype.{succ u3} Q (fun (x : Q) => Membership.mem.{u3, u3} Q (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) Q (Submodule.instSetLikeSubmodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12)) x q)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 (Subtype.{succ u2} P (fun (x : P) => Membership.mem.{u2, u2} P (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) P (Submodule.instSetLikeSubmodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)) x p)) (Subtype.{succ u3} Q (fun (x : Q) => Membership.mem.{u3, u3} Q (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) Q (Submodule.instSetLikeSubmodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12)) x q)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {P : Type.{u2}} {Q : Type.{u3}} [_inst_6 : AddCommMonoid.{u2} P] [_inst_7 : AddCommMonoid.{u3} Q] [_inst_11 : Module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (p : Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) (q : Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12), 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 (Subtype.{succ u2} P (fun (x : P) => Membership.mem.{u2, u2} P (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) P (Submodule.setLike.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)) x p)) (Subtype.{succ u3} Q (fun (x : Q) => Membership.mem.{u3, u3} Q (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) Q (Submodule.setLike.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12)) x q)) (Submodule.addCommMonoid.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.addCommMonoid.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q) (Submodule.module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.module.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q)) (TensorProduct.{u1, u2, u3} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 (Subtype.{succ u2} P (fun (x : P) => Membership.mem.{u2, u2} P (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) P (Submodule.setLike.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)) x p)) (Subtype.{succ u3} Q (fun (x : Q) => Membership.mem.{u3, u3} Q (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) Q (Submodule.setLike.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12)) x q)) (Submodule.addCommMonoid.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.addCommMonoid.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q) (Submodule.module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.module.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 (Subtype.{succ u2} P (fun (x : P) => Membership.mem.{u2, u2} P (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11) P (Submodule.setLike.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)) x p)) (Subtype.{succ u3} Q (fun (x : Q) => Membership.mem.{u3, u3} Q (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12) Q (Submodule.setLike.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12)) x q)) (Submodule.addCommMonoid.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.addCommMonoid.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q) (Submodule.module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11 p) (Submodule.module.{u1, u3} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 _inst_12 q)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_incl TensorProduct.mapInclₓ'. -/
 /-- Given submodules `p ⊆ P` and `q ⊆ Q`, this is the natural map: `p ⊗ q → P ⊗ Q`. -/
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -2066,7 +2066,7 @@ protected theorem add_left_neg (x : M ⊗[R] N) : -x + x = 0 :=
       rw [add_zero]
       apply (neg.aux R).map_zero)
     (fun x y => by
-      convert (add_tmul (-x) x y).symm
+      convert(add_tmul (-x) x y).symm
       rw [add_left_neg, zero_tmul])
     fun x y hx hy => by
     unfold Neg.neg SubNegMonoid.neg

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

@@ -278,7 +278,7 @@ def SMul.aux {R' : Type _} [SMul R' M] (r : R') : FreeAddMonoid (M × N) →+ M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] {R' : Type.{u4}} [_inst_16 : SMul.{u4, u2} R' M] (r : R') (m : M) (n : N), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (AddRightCancelMonoid.toAddMonoid.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (FreeAddMonoid.cancelAddMonoid.{max u2 u3} (Prod.{u2, u3} M N))))) (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (fun (_x : AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (AddRightCancelMonoid.toAddMonoid.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (FreeAddMonoid.cancelAddMonoid.{max u2 u3} (Prod.{u2, u3} M N))))) (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) => (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) -> (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (AddMonoidHom.hasCoeToFun.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (AddRightCancelMonoid.toAddMonoid.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (FreeAddMonoid.cancelAddMonoid.{max u2 u3} (Prod.{u2, u3} M N))))) (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (TensorProduct.SMul.aux.{u1, u2, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 R' _inst_16 r) (FreeAddMonoid.of.{max u2 u3} (Prod.{u2, u3} M N) (Prod.mk.{u2, u3} M N m n))) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 (SMul.smul.{u4, u2} R' M _inst_16 r m) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u3}} {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] {R' : Type.{u4}} [_inst_16 : SMul.{u4, u3} R' M] (r : R') (m : M) (n : N), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) => TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (FreeAddMonoid.of.{max u2 u3} (Prod.{u3, u2} M N) (Prod.mk.{u3, u2} M N m n))) (FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u3)} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (fun (_x : FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) => TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _x) (AddHomClass.toFunLike.{max u2 u3, max u2 u3, max u2 u3} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toAdd.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N)))))) (AddZeroClass.toAdd.{max u2 u3} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (AddMonoidHomClass.toAddHomClass.{max u2 u3, max u2 u3, max u2 u3} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoidHom.addMonoidHomClass.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)))) (TensorProduct.SMul.aux.{u1, u3, u2, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 R' _inst_16 r) (FreeAddMonoid.of.{max u2 u3} (Prod.{u3, u2} M N) (Prod.mk.{u3, u2} M N m n))) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 (HSMul.hSMul.{u4, u3, u3} R' M M (instHSMul.{u4, u3} R' M _inst_16) r m) n)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u3}} {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] {R' : Type.{u4}} [_inst_16 : SMul.{u4, u3} R' M] (r : R') (m : M) (n : N), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) => TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (FreeAddMonoid.of.{max u2 u3} (Prod.{u3, u2} M N) (Prod.mk.{u3, u2} M N m n))) (FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u3)} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (fun (_x : FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) => TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _x) (AddHomClass.toFunLike.{max u2 u3, max u2 u3, max u2 u3} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toAdd.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N)))))) (AddZeroClass.toAdd.{max u2 u3} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (AddMonoidHomClass.toAddHomClass.{max u2 u3, max u2 u3, max u2 u3} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoidHom.addMonoidHomClass.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)))) (TensorProduct.SMul.aux.{u1, u3, u2, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 R' _inst_16 r) (FreeAddMonoid.of.{max u2 u3} (Prod.{u3, u2} M N) (Prod.mk.{u3, u2} M N m n))) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 (HSMul.hSMul.{u4, u3, u3} R' M M (instHSMul.{u4, u3} R' M _inst_16) r m) n)
 Case conversion may be inaccurate. Consider using '#align tensor_product.smul.aux_of TensorProduct.SMul.aux_ofₓ'. -/
 theorem SMul.aux_of {R' : Type _} [SMul R' M] (r : R') (m : M) (n : N) :
     SMul.aux r (FreeAddMonoid.of (m, n)) = (r • m) ⊗ₜ[R] n :=
@@ -543,7 +543,7 @@ variable {R M N}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (m : M) (n : N), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, 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))) N (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (fun (_x : LinearMap.{u1, u1, 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))) N (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) => N -> (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} R R N (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u1} 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_inst_9 _inst_10) (TensorProduct.mk._proof_1.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) (fun (_x : LinearMap.{u1, u1, u2, 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))) M (LinearMap.{u1, u1, 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))) N (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, max u2 u3} R R N (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R 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(TensorProduct.mk._proof_1.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) => M -> (LinearMap.{u1, u1, 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))) N (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u3} R R M (LinearMap.{u1, u1, 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))) N (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, max u2 u3} R R N (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, max u2 u3} R R R N (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M 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 but is expected to have type
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_inst_4 _inst_5 _inst_9 _inst_10) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u2, max u3 u2} R R N (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, max u3 u2} R R R N 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_inst_1)) (AddMonoid.toZero.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddCommMonoid.toAddMonoid.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) (Module.toMulActionWithZero.{u1, max u3 u2} R (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.mk.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) m) n) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)
 Case conversion may be inaccurate. Consider using '#align tensor_product.mk_apply TensorProduct.mk_applyₓ'. -/
 @[simp]
 theorem mk_apply (m : M) (n : N) : mk R M N m n = m ⊗ₜ n :=
@@ -677,7 +677,7 @@ def liftAux : M ⊗[R] N →+ P :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (f : LinearMap.{u1, u1, u2, max 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 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11))))) (m : M) (n : N), Eq.{succ u4} P (coeFn.{max (succ u4) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u4)} (AddMonoidHom.{max u2 u3, u4} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (fun (_x : AddMonoidHom.{max u2 u3, u4} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) => (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> P) (AddMonoidHom.hasCoeToFun.{max u2 u3, u4} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (TensorProduct.liftAux.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max 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 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11))))) (fun (_x : LinearMap.{u1, u1, u2, max 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 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11))))) => M -> (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))) N P _inst_5 _inst_6 _inst_10 _inst_11)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u2}} {N : Type.{u1}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_11 : Module.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6] (f : LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11))))) (m : M) (n : N), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) (TensorProduct.tmul.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), max (succ u2) (succ u1), succ u4} (AddMonoidHom.{max u1 u2, u4} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) _x) (AddHomClass.toFunLike.{max (max u2 u1) u4, max u2 u1, u4} (AddMonoidHom.{max u1 u2, u4} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (AddZeroClass.toAdd.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (AddZeroClass.toAdd.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (AddMonoidHomClass.toAddHomClass.{max (max u2 u1) u4, max u2 u1, u4} (AddMonoidHom.{max u1 u2, u4} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (AddMonoidHom.addMonoidHomClass.{max u2 u1, u4} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))))) (TensorProduct.liftAux.{u3, u2, u1, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), succ u2, max (succ u1) (succ u4)} (LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u1 u4} R R M (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) f m) n)
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u2}} {N : Type.{u1}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_11 : Module.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6] (f : LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11))))) (m : M) (n : N), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) (TensorProduct.tmul.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), max (succ u2) (succ u1), succ u4} (AddMonoidHom.{max u1 u2, u4} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) _x) (AddHomClass.toFunLike.{max (max u2 u1) u4, max u2 u1, u4} (AddMonoidHom.{max u1 u2, u4} (TensorProduct.{u3, u2, u1} R _inst_1 M 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_inst_10) P (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (AddMonoidHom.addMonoidHomClass.{max u2 u1, u4} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))))) (TensorProduct.liftAux.{u3, u2, u1, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), succ u2, max (succ u1) (succ u4)} (LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u1 u4} R R M (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) f m) n)
 Case conversion may be inaccurate. Consider using '#align tensor_product.lift_aux_tmul TensorProduct.liftAux_tmulₓ'. -/
 theorem liftAux_tmul (m n) : liftAux f (m ⊗ₜ n) = f m n :=
   rfl
@@ -689,7 +689,7 @@ variable {f}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] {f : LinearMap.{u1, u1, u2, max 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 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11))))} (r : R) (x : TensorProduct.{u1, u2, u3} R _inst_1 M N 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(CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)))) r (coeFn.{max (succ u4) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u4)} (AddMonoidHom.{max u2 u3, u4} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (fun (_x : AddMonoidHom.{max u2 u3, u4} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) => (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> P) (AddMonoidHom.hasCoeToFun.{max u2 u3, u4} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (TensorProduct.liftAux.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) x))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Type.{u3}} {N : Type.{u2}} {P : Type.{u1}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u1} P] [_inst_9 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_11 : Module.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6] {f : LinearMap.{u4, u4, u3, max u1 u2} 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))) M (LinearMap.{u4, u4, u2, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u2, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u2, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))} (r : R) (x : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) (HSMul.hSMul.{u4, max u3 u2, max u3 u2} R (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u4, max u3 u2} R (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instSMulTensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) r x)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (AddMonoidHom.{max u2 u3, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 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u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u4, max u3 u2} R (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instSMulTensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) r x)) (HSMul.hSMul.{u4, u1, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (instHSMul.{u4, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (SMulZeroClass.toSMul.{u4, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) _inst_6)) (SMulWithZero.toSMulZeroClass.{u4, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) _inst_6)) (MulActionWithZero.toSMulWithZero.{u4, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) _inst_6)) (Module.toMulActionWithZero.{u4, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) r (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (AddMonoidHom.{max u2 u3, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) _x) (AddHomClass.toFunLike.{max (max u3 u2) u1, max u3 u2, u1} (AddMonoidHom.{max u2 u3, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (AddZeroClass.toAdd.{max u3 u2} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (AddZeroClass.toAdd.{u1} P (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (AddMonoidHomClass.toAddHomClass.{max (max u3 u2) u1, max u3 u2, u1} (AddMonoidHom.{max u2 u3, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (AddMonoidHom.addMonoidHomClass.{max u3 u2, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))))) (TensorProduct.liftAux.{u4, u3, u2, u1} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) x))
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Type.{u3}} {N : Type.{u2}} {P : Type.{u1}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u1} P] [_inst_9 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_11 : Module.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6] {f : LinearMap.{u4, u4, u3, max u1 u2} 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))) M (LinearMap.{u4, u4, u2, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u2, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u2, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))} (r : R) (x : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) (HSMul.hSMul.{u4, max u3 u2, max u3 u2} R (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u4, max u3 u2} R (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instSMulTensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) r x)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (AddMonoidHom.{max u2 u3, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) _x) (AddHomClass.toFunLike.{max (max u3 u2) u1, max u3 u2, u1} (AddMonoidHom.{max u2 u3, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (AddZeroClass.toAdd.{max u3 u2} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (AddZeroClass.toAdd.{u1} P (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (AddMonoidHomClass.toAddHomClass.{max (max u3 u2) u1, max u3 u2, u1} (AddMonoidHom.{max u2 u3, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (AddMonoidHom.addMonoidHomClass.{max u3 u2, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))))) (TensorProduct.liftAux.{u4, u3, u2, u1} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (HSMul.hSMul.{u4, max u3 u2, max u3 u2} R (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u4, max u3 u2} R (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instSMulTensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) r x)) (HSMul.hSMul.{u4, u1, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (instHSMul.{u4, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (SMulZeroClass.toSMul.{u4, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) _inst_6)) (SMulWithZero.toSMulZeroClass.{u4, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) _inst_6)) (MulActionWithZero.toSMulWithZero.{u4, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) _inst_6)) (Module.toMulActionWithZero.{u4, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) x) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) r (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (AddMonoidHom.{max u2 u3, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) _x) (AddHomClass.toFunLike.{max (max u3 u2) u1, max u3 u2, u1} (AddMonoidHom.{max u2 u3, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (AddZeroClass.toAdd.{max u3 u2} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (AddZeroClass.toAdd.{u1} P (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (AddMonoidHomClass.toAddHomClass.{max (max u3 u2) u1, max u3 u2, u1} (AddMonoidHom.{max u2 u3, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (AddMonoidHom.addMonoidHomClass.{max u3 u2, u1} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddMonoid.toAddZeroClass.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6))))) (TensorProduct.liftAux.{u4, u3, u2, u1} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) x))
 Case conversion may be inaccurate. Consider using '#align tensor_product.lift_aux.smul TensorProduct.liftAux.smulₓ'. -/
 @[simp]
 theorem liftAux.smul (r : R) (x) : liftAux f (r • x) = r • liftAux f x :=
@@ -716,7 +716,7 @@ variable {f}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] {f : LinearMap.{u1, u1, u2, max 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 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11))))} (x : M) (y : N), Eq.{succ u4} P (coeFn.{max (succ (max 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 but is expected to have type
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(fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u1, u4} R R (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (TensorProduct.lift.{u3, u2, u1, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x y)) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) x) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), succ u2, max (succ u1) (succ u4)} (LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u1 u4} R R M (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) f x) y)
 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.tmul TensorProduct.lift.tmulₓ'. -/
 @[simp]
 theorem lift.tmul (x y) : lift f (x ⊗ₜ y) = f x y :=
@@ -727,7 +727,7 @@ theorem lift.tmul (x y) : lift f (x ⊗ₜ y) = f x y :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] {f : LinearMap.{u1, u1, u2, max 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 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11))))} (x : M) (y : N), Eq.{succ u4} P (LinearMap.toFun.{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 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (TensorProduct.lift.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x y)) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max 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 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11))))) (fun (_x : LinearMap.{u1, u1, u2, max 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 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11))))) => M -> (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))) N P _inst_5 _inst_6 _inst_10 _inst_11)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_9 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _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, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x) y)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u2}} {N : Type.{u1}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_11 : Module.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6] {f : LinearMap.{u3, u3, u2, max u4 u1} 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 (LinearMap.{u3, u3, u1, 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u3, u3, u1, u4} R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u4} R R R N P (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_11 (smulCommClass_self.{u3, u4} R P (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u4} R P (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_6)) (Module.toMulActionWithZero.{u3, u4} R P (CommSemiring.toSemiring.{u3} R _inst_1) _inst_6 _inst_11))))} (x : M) (y : N), Eq.{succ u4} ((fun 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.tmul' TensorProduct.lift.tmul'ₓ'. -/
 @[simp]
 theorem lift.tmul' (x y) : (lift f).1 (x ⊗ₜ y) = f x y :=
@@ -738,7 +738,7 @@ theorem lift.tmul' (x y) : (lift f).1 (x ⊗ₜ y) = f x y :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align tensor_product.ext' TensorProduct.ext'ₓ'. -/
 theorem ext' {g h : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x ⊗ₜ y)) : g = h :=
   LinearMap.ext fun z =>
@@ -750,7 +750,7 @@ theorem ext' {g h : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.unique TensorProduct.lift.uniqueₓ'. -/
 theorem lift.unique {g : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = f x y) : g = lift f :=
   ext' fun m n => by rw [H, lift.tmul]
@@ -823,7 +823,7 @@ variable {R M N P}
 lean 3 declaration is
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(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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R 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(LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P 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 Case conversion may be inaccurate. Consider using '#align tensor_product.uncurry_apply TensorProduct.uncurry_applyₓ'. -/
 @[simp]
 theorem uncurry_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
@@ -848,7 +848,7 @@ def lift.equiv : (M →ₗ[R] N →ₗ[R] P) ≃ₗ[R] M ⊗ N →ₗ[R] P :=
 lean 3 declaration is
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 but is expected to have type
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P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R 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(SMulHomClass.toFunLike.{max (max u3 u1) u2, u4, max (max u3 u1) u2, max (max u3 u1) u2} (LinearEquiv.{u4, u4, max (max u2 u1) u3, max u2 u1 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))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N 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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P 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_inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (SMulZeroClass.toSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toZero.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} 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(LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) 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_inst_10) _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u2} R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u2} R R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (SemilinearMapClass.distribMulActionHomClass.{u4, max (max u3 u1) u2, max (max u3 u1) u2, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, 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_inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, max u1 u2} R R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u2} R R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (fun (_x : LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) => LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u4, max (max u3 u1) u2, max (max u3 u1) u2} (LinearEquiv.{u4, u4, max (max u2 u1) u3, max u2 u1 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))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u2} R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, max u1 u2} R R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) 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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u2} R P 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_inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (SMulZeroClass.toSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toZero.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, max u1 u2} R R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R 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_inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.equiv_apply TensorProduct.lift.equiv_applyₓ'. -/
 @[simp]
 theorem lift.equiv_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
@@ -860,7 +860,7 @@ theorem lift.equiv_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
 lean 3 declaration is
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(AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, 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_inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, 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_inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u2, max u3 u1} R R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 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(CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P 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 Case conversion may be inaccurate. Consider using '#align tensor_product.lift.equiv_symm_apply TensorProduct.lift.equiv_symm_applyₓ'. -/
 @[simp]
 theorem lift.equiv_symm_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) :
@@ -886,7 +886,7 @@ variable {R M N P}
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.lcurry_apply TensorProduct.lcurry_applyₓ'. -/
 @[simp]
 theorem lcurry_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) : lcurry R M N P f m n = f (m ⊗ₜ n) :=
@@ -909,7 +909,7 @@ def curry (f : M ⊗ N →ₗ[R] P) : M →ₗ[R] N →ₗ[R] P :=
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.curry_apply TensorProduct.curry_applyₓ'. -/
 @[simp]
 theorem curry_apply (f : M ⊗ N →ₗ[R] P) (m : M) (n : N) : curry f m n = f (m ⊗ₜ n) :=
@@ -930,7 +930,7 @@ theorem curry_injective : Function.Injective (curry : (M ⊗[R] N →ₗ[R] P) 
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.ext_threefold TensorProduct.ext_threefoldₓ'. -/
 theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
     (H : ∀ x y z, g (x ⊗ₜ y ⊗ₜ z) = h (x ⊗ₜ y ⊗ₜ z)) : g = h :=
@@ -943,7 +943,7 @@ theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align tensor_product.ext_fourfold TensorProduct.ext_fourfoldₓ'. -/
 -- We'll need this one for checking the pentagon identity!
 theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
@@ -957,7 +957,7 @@ theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
 lean 3 declaration is
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(TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) _inst_8 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, max u2 u3, max u4 u5} R _inst_1 (TensorProduct.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) _inst_13 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) ψ (TensorProduct.tmul.{u6, max u2 u3, max u4 u5} R _inst_1 (TensorProduct.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.tmul.{u6, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 w x) (TensorProduct.tmul.{u6, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12 y z)))) -> (Eq.{max (max (max (max (succ u2) (succ u3)) (succ u4)) (succ u5)) (succ u1)} (LinearMap.{u6, u6, max (max u5 u4) u3 u2, u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R 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 Case conversion may be inaccurate. Consider using '#align tensor_product.ext_fourfold' TensorProduct.ext_fourfold'ₓ'. -/
 /-- Two linear maps (M ⊗ N) ⊗ (P ⊗ Q) → S which agree on all elements of the
 form (m ⊗ₜ n) ⊗ₜ (p ⊗ₜ q) are equal. -/
@@ -1163,7 +1163,7 @@ def map (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : M ⊗ N →ₗ[R] P ⊗ Q :=
 lean 3 declaration is
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(coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (fun (_x : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u1, u3, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) 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 but is expected to have type
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Q) n) _inst_6 _inst_7 _inst_11 _inst_12 (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) f m) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => Q) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) g n))
+  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12) (m : M) (n : N), Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.tmul.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (LinearMap.{u5, u5, max u2 u4, max u1 u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u5, u4, 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Q) n) _inst_6 _inst_7 _inst_11 _inst_12 (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) f m) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => Q) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) g n))
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_tmul TensorProduct.map_tmulₓ'. -/
 @[simp]
 theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f g (m ⊗ₜ n) = f m ⊗ₜ g n :=
@@ -1174,7 +1174,7 @@ theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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max u4 u5} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.map.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)) (Submodule.span.{u1, max u4 u5} R (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (setOf.{max u4 u5} (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (fun (t : TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) => Exists.{succ u2} M (fun (m : M) => Exists.{succ u3} N (fun (n : N) => Eq.{succ (max u4 u5)} (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.tmul.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12 (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (fun (_x : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12) (fun (_x : LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12) => N -> Q) (LinearMap.hasCoeToFun.{u1, u1, u3, u5} R R N Q (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) g n)) t)))))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => Q) n) _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.tmul.{u5, u3, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => P) m) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => Q) n) _inst_6 _inst_7 _inst_11 _inst_12 (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) f m) 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+  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => Q) n) _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.tmul.{u5, u3, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => P) m) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => Q) n) _inst_6 _inst_7 _inst_11 _inst_12 (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) f m) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => Q) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) g n)) t)))))
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_range_eq_span_tmul TensorProduct.map_range_eq_span_tmulₓ'. -/
 theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (map f g).range = Submodule.span R { t | ∃ m n, f m ⊗ₜ g n = t } :=
@@ -1374,7 +1374,7 @@ variable {R M N P Q}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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 but is expected to have type
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(TensorProduct.mapBilinear.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12) f) g) (TensorProduct.map.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)
 Case conversion may be inaccurate. Consider using '#align tensor_product.map_bilinear_apply TensorProduct.mapBilinear_applyₓ'. -/
 @[simp]
 theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear R M N P Q f g = map f g :=
@@ -1385,7 +1385,7 @@ theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {P : Type.{u3}} {Q : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u4} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_11 : Module.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u4} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (p : P) (f : LinearMap.{u1, u1, 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 Q _inst_4 _inst_7 _inst_9 _inst_12) (m : M), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.ltensorHomToHomLtensor_applyₓ'. -/
 @[simp]
 theorem ltensorHomToHomLtensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
@@ -1397,7 +1397,7 @@ theorem ltensorHomToHomLtensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {P : Type.{u3}} {Q : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u4} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_11 : Module.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u4} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : 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))) M P _inst_4 _inst_6 _inst_9 _inst_11) (q : Q) (m : M), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) 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_inst_1)))) f m) q)
 Case conversion may be inaccurate. Consider using '#align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rtensorHomToHomRtensor_applyₓ'. -/
 @[simp]
 theorem rtensorHomToHomRtensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
@@ -1409,7 +1409,7 @@ theorem rtensorHomToHomRtensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7] (f : LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u1, u1, u3, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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_inst_12) (TensorProduct.tmul.{u1, max u2 u4, max u3 u5} R _inst_1 (LinearMap.{u1, u1, 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 P _inst_4 _inst_6 _inst_9 _inst_11) (LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12) (LinearMap.addCommMonoid.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u5} R R N Q (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u4} R R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _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 (TensorProduct.homTensorHomMap._proof_1.{u1, u4} R _inst_1 P _inst_6 _inst_11)) (LinearMap.module.{u1, u1, u1, u3, u5} R R R N Q (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_12 (TensorProduct.homTensorHomMap._proof_2.{u1, u5} R _inst_1 Q _inst_7 _inst_12)) f g)) (TensorProduct.map.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : CommSemiring.{u5} R] {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} {Q : Type.{u1}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_7 : AddCommMonoid.{u1} Q] [_inst_9 : Module.{u5, u4} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4] [_inst_10 : Module.{u5, u2} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5] [_inst_11 : Module.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6] [_inst_12 : Module.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (f : LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (g : LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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(Module.toMulActionWithZero.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u5, u2, u1} R R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_12 (smulCommClass_self.{u5, u1} R Q (CommSemiring.toCommMonoid.{u5} R _inst_1) (MulActionWithZero.toMulAction.{u5, u1} R Q (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (AddMonoid.toZero.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q _inst_7)) (Module.toMulActionWithZero.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_12))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u5, max u4 u2, max u3 u1} R R R (TensorProduct.{u5, u4, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u5, u3, u1} 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(MulActionWithZero.toMulAction.{u5, max u3 u1} R (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (AddMonoid.toZero.{max u3 u1} (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (AddCommMonoid.toAddMonoid.{max u3 u1} (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12))) (Module.toMulActionWithZero.{u5, max u3 u1} R (TensorProduct.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u5} R _inst_1) (TensorProduct.addCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u5, u3, u1} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12))))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (TensorProduct.homTensorHomMap.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12) (TensorProduct.tmul.{u5, max u4 u3, max u2 u1} R _inst_1 (LinearMap.{u5, u5, u4, u3} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M P _inst_4 _inst_6 _inst_9 _inst_11) (LinearMap.{u5, u5, u2, u1} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) N Q _inst_5 _inst_7 _inst_10 _inst_12) (LinearMap.addCommMonoid.{u5, u5, u4, u3} R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (LinearMap.addCommMonoid.{u5, u5, u2, u1} R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u5, u4, u3} R R R M P (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_4 _inst_6 _inst_9 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_11 (smulCommClass_self.{u5, u3} R P (CommSemiring.toCommMonoid.{u5} R _inst_1) (MulActionWithZero.toMulAction.{u5, u3} R P (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_6)) (Module.toMulActionWithZero.{u5, u3} R P (CommSemiring.toSemiring.{u5} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u5, u5, u5, u2, u1} R R R N Q (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_12 (smulCommClass_self.{u5, u1} R Q (CommSemiring.toCommMonoid.{u5} R _inst_1) (MulActionWithZero.toMulAction.{u5, u1} R Q (Semiring.toMonoidWithZero.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)) (AddMonoid.toZero.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q _inst_7)) (Module.toMulActionWithZero.{u5, u1} R Q (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_12)))) f g)) (TensorProduct.map.{u5, u4, u2, u3, u1} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)
 Case conversion may be inaccurate. Consider using '#align tensor_product.hom_tensor_hom_map_apply TensorProduct.homTensorHomMap_applyₓ'. -/
 @[simp]
 theorem homTensorHomMap_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
@@ -1630,7 +1630,7 @@ variable (g : P →ₗ[R] Q) (f : N →ₗ[R] P)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{succ (max u2 u4)} (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (coeFn.{max (succ (max u2 u3)) (succ (max u2 u4)), max (succ (max u2 u3)) (succ (max u2 u4))} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (fun (_x : LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) => (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, max u2 u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.ltensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11 m (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f n))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u1 u4, max u3 u4} 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))) (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.ltensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u2, u4, u3} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => P) n) _inst_4 _inst_6 _inst_9 _inst_11 m (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u1 u4, max u3 u4} 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))) (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u4, u3} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.ltensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u2, u4, u3} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) n) _inst_4 _inst_6 _inst_9 _inst_11 m (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n))
 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_tmul LinearMap.ltensor_tmulₓ'. -/
 @[simp]
 theorem ltensor_tmul (m : M) (n : N) : f.ltensor M (m ⊗ₜ n) = m ⊗ₜ f n :=
@@ -1641,7 +1641,7 @@ theorem ltensor_tmul (m : M) (n : N) : f.ltensor M (m ⊗ₜ n) = m ⊗ₜ f n :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{succ (max u4 u2)} (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (coeFn.{max (succ (max u3 u2)) (succ (max u4 u2)), max (succ (max u3 u2)) (succ (max u4 u2))} (LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (fun (_x : LinearMap.{u1, u1, max u3 u2, max u4 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) => (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) -> (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u2, max u4 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.rtensor.{u1, u2, u3, u4} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (TensorProduct.tmul.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f n) m)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u4 u1, max u4 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))) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.rtensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (TensorProduct.tmul.{u2, u3, u4} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => P) n) M _inst_6 _inst_4 _inst_11 _inst_9 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n) m)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Type.{u4}) {N : Type.{u1}} {P : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_6 : AddCommMonoid.{u3} P] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u1} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_11 : Module.{u2, u3} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (m : M) (n : N), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u2, u2, max u4 u1, max u4 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))) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9)) (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u1, max u4 u3} R R (TensorProduct.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (TensorProduct.addCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u3, u4} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.rtensor.{u2, u4, u1, u3} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 f) (TensorProduct.tmul.{u2, u1, u4} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9 n m)) (TensorProduct.tmul.{u2, u3, u4} R _inst_1 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) n) M _inst_6 _inst_4 _inst_11 _inst_9 (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f n) m)
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_tmul LinearMap.rtensor_tmulₓ'. -/
 @[simp]
 theorem rtensor_tmul (m : M) (n : N) : f.rtensor M (n ⊗ₜ m) = f n ⊗ₜ m :=
@@ -1694,7 +1694,7 @@ def rtensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], Eq.{max (max (succ u3) (succ u4)) (succ (max u2 u3)) (succ (max u2 u4))} ((fun (_x : LinearMap.{u1, u1, max u3 u4, max (max u2 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))) (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11)) (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align linear_map.coe_ltensor_hom LinearMap.coe_ltensorHomₓ'. -/
 @[simp]
 theorem coe_ltensorHom : (ltensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R] M ⊗[R] P) = ltensor M :=
@@ -1705,7 +1705,7 @@ theorem coe_ltensorHom : (ltensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R
 lean 3 declaration is
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 but is expected to have type
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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.rtensorHom.{u1, u4, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11)) (LinearMap.rtensor.{u1, u4, u3, u2} R _inst_1 M N P _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11)
 Case conversion may be inaccurate. Consider using '#align linear_map.coe_rtensor_hom LinearMap.coe_rtensorHomₓ'. -/
 @[simp]
 theorem coe_rtensorHom : (rtensorHom M : (N →ₗ[R] P) → N ⊗[R] M →ₗ[R] P ⊗[R] M) = rtensor M :=
@@ -1794,7 +1794,7 @@ theorem ltensor_comp : (g.comp f).ltensor M = (g.ltensor M).comp (f.ltensor M) :
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_apply LinearMap.ltensor_comp_applyₓ'. -/
 theorem ltensor_comp_apply (x : M ⊗[R] N) :
     (g.comp f).ltensor M x = (g.ltensor M) ((f.ltensor M) x) := by rw [ltensor_comp, coe_comp]
@@ -1816,7 +1816,7 @@ theorem rtensor_comp : (g.comp f).rtensor M = (g.rtensor M).comp (f.rtensor M) :
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_apply LinearMap.rtensor_comp_applyₓ'. -/
 theorem rtensor_comp_apply (x : N ⊗[R] M) :
     (g.comp f).rtensor M x = (g.rtensor M) ((f.rtensor M) x) := by rw [rtensor_comp, coe_comp]
@@ -1859,7 +1859,7 @@ theorem ltensor_id : (id : N →ₗ[R] N).ltensor M = id :=
 lean 3 declaration is
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 but is expected to have type
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+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Type.{u2}) (N : Type.{u1}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (x : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) x) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) => TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u1, max u2 u1} R R (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.ltensor.{u3, u2, u1, u1} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10)) x) x
 Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_id_apply LinearMap.ltensor_id_applyₓ'. -/
 -- `simp` can prove this.
 theorem ltensor_id_apply (x : M ⊗[R] N) : (LinearMap.id : N →ₗ[R] N).ltensor M x = x := by
@@ -1881,7 +1881,7 @@ theorem rtensor_id : (id : N →ₗ[R] N).rtensor M = id :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) (N : Type.{u3}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (x : TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9), Eq.{succ (max u3 u2)} (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (coeFn.{succ (max u3 u2), succ (max u3 u2)} (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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (fun (_x : 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, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) => (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) -> (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u2, max u3 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.rtensor.{u1, u2, u3, u3} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)) x) x
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Type.{u1}) (N : Type.{u2}) [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (x : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) x) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u1 u2, max u1 u2} R R (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.rtensor.{u3, u1, u2, u2} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10)) x) x
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Type.{u1}) (N : Type.{u2}) [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] (x : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) x) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u3, u3, max u1 u2, max u1 u2} 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))) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9)) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) => TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u1 u2, max u1 u2} R R (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.rtensor.{u3, u1, u2, u2} R _inst_1 M N N _inst_4 _inst_5 _inst_5 _inst_9 _inst_10 _inst_10 (LinearMap.id.{u3, u2} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_10)) x) x
 Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_id_apply LinearMap.rtensor_id_applyₓ'. -/
 -- `simp` can prove this.
 theorem rtensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rtensor M x = x := by
@@ -2029,7 +2029,7 @@ variable {R}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] (m : M) (n : N), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (TensorProduct.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (AddMonoid.toAddZeroClass.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (AddRightCancelMonoid.toAddMonoid.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (FreeAddMonoid.cancelAddMonoid.{max u2 u3} (Prod.{u2, u3} M N))))) (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8)) (fun (_x : AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (TensorProduct.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (AddMonoid.toAddZeroClass.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (AddRightCancelMonoid.toAddMonoid.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (FreeAddMonoid.cancelAddMonoid.{max u2 u3} (Prod.{u2, u3} M N))))) (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8)) => (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) -> (TensorProduct.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8)) (AddMonoidHom.hasCoeToFun.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (TensorProduct.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8) (AddMonoid.toAddZeroClass.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (AddRightCancelMonoid.toAddMonoid.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u2, u3} M N)) (FreeAddMonoid.cancelAddMonoid.{max u2 u3} (Prod.{u2, u3} M N))))) (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8)) (TensorProduct.Neg.aux.{u1, u2, u3} R _inst_1 M N _inst_2 _inst_3 _inst_7 _inst_8) (FreeAddMonoid.of.{max u2 u3} (Prod.{u2, u3} M N) (Prod.mk.{u2, u3} M N m n))) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8 (Neg.neg.{u2} M (SubNegMonoid.toHasNeg.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))) m) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u3}} {N : Type.{u2}} [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} N] [_inst_7 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_8 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3)] (m : M) (n : N), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) => TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (FreeAddMonoid.of.{max u2 u3} (Prod.{u3, u2} M N) (Prod.mk.{u3, u2} M N m n))) (FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u3)} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8)) (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (fun (_x : FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) => TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) _x) (AddHomClass.toFunLike.{max u2 u3, max u2 u3, max u2 u3} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8)) (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (AddZeroClass.toAdd.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N)))))) (AddZeroClass.toAdd.{max u2 u3} (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8)) (AddMonoidHomClass.toAddHomClass.{max u2 u3, max u2 u3, max u2 u3} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8)) (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (AddMonoidHom.addMonoidHomClass.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8)))) (TensorProduct.Neg.aux.{u1, u3, u2} R _inst_1 M N _inst_2 _inst_3 _inst_7 _inst_8) (FreeAddMonoid.of.{max u2 u3} (Prod.{u3, u2} M N) (Prod.mk.{u3, u2} M N m n))) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8 (Neg.neg.{u3} M (NegZeroClass.toNeg.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) m) n)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u3}} {N : Type.{u2}} [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} N] [_inst_7 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_8 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3)] (m : M) (n : N), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) => TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (FreeAddMonoid.of.{max u2 u3} (Prod.{u3, u2} M N) (Prod.mk.{u3, u2} M N m n))) (FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u3)} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8)) (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (fun (_x : FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) => TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) _x) (AddHomClass.toFunLike.{max u2 u3, max u2 u3, max u2 u3} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8)) (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (AddZeroClass.toAdd.{max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N)))))) (AddZeroClass.toAdd.{max u2 u3} (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8)) (AddMonoidHomClass.toAddHomClass.{max u2 u3, max u2 u3, max u2 u3} (AddMonoidHom.{max u2 u3, max u2 u3} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddCancelMonoid.toAddRightCancelMonoid.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (FreeAddMonoid.instAddCancelMonoidFreeAddMonoid.{max u3 u2} (Prod.{u3, u2} M N))))) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8)) (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (TensorProduct.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8) (AddMonoid.toAddZeroClass.{max u3 u2} (FreeAddMonoid.{max u2 u3} (Prod.{u3, u2} M N)) (AddRightCancelMonoid.toAddMonoid.{max u3 u2} (FreeAddMonoid.{max 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(TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8)))) (TensorProduct.Neg.aux.{u1, u3, u2} R _inst_1 M N _inst_2 _inst_3 _inst_7 _inst_8) (FreeAddMonoid.of.{max u2 u3} (Prod.{u3, u2} M N) (Prod.mk.{u3, u2} M N m n))) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_7 _inst_8 (Neg.neg.{u3} M (NegZeroClass.toNeg.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) m) n)
 Case conversion may be inaccurate. Consider using '#align tensor_product.neg.aux_of TensorProduct.Neg.aux_ofₓ'. -/
 theorem Neg.aux_of (m : M) (n : N) : Neg.aux R (FreeAddMonoid.of (m, n)) = (-m) ⊗ₜ[R] n :=
   rfl

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro
 
 ! This file was ported from Lean 3 source module linear_algebra.tensor_product
-! leanprover-community/mathlib commit b0c712376e4ef44c53c3b872157ef44dfe9f9599
+! leanprover-community/mathlib commit 832f7b9162039c28b9361289c8681f155cae758f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Algebra.Module.Submodule.Bilinear
 /-!
 # Tensor product of modules over commutative semirings.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file constructs the tensor product of modules over commutative semirings. Given a semiring
 `R` and modules over it `M` and `N`, the standard construction of the tensor product is
 `tensor_product R M N`. It is also a module over `R`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -66,6 +66,7 @@ section
 -- open free_add_monoid
 variable (R)
 
+#print TensorProduct.Eqv /-
 /-- The relation on `free_add_monoid (M × N)` that generates a congruence whose quotient is
 the tensor product. -/
 inductive Eqv : FreeAddMonoid (M × N) → FreeAddMonoid (M × N) → Prop
@@ -84,6 +85,7 @@ inductive Eqv : FreeAddMonoid (M × N) → FreeAddMonoid (M × N) → Prop
     ∀ (r : R) (m : M) (n : N), eqv (FreeAddMonoid.of (r • m, n)) (FreeAddMonoid.of (m, r • n))
   | add_comm : ∀ x y, eqv (x + y) (y + x)
 #align tensor_product.eqv TensorProduct.Eqv
+-/
 
 end
 
@@ -91,11 +93,13 @@ end TensorProduct
 
 variable (R)
 
+#print TensorProduct /-
 /-- The tensor product of two modules `M` and `N` over the same commutative semiring `R`.
 The localized notations are `M ⊗ N` and `M ⊗[R] N`, accessed by `open_locale tensor_product`. -/
 def TensorProduct : Type _ :=
   (addConGen (TensorProduct.Eqv R M N)).Quotient
 #align tensor_product TensorProduct
+-/
 
 variable {R}
 
@@ -123,11 +127,13 @@ instance : Inhabited (M ⊗[R] N) :=
 
 variable (R) {M N}
 
+#print TensorProduct.tmul /-
 /-- The canonical function `M → N → M ⊗ N`. The localized notations are `m ⊗ₜ n` and `m ⊗ₜ[R] n`,
 accessed by `open_locale tensor_product`. -/
 def tmul (m : M) (n : N) : M ⊗[R] N :=
   AddCon.mk' _ <| FreeAddMonoid.of (m, n)
 #align tensor_product.tmul TensorProduct.tmul
+-/
 
 variable {R}
 
@@ -137,6 +143,12 @@ infixl:100 " ⊗ₜ " => tmul _
 -- mathport name: «expr ⊗ₜ[ ] »
 notation:100 x " ⊗ₜ[" R "] " y:100 => tmul R x y
 
+/- warning: tensor_product.induction_on -> TensorProduct.induction_on is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] {C : (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> Prop} (z : TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), (C (OfNat.ofNat.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 0 (OfNat.mk.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 0 (Zero.zero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)))))) -> (forall {x : M} {y : N}, C (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x y)) -> (forall {x : TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10} {y : TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10}, (C x) -> (C y) -> (C (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHAdd.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toHasAdd.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) x y))) -> (C z)
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Type.{u2}} {N : Type.{u1}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u1} N] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4] [_inst_10 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] {C : (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) -> Prop} (z : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), (C (OfNat.ofNat.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 0 (Zero.toOfNat0.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toZero.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))))) -> (forall (x : M) (y : N), C (TensorProduct.tmul.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x y)) -> (forall (x : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (y : TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), (C x) -> (C y) -> (C (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHAdd.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toAdd.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u3, u2, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) x y))) -> (C z)
+Case conversion may be inaccurate. Consider using '#align tensor_product.induction_on TensorProduct.induction_onₓ'. -/
 @[elab_as_elim]
 protected theorem induction_on {C : M ⊗[R] N → Prop} (z : M ⊗[R] N) (C0 : C 0)
     (C1 : ∀ {x y}, C <| x ⊗ₜ[R] y) (Cp : ∀ {x y}, C x → C y → C (x + y)) : C z :=
@@ -149,6 +161,12 @@ protected theorem induction_on {C : M ⊗[R] N → Prop} (z : M ⊗[R] N) (C0 :
 
 variable (M)
 
+/- warning: tensor_product.zero_tmul -> TensorProduct.zero_tmul is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.zero_tmul TensorProduct.zero_tmulₓ'. -/
 @[simp]
 theorem zero_tmul (n : N) : (0 : M) ⊗ₜ[R] n = 0 :=
   Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_zero_left _
@@ -156,12 +174,24 @@ theorem zero_tmul (n : N) : (0 : M) ⊗ₜ[R] n = 0 :=
 
 variable {M}
 
+/- warning: tensor_product.add_tmul -> TensorProduct.add_tmul is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align tensor_product.add_tmul TensorProduct.add_tmulₓ'. -/
 theorem add_tmul (m₁ m₂ : M) (n : N) : (m₁ + m₂) ⊗ₜ n = m₁ ⊗ₜ n + m₂ ⊗ₜ[R] n :=
   Eq.symm <| Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_add_left _ _ _
 #align tensor_product.add_tmul TensorProduct.add_tmul
 
 variable (N)
 
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} (N : Type.{u3}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (m : M), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m (OfNat.ofNat.{u3} N 0 (OfNat.mk.{u3} N 0 (Zero.zero.{u3} N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))))))) (OfNat.ofNat.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 0 (OfNat.mk.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 0 (Zero.zero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u3}} (N : Type.{u2}) [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (m : M), Eq.{max (succ u3) (succ u2)} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5))))) (OfNat.ofNat.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 0 (Zero.toOfNat0.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toZero.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))))
+Case conversion may be inaccurate. Consider using '#align tensor_product.tmul_zero TensorProduct.tmul_zeroₓ'. -/
 @[simp]
 theorem tmul_zero (m : M) : m ⊗ₜ[R] (0 : N) = 0 :=
   Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_zero_right _
@@ -169,6 +199,12 @@ theorem tmul_zero (m : M) : m ⊗ₜ[R] (0 : N) = 0 :=
 
 variable {N}
 
+/- warning: tensor_product.tmul_add -> TensorProduct.tmul_add is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (m : M) (n₁ : N) (n₂ : N), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m (HAdd.hAdd.{u3, u3, u3} N N N (instHAdd.{u3} N (AddZeroClass.toHasAdd.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)))) n₁ n₂)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHAdd.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toHasAdd.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n₁) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n₂))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u3}} {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (m : M) (n₁ : N) (n₂ : N), Eq.{max (succ u3) (succ u2)} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m (HAdd.hAdd.{u2, u2, u2} N N N (instHAdd.{u2} N (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)))) n₁ n₂)) (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHAdd.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toAdd.{max u3 u2} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n₁) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n₂))
+Case conversion may be inaccurate. Consider using '#align tensor_product.tmul_add TensorProduct.tmul_addₓ'. -/
 theorem tmul_add (m : M) (n₁ n₂ : N) : m ⊗ₜ (n₁ + n₂) = m ⊗ₜ n₁ + m ⊗ₜ[R] n₂ :=
   Eq.symm <| Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_add_right _ _ _
 #align tensor_product.tmul_add TensorProduct.tmul_add
@@ -177,6 +213,7 @@ section
 
 variable (R R' M N)
 
+#print TensorProduct.CompatibleSMul /-
 /-- A typeclass for `has_smul` structures which can be moved across a tensor product.
 
 This typeclass is generated automatically from a `is_scalar_tower` instance, but exists so that
@@ -187,43 +224,74 @@ Note that `module R' (M ⊗[R] N)` is available even without this typeclass on `
 needed if `tensor_product.smul_tmul`, `tensor_product.smul_tmul'`, or `tensor_product.tmul_smul` is
 used.
 -/
-class CompatibleSmul [DistribMulAction R' N] where
+class CompatibleSMul [DistribMulAction R' N] where
   smul_tmul : ∀ (r : R') (m : M) (n : N), (r • m) ⊗ₜ n = m ⊗ₜ[R] (r • n)
-#align tensor_product.compatible_smul TensorProduct.CompatibleSmul
+#align tensor_product.compatible_smul TensorProduct.CompatibleSMul
+-/
 
 end
 
+/- warning: tensor_product.compatible_smul.is_scalar_tower -> TensorProduct.CompatibleSMul.isScalarTower is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMul.{u2, u1} R' R] [_inst_17 : IsScalarTower.{u2, u1, u3} R' R M _inst_16 (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_9)))) (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] [_inst_18 : DistribMulAction.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5)] [_inst_19 : IsScalarTower.{u2, u1, u4} R' R N _inst_16 (SMulZeroClass.toHasSmul.{u1, u4} R N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u4} R N (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} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5))) (MulActionWithZero.toSMulWithZero.{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_5))) (Module.toMulActionWithZero.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)))) (SMulZeroClass.toHasSmul.{u2, u4} R' N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5))) (DistribSMul.toSmulZeroClass.{u2, u4} R' N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (DistribMulAction.toDistribSMul.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5) _inst_18)))], TensorProduct.CompatibleSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_18
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMul.{u2, u1} R' R] [_inst_17 : IsScalarTower.{u2, u1, u3} R' R M _inst_16 (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_9)))) (SMulZeroClass.toSMul.{u2, u3} R' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] [_inst_18 : DistribMulAction.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5)] [_inst_19 : IsScalarTower.{u2, u1, u4} R' R N _inst_16 (SMulZeroClass.toSMul.{u1, u4} R N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u4} R N (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u4} R N (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (Module.toMulActionWithZero.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)))) (SMulZeroClass.toSMul.{u2, u4} R' N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (DistribSMul.toSMulZeroClass.{u2, u4} R' N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (DistribMulAction.toDistribSMul.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5) _inst_18)))], TensorProduct.CompatibleSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_18
+Case conversion may be inaccurate. Consider using '#align tensor_product.compatible_smul.is_scalar_tower TensorProduct.CompatibleSMul.isScalarTowerₓ'. -/
 /-- Note that this provides the default `compatible_smul R R M N` instance through
 `mul_action.is_scalar_tower.left`. -/
-instance (priority := 100) CompatibleSmul.isScalarTower [SMul R' R] [IsScalarTower R' R M]
-    [DistribMulAction R' N] [IsScalarTower R' R N] : CompatibleSmul R R' M N :=
+instance (priority := 100) CompatibleSMul.isScalarTower [SMul R' R] [IsScalarTower R' R M]
+    [DistribMulAction R' N] [IsScalarTower R' R N] : CompatibleSMul R R' M N :=
   ⟨fun r m n => by
     conv_lhs => rw [← one_smul R m]
     conv_rhs => rw [← one_smul R n]
     rw [← smul_assoc, ← smul_assoc]
     exact Quotient.sound' <| AddConGen.Rel.of _ _ <| eqv.of_smul _ _ _⟩
-#align tensor_product.compatible_smul.is_scalar_tower TensorProduct.CompatibleSmul.isScalarTower
-
+#align tensor_product.compatible_smul.is_scalar_tower TensorProduct.CompatibleSMul.isScalarTower
+
+/- warning: tensor_product.smul_tmul -> TensorProduct.smul_tmul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : DistribMulAction.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5)] [_inst_17 : TensorProduct.CompatibleSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16] (r : R') (m : M) (n : N), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 (SMul.smul.{u2, u3} R' M (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14))) r m) n) (TensorProduct.tmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m (SMul.smul.{u2, u4} R' N (SMulZeroClass.toHasSmul.{u2, u4} R' N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5))) (DistribSMul.toSmulZeroClass.{u2, u4} R' N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (DistribMulAction.toDistribSMul.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5) _inst_16))) r n))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.smul_tmul TensorProduct.smul_tmulₓ'. -/
 /-- `smul` can be moved from one side of the product to the other .-/
-theorem smul_tmul [DistribMulAction R' N] [CompatibleSmul R R' M N] (r : R') (m : M) (n : N) :
+theorem smul_tmul [DistribMulAction R' N] [CompatibleSMul R R' M N] (r : R') (m : M) (n : N) :
     (r • m) ⊗ₜ n = m ⊗ₜ[R] (r • n) :=
-  CompatibleSmul.smul_tmul _ _ _
+  CompatibleSMul.smul_tmul _ _ _
 #align tensor_product.smul_tmul TensorProduct.smul_tmul
 
+/- warning: tensor_product.smul.aux -> TensorProduct.SMul.aux is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.smul.aux TensorProduct.SMul.auxₓ'. -/
 /-- Auxiliary function to defining scalar multiplication on tensor product. -/
-def Smul.aux {R' : Type _} [SMul R' M] (r : R') : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
+def SMul.aux {R' : Type _} [SMul R' M] (r : R') : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
   FreeAddMonoid.lift fun p : M × N => (r • p.1) ⊗ₜ p.2
-#align tensor_product.smul.aux TensorProduct.Smul.aux
-
-theorem Smul.aux_of {R' : Type _} [SMul R' M] (r : R') (m : M) (n : N) :
-    Smul.aux r (FreeAddMonoid.of (m, n)) = (r • m) ⊗ₜ[R] n :=
+#align tensor_product.smul.aux TensorProduct.SMul.aux
+
+/- warning: tensor_product.smul.aux_of -> TensorProduct.SMul.aux_of is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.smul.aux_of TensorProduct.SMul.aux_ofₓ'. -/
+theorem SMul.aux_of {R' : Type _} [SMul R' M] (r : R') (m : M) (n : N) :
+    SMul.aux r (FreeAddMonoid.of (m, n)) = (r • m) ⊗ₜ[R] n :=
   rfl
-#align tensor_product.smul.aux_of TensorProduct.Smul.aux_of
+#align tensor_product.smul.aux_of TensorProduct.SMul.aux_of
 
 variable [SMulCommClass R R' M]
 
 variable [SMulCommClass R R'' M]
 
+/- warning: tensor_product.left_has_smul -> TensorProduct.leftHasSMul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))], SMul.{u2, max u3 u4} R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toSMul.{u2, u3} R' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))], SMul.{u2, max u4 u3} R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)
+Case conversion may be inaccurate. Consider using '#align tensor_product.left_has_smul TensorProduct.leftHasSMulₓ'. -/
 /-- Given two modules over a commutative semiring `R`, if one of the factors carries a
 (distributive) action of a second type of scalars `R'`, which commutes with the action of `R`, then
 the tensor product (over `R`) carries an action of `R'`.
@@ -236,9 +304,9 @@ action. Two natural ways in which this situation arises are:
 Note that in the special case that `R = R'`, since `R` is commutative, we just get the usual scalar
 action on a tensor product of two modules. This special case is important enough that, for
 performance reasons, we define it explicitly below. -/
-instance leftHasSmul : SMul R' (M ⊗[R] N) :=
+instance leftHasSMul : SMul R' (M ⊗[R] N) :=
   ⟨fun r =>
-    (addConGen (TensorProduct.Eqv R M N)).lift (Smul.aux r : _ →+ M ⊗[R] N) <|
+    (addConGen (TensorProduct.Eqv R M N)).lift (SMul.aux r : _ →+ M ⊗[R] N) <|
       AddCon.addConGen_le fun x y hxy =>
         match x, y, hxy with
         | _, _, eqv.of_zero_left n =>
@@ -254,19 +322,37 @@ instance leftHasSmul : SMul R' (M ⊗[R] N) :=
           (AddCon.ker_rel _).2 <| by rw [smul.aux_of, smul.aux_of, ← smul_comm, smul_tmul]
         | _, _, eqv.add_comm x y =>
           (AddCon.ker_rel _).2 <| by simp_rw [AddMonoidHom.map_add, add_comm]⟩
-#align tensor_product.left_has_smul TensorProduct.leftHasSmul
+#align tensor_product.left_has_smul TensorProduct.leftHasSMul
 
 instance : SMul R (M ⊗[R] N) :=
-  TensorProduct.leftHasSmul
-
+  TensorProduct.leftHasSMul
+
+/- warning: tensor_product.smul_zero -> TensorProduct.smul_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] (r : R'), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (SMul.smul.{u2, max u3 u4} R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16) r (OfNat.ofNat.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 0 (OfNat.mk.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 0 (Zero.zero.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toHasZero.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)))))) (OfNat.ofNat.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 0 (OfNat.mk.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 0 (Zero.zero.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toHasZero.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {R' : Type.{u1}} [_inst_2 : Monoid.{u1} R'] {M : Type.{u4}} {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u3} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u1, u4} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u4} M _inst_4)] [_inst_16 : SMulCommClass.{u2, u1, u4} R R' M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (Module.toMulActionWithZero.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_9)))) (SMulZeroClass.toSMul.{u1, u4} R' M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (DistribSMul.toSMulZeroClass.{u1, u4} R' M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (DistribMulAction.toDistribSMul.{u1, u4} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u4} M _inst_4) _inst_14)))] (r : R'), Eq.{max (succ u4) (succ u3)} (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (HSMul.hSMul.{u1, max u4 u3, max u4 u3} R' (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u1, max u4 u3} R' (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u2, u1, u4, u3} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16)) r (OfNat.ofNat.{max u4 u3} (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 0 (Zero.toOfNat0.{max u4 u3} (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toZero.{max u4 u3} (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))))) (OfNat.ofNat.{max u4 u3} (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) 0 (Zero.toOfNat0.{max u4 u3} (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toZero.{max u4 u3} (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))))
+Case conversion may be inaccurate. Consider using '#align tensor_product.smul_zero TensorProduct.smul_zeroₓ'. -/
 protected theorem smul_zero (r : R') : (r • 0 : M ⊗[R] N) = 0 :=
   AddMonoidHom.map_zero _
 #align tensor_product.smul_zero TensorProduct.smul_zero
 
+/- warning: tensor_product.smul_add -> TensorProduct.smul_add is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] (r : R') (x : TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (y : TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (SMul.smul.{u2, max u3 u4} R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16) r (HAdd.hAdd.{max u3 u4, max u3 u4, max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHAdd.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toHasAdd.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) x y)) (HAdd.hAdd.{max u3 u4, max u3 u4, max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHAdd.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toHasAdd.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) (SMul.smul.{u2, max u3 u4} R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16) r x) (SMul.smul.{u2, max u3 u4} R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16) r y))
+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {R' : Type.{u1}} [_inst_2 : Monoid.{u1} R'] {M : Type.{u3}} {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u1, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u4, u1, u3} R R' M (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_9)))) (SMulZeroClass.toSMul.{u1, u3} R' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u1, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u1, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] (r : R') (x : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (y : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), Eq.{max (succ u3) (succ u2)} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R' (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u1, max u3 u2} R' (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u4, u1, u3, u2} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16)) r (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHAdd.{max u3 u2} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toAdd.{max u3 u2} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) x y)) (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHAdd.{max u3 u2} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toAdd.{max u3 u2} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R' (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u1, max u3 u2} R' (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u4, u1, u3, u2} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16)) r x) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R' (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u1, max u3 u2} R' (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u4, u1, u3, u2} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16)) r y))
+Case conversion may be inaccurate. Consider using '#align tensor_product.smul_add TensorProduct.smul_addₓ'. -/
 protected theorem smul_add (r : R') (x y : M ⊗[R] N) : r • (x + y) = r • x + r • y :=
   AddMonoidHom.map_add _ _ _
 #align tensor_product.smul_add TensorProduct.smul_add
 
+/- warning: tensor_product.zero_smul -> TensorProduct.zero_smul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.zero_smul TensorProduct.zero_smulₓ'. -/
 protected theorem zero_smul (x : M ⊗[R] N) : (0 : R'') • x = 0 :=
   have : ∀ (r : R'') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   TensorProduct.induction_on x (by rw [TensorProduct.smul_zero])
@@ -274,12 +360,24 @@ protected theorem zero_smul (x : M ⊗[R] N) : (0 : R'') • x = 0 :=
     rw [TensorProduct.smul_add, ihx, ihy, add_zero]
 #align tensor_product.zero_smul TensorProduct.zero_smul
 
+/- warning: tensor_product.one_smul -> TensorProduct.one_smul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.one_smul TensorProduct.one_smulₓ'. -/
 protected theorem one_smul (x : M ⊗[R] N) : (1 : R') • x = x :=
   have : ∀ (r : R') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   TensorProduct.induction_on x (by rw [TensorProduct.smul_zero]) (fun m n => by rw [this, one_smul])
     fun x y ihx ihy => by rw [TensorProduct.smul_add, ihx, ihy]
 #align tensor_product.one_smul TensorProduct.one_smul
 
+/- warning: tensor_product.add_smul -> TensorProduct.add_smul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {R'' : Type.{u1}} [_inst_3 : Semiring.{u1} R''] {M : Type.{u3}} {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_10 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5] [_inst_15 : Module.{u1, u3} R'' M _inst_3 _inst_4] [_inst_17 : SMulCommClass.{u4, u1, u3} R R'' M (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_9)))) (SMulZeroClass.toSMul.{u1, u3} R'' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R'' M (MonoidWithZero.toZero.{u1} R'' (Semiring.toMonoidWithZero.{u1} R'' _inst_3)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R'' M (Semiring.toMonoidWithZero.{u1} R'' _inst_3) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R'' M _inst_3 _inst_4 _inst_15))))] (r : R'') (s : R'') (x : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10), Eq.{max (succ u3) (succ u2)} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R'' (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u1, max u3 u2} R'' (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u4, u1, u3, u2} R _inst_1 R'' (MonoidWithZero.toMonoid.{u1} R'' (Semiring.toMonoidWithZero.{u1} R'' _inst_3)) M N _inst_4 _inst_5 _inst_9 _inst_10 (Module.toDistribMulAction.{u1, u3} R'' M _inst_3 _inst_4 _inst_15) _inst_17)) (HAdd.hAdd.{u1, u1, u1} R'' R'' R'' (instHAdd.{u1} R'' (Distrib.toAdd.{u1} R'' (NonUnitalNonAssocSemiring.toDistrib.{u1} R'' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R'' (Semiring.toNonAssocSemiring.{u1} R'' _inst_3))))) r s) x) (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHAdd.{max u3 u2} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (AddZeroClass.toAdd.{max u3 u2} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addZeroClass.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R'' (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u1, max u3 u2} R'' (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u4, u1, u3, u2} R _inst_1 R'' (MonoidWithZero.toMonoid.{u1} R'' (Semiring.toMonoidWithZero.{u1} R'' _inst_3)) M N _inst_4 _inst_5 _inst_9 _inst_10 (Module.toDistribMulAction.{u1, u3} R'' M _inst_3 _inst_4 _inst_15) _inst_17)) r x) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R'' (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u1, max u3 u2} R'' (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u4, u1, u3, u2} R _inst_1 R'' (MonoidWithZero.toMonoid.{u1} R'' (Semiring.toMonoidWithZero.{u1} R'' _inst_3)) M N _inst_4 _inst_5 _inst_9 _inst_10 (Module.toDistribMulAction.{u1, u3} R'' M _inst_3 _inst_4 _inst_15) _inst_17)) s x))
+Case conversion may be inaccurate. Consider using '#align tensor_product.add_smul TensorProduct.add_smulₓ'. -/
 protected theorem add_smul (r s : R'') (x : M ⊗[R] N) : (r + s) • x = r • x + s • x :=
   have : ∀ (r : R'') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   TensorProduct.induction_on x (by simp_rw [TensorProduct.smul_zero, add_zero])
@@ -296,6 +394,12 @@ instance : AddCommMonoid (M ⊗[R] N) :=
     nsmul_zero := by simp [TensorProduct.zero_smul]
     nsmul_succ := by simp [Nat.succ_eq_one_add, TensorProduct.one_smul, TensorProduct.add_smul] }
 
+/- warning: tensor_product.left_distrib_mul_action -> TensorProduct.leftDistribMulAction is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))], DistribMulAction.{u2, max u3 u4} R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_2 (AddCommMonoid.toAddMonoid.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toSMul.{u2, u3} R' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))], DistribMulAction.{u2, max u4 u3} R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_2 (AddCommMonoid.toAddMonoid.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10))
+Case conversion may be inaccurate. Consider using '#align tensor_product.left_distrib_mul_action TensorProduct.leftDistribMulActionₓ'. -/
 instance leftDistribMulAction : DistribMulAction R' (M ⊗[R] N) :=
   have : ∀ (r : R') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
   { smul := (· • ·)
@@ -313,26 +417,46 @@ instance leftDistribMulAction : DistribMulAction R' (M ⊗[R] N) :=
 instance : DistribMulAction R (M ⊗[R] N) :=
   TensorProduct.leftDistribMulAction
 
+/- warning: tensor_product.smul_tmul' -> TensorProduct.smul_tmul' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] (r : R') (m : M) (n : N), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (SMul.smul.{u2, max u3 u4} R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16) r (TensorProduct.tmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 (SMul.smul.{u2, u3} R' M (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14))) r m) n)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {R' : Type.{u1}} [_inst_2 : Monoid.{u1} R'] {M : Type.{u4}} {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u3} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u1, u4} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u4} M _inst_4)] [_inst_16 : SMulCommClass.{u2, u1, u4} R R' M (SMulZeroClass.toSMul.{u2, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (Module.toMulActionWithZero.{u2, u4} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_9)))) (SMulZeroClass.toSMul.{u1, u4} R' M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (DistribSMul.toSMulZeroClass.{u1, u4} R' M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (DistribMulAction.toDistribSMul.{u1, u4} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u4} M _inst_4) _inst_14)))] (r : R') (m : M) (n : N), Eq.{max (succ u4) (succ u3)} (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (HSMul.hSMul.{u1, max u3 u4, max u4 u3} R' (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u1, max u4 u3} R' (TensorProduct.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u2, u1, u4, u3} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16)) r (TensorProduct.tmul.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n)) (TensorProduct.tmul.{u2, u4, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 (HSMul.hSMul.{u1, u4, u4} R' M M (instHSMul.{u1, u4} R' M (SMulZeroClass.toSMul.{u1, u4} R' M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (DistribSMul.toSMulZeroClass.{u1, u4} R' M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (DistribMulAction.toDistribSMul.{u1, u4} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u4} M _inst_4) _inst_14)))) r m) n)
+Case conversion may be inaccurate. Consider using '#align tensor_product.smul_tmul' TensorProduct.smul_tmul'ₓ'. -/
 theorem smul_tmul' (r : R') (m : M) (n : N) : r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n :=
   rfl
 #align tensor_product.smul_tmul' TensorProduct.smul_tmul'
 
+/- warning: tensor_product.tmul_smul -> TensorProduct.tmul_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] [_inst_18 : DistribMulAction.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5)] [_inst_19 : TensorProduct.CompatibleSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_18] (r : R') (x : M) (y : N), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x (SMul.smul.{u2, u4} R' N (SMulZeroClass.toHasSmul.{u2, u4} R' N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5))) (DistribSMul.toSmulZeroClass.{u2, u4} R' N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (DistribMulAction.toDistribSMul.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5) _inst_18))) r y)) (SMul.smul.{u2, max u3 u4} R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16) r (TensorProduct.tmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x y))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {R' : Type.{u4}} [_inst_2 : Monoid.{u4} R'] {M : Type.{u1}} {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] [_inst_10 : Module.{u2, u3} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u4, u1} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u1} M _inst_4)] [_inst_16 : SMulCommClass.{u2, u4, u1} R R' M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_9)))) (SMulZeroClass.toSMul.{u4, u1} R' M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (DistribSMul.toSMulZeroClass.{u4, u1} R' M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (DistribMulAction.toDistribSMul.{u4, u1} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u1} M _inst_4) _inst_14)))] [_inst_18 : DistribMulAction.{u4, u3} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u3} N _inst_5)] [_inst_19 : TensorProduct.CompatibleSMul.{u2, u4, u1, u3} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_18] (r : R') (x : M) (y : N), Eq.{max (succ u1) (succ u3)} (TensorProduct.{u2, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u2, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x (HSMul.hSMul.{u4, u3, u3} R' N N (instHSMul.{u4, u3} R' N (SMulZeroClass.toSMul.{u4, u3} R' N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (DistribSMul.toSMulZeroClass.{u4, u3} R' N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5)) (DistribMulAction.toDistribSMul.{u4, u3} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u3} N _inst_5) _inst_18)))) r y)) (HSMul.hSMul.{u4, max u3 u1, max u1 u3} R' (TensorProduct.{u2, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u2, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u4, max u1 u3} R' (TensorProduct.{u2, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u2, u4, u1, u3} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16)) r (TensorProduct.tmul.{u2, u1, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 x y))
+Case conversion may be inaccurate. Consider using '#align tensor_product.tmul_smul TensorProduct.tmul_smulₓ'. -/
 @[simp]
-theorem tmul_smul [DistribMulAction R' N] [CompatibleSmul R R' M N] (r : R') (x : M) (y : N) :
+theorem tmul_smul [DistribMulAction R' N] [CompatibleSMul R R' M N] (r : R') (x : M) (y : N) :
     x ⊗ₜ (r • y) = r • x ⊗ₜ[R] y :=
   (smul_tmul _ _ _).symm
 #align tensor_product.tmul_smul TensorProduct.tmul_smul
 
+/- warning: tensor_product.smul_tmul_smul -> TensorProduct.smul_tmul_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (r : R) (s : R) (m : M) (n : N), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} 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.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_9)))) r m) (SMul.smul.{u1, u3} R N (SMulZeroClass.toHasSmul.{u1, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u3} R N (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} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_5))) (Module.toMulActionWithZero.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10)))) s n)) (SMul.smul.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.hasSmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) r s) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u3}} {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] (r : R) (s : R) (m : M) (n : N), Eq.{max (succ u3) (succ u2)} (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M (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_9))))) r m) (HSMul.hSMul.{u1, u2, u2} R N N (instHSMul.{u1, u2} R N (SMulZeroClass.toSMul.{u1, u2} R N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} R N (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} R N (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_5)) (Module.toMulActionWithZero.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_10))))) s n)) (HSMul.hSMul.{u1, max u2 u3, max u3 u2} R (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (instHSMul.{u1, max u3 u2} R (TensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instSMulTensorProduct.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) r s) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10 m n))
+Case conversion may be inaccurate. Consider using '#align tensor_product.smul_tmul_smul TensorProduct.smul_tmul_smulₓ'. -/
 theorem smul_tmul_smul (r s : R) (m : M) (n : N) : (r • m) ⊗ₜ[R] (s • n) = (r * s) • m ⊗ₜ[R] n := by
   simp only [tmul_smul, smul_tmul, mul_smul]
 #align tensor_product.smul_tmul_smul TensorProduct.smul_tmul_smul
 
+#print TensorProduct.leftModule /-
 instance leftModule : Module R'' (M ⊗[R] N) :=
   { TensorProduct.leftDistribMulAction with
     smul := (· • ·)
     add_smul := TensorProduct.add_smul
     zero_smul := TensorProduct.zero_smul }
 #align tensor_product.left_module TensorProduct.leftModule
+-/
 
 instance : Module R (M ⊗[R] N) :=
   TensorProduct.leftModule
@@ -350,6 +474,12 @@ variable {R'₂ : Type _} [Monoid R'₂] [DistribMulAction R'₂ M]
 
 variable [SMulCommClass R R'₂ M] [SMul R'₂ R']
 
+/- warning: tensor_product.is_scalar_tower_left -> TensorProduct.isScalarTower_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] {R'₂ : Type.{u5}} [_inst_18 : Monoid.{u5} R'₂] [_inst_19 : DistribMulAction.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_20 : SMulCommClass.{u1, u5, u3} R R'₂ M (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_9)))) (SMulZeroClass.toHasSmul.{u5, u3} R'₂ M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u5, u3} R'₂ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_19)))] [_inst_21 : SMul.{u5, u2} R'₂ R'] [_inst_22 : IsScalarTower.{u5, u2, u3} R'₂ R' M _inst_21 (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14))) (SMulZeroClass.toHasSmul.{u5, u3} R'₂ M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u5, u3} R'₂ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_19)))], IsScalarTower.{u5, u2, max u3 u4} R'₂ R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_21 (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16) (TensorProduct.leftHasSMul.{u1, u5, u3, u4} R _inst_1 R'₂ _inst_18 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_19 _inst_20)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toSMul.{u2, u3} R' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] {R'₂ : Type.{u5}} [_inst_18 : Monoid.{u5} R'₂] [_inst_19 : DistribMulAction.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_20 : SMulCommClass.{u1, u5, u3} R R'₂ M (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_9)))) (SMulZeroClass.toSMul.{u5, u3} R'₂ M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u5, u3} R'₂ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_19)))] [_inst_21 : SMul.{u5, u2} R'₂ R'] [_inst_22 : IsScalarTower.{u5, u2, u3} R'₂ R' M _inst_21 (SMulZeroClass.toSMul.{u2, u3} R' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14))) (SMulZeroClass.toSMul.{u5, u3} R'₂ M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u5, u3} R'₂ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_19)))], IsScalarTower.{u5, u2, max u4 u3} R'₂ R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_21 (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16) (TensorProduct.leftHasSMul.{u1, u5, u3, u4} R _inst_1 R'₂ _inst_18 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_19 _inst_20)
+Case conversion may be inaccurate. Consider using '#align tensor_product.is_scalar_tower_left TensorProduct.isScalarTower_leftₓ'. -/
 /-- `is_scalar_tower R'₂ R' M` implies `is_scalar_tower R'₂ R' (M ⊗[R] N)` -/
 instance isScalarTower_left [IsScalarTower R'₂ R' M] : IsScalarTower R'₂ R' (M ⊗[R] N) :=
   ⟨fun s r x =>
@@ -360,8 +490,14 @@ instance isScalarTower_left [IsScalarTower R'₂ R' M] : IsScalarTower R'₂ R'
 
 variable [DistribMulAction R'₂ N] [DistribMulAction R' N]
 
-variable [CompatibleSmul R R'₂ M N] [CompatibleSmul R R' M N]
+variable [CompatibleSMul R R'₂ M N] [CompatibleSMul R R' M N]
 
+/- warning: tensor_product.is_scalar_tower_right -> TensorProduct.isScalarTower_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] {R'₂ : Type.{u5}} [_inst_18 : Monoid.{u5} R'₂] [_inst_19 : DistribMulAction.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_20 : SMulCommClass.{u1, u5, u3} R R'₂ M (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_9)))) (SMulZeroClass.toHasSmul.{u5, u3} R'₂ M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u5, u3} R'₂ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_19)))] [_inst_21 : SMul.{u5, u2} R'₂ R'] [_inst_22 : DistribMulAction.{u5, u4} R'₂ N _inst_18 (AddCommMonoid.toAddMonoid.{u4} N _inst_5)] [_inst_23 : DistribMulAction.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5)] [_inst_24 : TensorProduct.CompatibleSMul.{u1, u5, u3, u4} R _inst_1 R'₂ _inst_18 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_19 _inst_22] [_inst_25 : TensorProduct.CompatibleSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_23] [_inst_26 : IsScalarTower.{u5, u2, u4} R'₂ R' N _inst_21 (SMulZeroClass.toHasSmul.{u2, u4} R' N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5))) (DistribSMul.toSmulZeroClass.{u2, u4} R' N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (DistribMulAction.toDistribSMul.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5) _inst_23))) (SMulZeroClass.toHasSmul.{u5, u4} R'₂ N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5))) (DistribSMul.toSmulZeroClass.{u5, u4} R'₂ N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (DistribMulAction.toDistribSMul.{u5, u4} R'₂ N _inst_18 (AddCommMonoid.toAddMonoid.{u4} N _inst_5) _inst_22)))], IsScalarTower.{u5, u2, max u3 u4} R'₂ R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_21 (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16) (TensorProduct.leftHasSMul.{u1, u5, u3, u4} R _inst_1 R'₂ _inst_18 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_19 _inst_20)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toSMul.{u2, u3} R' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] {R'₂ : Type.{u5}} [_inst_18 : Monoid.{u5} R'₂] [_inst_19 : DistribMulAction.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_20 : SMulCommClass.{u1, u5, u3} R R'₂ M (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_9)))) (SMulZeroClass.toSMul.{u5, u3} R'₂ M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u5, u3} R'₂ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u5, u3} R'₂ M _inst_18 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_19)))] [_inst_21 : SMul.{u5, u2} R'₂ R'] [_inst_22 : DistribMulAction.{u5, u4} R'₂ N _inst_18 (AddCommMonoid.toAddMonoid.{u4} N _inst_5)] [_inst_23 : DistribMulAction.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5)] [_inst_24 : TensorProduct.CompatibleSMul.{u1, u5, u3, u4} R _inst_1 R'₂ _inst_18 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_19 _inst_22] [_inst_25 : TensorProduct.CompatibleSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_23] [_inst_26 : IsScalarTower.{u5, u2, u4} R'₂ R' N _inst_21 (SMulZeroClass.toSMul.{u2, u4} R' N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (DistribSMul.toSMulZeroClass.{u2, u4} R' N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (DistribMulAction.toDistribSMul.{u2, u4} R' N _inst_2 (AddCommMonoid.toAddMonoid.{u4} N _inst_5) _inst_23))) (SMulZeroClass.toSMul.{u5, u4} R'₂ N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (DistribSMul.toSMulZeroClass.{u5, u4} R'₂ N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_5)) (DistribMulAction.toDistribSMul.{u5, u4} R'₂ N _inst_18 (AddCommMonoid.toAddMonoid.{u4} N _inst_5) _inst_22)))], IsScalarTower.{u5, u2, max u4 u3} R'₂ R' (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_21 (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16) (TensorProduct.leftHasSMul.{u1, u5, u3, u4} R _inst_1 R'₂ _inst_18 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_19 _inst_20)
+Case conversion may be inaccurate. Consider using '#align tensor_product.is_scalar_tower_right TensorProduct.isScalarTower_rightₓ'. -/
 /-- `is_scalar_tower R'₂ R' N` implies `is_scalar_tower R'₂ R' (M ⊗[R] N)` -/
 instance isScalarTower_right [IsScalarTower R'₂ R' N] : IsScalarTower R'₂ R' (M ⊗[R] N) :=
   ⟨fun s r x =>
@@ -372,6 +508,12 @@ instance isScalarTower_right [IsScalarTower R'₂ R' N] : IsScalarTower R'₂ R'
 
 end
 
+/- warning: tensor_product.is_scalar_tower -> TensorProduct.isScalarTower is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] [_inst_18 : SMul.{u2, u1} R' R] [_inst_19 : IsScalarTower.{u2, u1, u3} R' R M _inst_18 (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_9)))) (SMulZeroClass.toHasSmul.{u2, u3} R' M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))], IsScalarTower.{u2, u1, max u3 u4} R' R (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_18 (TensorProduct.hasSmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {R' : Type.{u2}} [_inst_2 : Monoid.{u2} R'] {M : Type.{u3}} {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_14 : DistribMulAction.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4)] [_inst_16 : SMulCommClass.{u1, u2, u3} R R' M (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_9)))) (SMulZeroClass.toSMul.{u2, u3} R' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))] [_inst_18 : SMul.{u2, u1} R' R] [_inst_19 : IsScalarTower.{u2, u1, u3} R' R M _inst_18 (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_9)))) (SMulZeroClass.toSMul.{u2, u3} R' M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribSMul.toSMulZeroClass.{u2, u3} R' M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} R' M _inst_2 (AddCommMonoid.toAddMonoid.{u3} M _inst_4) _inst_14)))], IsScalarTower.{u2, u1, max u4 u3} R' R (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_18 (TensorProduct.instSMulTensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 R' _inst_2 M N _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_16)
+Case conversion may be inaccurate. Consider using '#align tensor_product.is_scalar_tower TensorProduct.isScalarTowerₓ'. -/
 /-- A short-cut instance for the common case, where the requirements for the `compatible_smul`
 instances are sufficient. -/
 instance isScalarTower [SMul R' R] [IsScalarTower R' R M] : IsScalarTower R' R (M ⊗[R] N) :=
@@ -381,6 +523,12 @@ instance isScalarTower [SMul R' R] [IsScalarTower R' R M] : IsScalarTower R' R (
 -- or right
 variable (R M N)
 
+/- warning: tensor_product.mk -> TensorProduct.mk is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align tensor_product.mk TensorProduct.mkₓ'. -/
 /-- The canonical bilinear map `M → N → M ⊗[R] N`. -/
 def mk : M →ₗ[R] N →ₗ[R] M ⊗[R] N :=
   LinearMap.mk₂ R (· ⊗ₜ ·) add_tmul (fun c m n => by rw [smul_tmul, tmul_smul]) tmul_add tmul_smul
@@ -388,15 +536,33 @@ def mk : M →ₗ[R] N →ₗ[R] M ⊗[R] N :=
 
 variable {R M N}
 
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 @[simp]
 theorem mk_apply (m : M) (n : N) : mk R M N m n = m ⊗ₜ n :=
   rfl
 #align tensor_product.mk_apply TensorProduct.mk_apply
 
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 theorem ite_tmul (x₁ : M) (x₂ : N) (P : Prop) [Decidable P] :
     (if P then x₁ else 0) ⊗ₜ[R] x₂ = if P then x₁ ⊗ₜ x₂ else 0 := by split_ifs <;> simp
 #align tensor_product.ite_tmul TensorProduct.ite_tmul
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.tmul_ite TensorProduct.tmul_iteₓ'. -/
 theorem tmul_ite (x₁ : M) (x₂ : N) (P : Prop) [Decidable P] :
     (x₁ ⊗ₜ[R] if P then x₂ else 0) = if P then x₁ ⊗ₜ x₂ else 0 := by split_ifs <;> simp
 #align tensor_product.tmul_ite TensorProduct.tmul_ite
@@ -405,6 +571,12 @@ section
 
 open BigOperators
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.sum_tmul TensorProduct.sum_tmulₓ'. -/
 theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
     (∑ a in s, m a) ⊗ₜ[R] n = ∑ a in s, m a ⊗ₜ[R] n := by
   classical
@@ -413,6 +585,12 @@ theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
     · simp [Finset.sum_insert has, add_tmul, ih]
 #align tensor_product.sum_tmul TensorProduct.sum_tmul
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.tmul_sum TensorProduct.tmul_sumₓ'. -/
 theorem tmul_sum (m : M) {α : Type _} (s : Finset α) (n : α → N) :
     (m ⊗ₜ[R] ∑ a in s, n a) = ∑ a in s, m ⊗ₜ[R] n a := by
   classical
@@ -425,6 +603,12 @@ end
 
 variable (R M N)
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.span_tmul_eq_top TensorProduct.span_tmul_eq_topₓ'. -/
 /-- The simple (aka pure) elements span the tensor product. -/
 theorem span_tmul_eq_top : Submodule.span R { t : M ⊗[R] N | ∃ m n, m ⊗ₜ n = t } = ⊤ :=
   by
@@ -438,6 +622,12 @@ theorem span_tmul_eq_top : Submodule.span R { t : M ⊗[R] N | ∃ m n, m ⊗ₜ
     exact Submodule.add_mem _ ht₁ ht₂
 #align tensor_product.span_tmul_eq_top TensorProduct.span_tmul_eq_top
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map₂_mk_top_top_eq_top TensorProduct.map₂_mk_top_top_eq_topₓ'. -/
 @[simp]
 theorem map₂_mk_top_top_eq_top : Submodule.map₂ (mk R M N) ⊤ ⊤ = ⊤ :=
   by
@@ -453,6 +643,7 @@ variable {M N P Q}
 
 variable (f : M →ₗ[R] N →ₗ[R] P)
 
+#print TensorProduct.liftAux /-
 /-- Auxiliary function to constructing a linear map `M ⊗ N → P` given a bilinear map `M → N → P`
 with the property that its composition with the canonical bilinear map `M → N → M ⊗ N` is
 the given bilinear map `M → N → P`. -/
@@ -477,13 +668,26 @@ def liftAux : M ⊗[R] N →+ P :=
       | _, _, eqv.add_comm x y =>
         (AddCon.ker_rel _).2 <| by simp_rw [AddMonoidHom.map_add, add_comm]
 #align tensor_product.lift_aux TensorProduct.liftAux
+-/
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.lift_aux_tmul TensorProduct.liftAux_tmulₓ'. -/
 theorem liftAux_tmul (m n) : liftAux f (m ⊗ₜ n) = f m n :=
   rfl
 #align tensor_product.lift_aux_tmul TensorProduct.liftAux_tmul
 
 variable {f}
 
+/- warning: tensor_product.lift_aux.smul -> TensorProduct.liftAux.smul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.lift_aux.smul TensorProduct.liftAux.smulₓ'. -/
 @[simp]
 theorem liftAux.smul (r : R) (x) : liftAux f (r • x) = r • liftAux f x :=
   TensorProduct.induction_on x (smul_zero _).symm
@@ -494,47 +698,97 @@ theorem liftAux.smul (r : R) (x) : liftAux f (r • x) = r • liftAux f x :=
 
 variable (f)
 
+#print TensorProduct.lift /-
 /-- Constructing a linear map `M ⊗ N → P` given a bilinear map `M → N → P` with the property that
 its composition with the canonical bilinear map `M → N → M ⊗ N` is
 the given bilinear map `M → N → P`. -/
 def lift : M ⊗ N →ₗ[R] P :=
   { liftAux f with map_smul' := liftAux.smul }
 #align tensor_product.lift TensorProduct.lift
+-/
 
 variable {f}
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.lift.tmul TensorProduct.lift.tmulₓ'. -/
 @[simp]
 theorem lift.tmul (x y) : lift f (x ⊗ₜ y) = f x y :=
   rfl
 #align tensor_product.lift.tmul TensorProduct.lift.tmul
 
+/- warning: tensor_product.lift.tmul' -> TensorProduct.lift.tmul' is a dubious translation:
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 @[simp]
 theorem lift.tmul' (x y) : (lift f).1 (x ⊗ₜ y) = f x y :=
   rfl
 #align tensor_product.lift.tmul' TensorProduct.lift.tmul'
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.ext' TensorProduct.ext'ₓ'. -/
 theorem ext' {g h : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x ⊗ₜ y)) : g = h :=
   LinearMap.ext fun z =>
     TensorProduct.induction_on z (by simp_rw [LinearMap.map_zero]) H fun x y ihx ihy => by
       rw [g.map_add, h.map_add, ihx, ihy]
 #align tensor_product.ext' TensorProduct.ext'
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.lift.unique TensorProduct.lift.uniqueₓ'. -/
 theorem lift.unique {g : M ⊗[R] N →ₗ[R] P} (H : ∀ x y, g (x ⊗ₜ y) = f x y) : g = lift f :=
   ext' fun m n => by rw [H, lift.tmul]
 #align tensor_product.lift.unique TensorProduct.lift.unique
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.lift_mk TensorProduct.lift_mkₓ'. -/
 theorem lift_mk : lift (mk R M N) = LinearMap.id :=
   Eq.symm <| lift.unique fun x y => rfl
 #align tensor_product.lift_mk TensorProduct.lift_mk
 
+/- warning: tensor_product.lift_compr₂ -> TensorProduct.lift_compr₂ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.lift_compr₂ TensorProduct.lift_compr₂ₓ'. -/
 theorem lift_compr₂ (g : P →ₗ[R] Q) : lift (f.compr₂ g) = g.comp (lift f) :=
   Eq.symm <| lift.unique fun x y => by simp
 #align tensor_product.lift_compr₂ TensorProduct.lift_compr₂
 
+/- warning: tensor_product.lift_mk_compr₂ -> TensorProduct.lift_mk_compr₂ is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.lift_mk_compr₂ TensorProduct.lift_mk_compr₂ₓ'. -/
 theorem lift_mk_compr₂ (f : M ⊗ N →ₗ[R] P) : lift ((mk R M N).compr₂ f) = f := by
   rw [lift_compr₂ f, lift_mk, LinearMap.comp_id]
 #align tensor_product.lift_mk_compr₂ TensorProduct.lift_mk_compr₂
 
+/- warning: tensor_product.ext -> TensorProduct.ext is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align tensor_product.ext TensorProduct.extₓ'. -/
 /-- This used to be an `@[ext]` lemma, but it fails very slowly when the `ext` tactic tries to apply
 it in some cases, notably when one wants to show equality of two linear maps. The `@[ext]`
 attribute is now added locally where it is needed. Using this as the `@[ext]` lemma instead of
@@ -551,15 +805,23 @@ example : M → N → (M → N → P) → P := fun m => flip fun f => f m
 
 variable (R M N P)
 
+#print TensorProduct.uncurry /-
 /-- Linearly constructing a linear map `M ⊗ N → P` given a bilinear map `M → N → P`
 with the property that its composition with the canonical bilinear map `M → N → M ⊗ N` is
 the given bilinear map `M → N → P`. -/
 def uncurry : (M →ₗ[R] N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] P :=
   LinearMap.flip <| lift <| (LinearMap.lflip _ _ _ _).comp (LinearMap.flip LinearMap.id)
 #align tensor_product.uncurry TensorProduct.uncurry
+-/
 
 variable {R M N P}
 
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(LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P 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+Case conversion may be inaccurate. Consider using '#align tensor_product.uncurry_apply TensorProduct.uncurry_applyₓ'. -/
 @[simp]
 theorem uncurry_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
     uncurry R M N P f (m ⊗ₜ n) = f m n := by rw [uncurry, LinearMap.flip_apply, lift.tmul] <;> rfl
@@ -567,6 +829,7 @@ theorem uncurry_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
 
 variable (R M N P)
 
+#print TensorProduct.lift.equiv /-
 /-- A linear equivalence constructing a linear map `M ⊗ N → P` given a bilinear map `M → N → P`
 with the property that its composition with the canonical bilinear map `M → N → M ⊗ N` is
 the given bilinear map `M → N → P`. -/
@@ -576,19 +839,38 @@ def lift.equiv : (M →ₗ[R] N →ₗ[R] P) ≃ₗ[R] M ⊗ N →ₗ[R] P :=
     left_inv := fun f => LinearMap.ext₂ fun m n => lift.tmul _ _
     right_inv := fun f => ext' fun m n => lift.tmul _ _ }
 #align tensor_product.lift.equiv TensorProduct.lift.equiv
+-/
 
+/- warning: tensor_product.lift.equiv_apply -> TensorProduct.lift.equiv_apply is a dubious translation:
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LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R 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(SMulHomClass.toFunLike.{max (max u3 u1) u2, u4, max (max u3 u1) u2, max (max u3 u1) u2} (LinearEquiv.{u4, u4, max (max u2 u1) u3, max u2 u1 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))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N 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_inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (SMulZeroClass.toSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toZero.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 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_inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R 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R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, max u1 u2} R R R M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) 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R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u4, u4, u4, u4, u1, u2} R R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) 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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))))) (Module.toDistribMulAction.{u4, max (max u3 u1) u2} R (LinearMap.{u4, u4, max u1 u3, u2} 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, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u2} R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u2} R R R (TensorProduct.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_6)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (SemilinearMapClass.distribMulActionHomClass.{u4, max (max u3 u1) u2, max (max u3 u1) u2, max (max u3 u1) u2} R (LinearMap.{u4, u4, u3, max u2 u1} 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))) M (LinearMap.{u4, u4, u1, u2} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P 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 @[simp]
 theorem lift.equiv_apply (f : M →ₗ[R] N →ₗ[R] P) (m : M) (n : N) :
     lift.equiv R M N P f (m ⊗ₜ n) = f m n :=
   uncurry_apply f m n
 #align tensor_product.lift.equiv_apply TensorProduct.lift.equiv_apply
 
+/- warning: tensor_product.lift.equiv_symm_apply -> TensorProduct.lift.equiv_symm_apply is a dubious translation:
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(RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (LinearMap.addCommMonoid.{u4, u4, max u2 u3, u1} R R (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u3) 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_inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u2 u3, u1} R R R (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))))))) (SMulZeroClass.toSMul.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R 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(AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, u2, max u1 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))) M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u2, max u3 u1} R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u2, max u3 u1} R R R M (LinearMap.{u4, u4, u3, u1} 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))) N P _inst_5 _inst_6 _inst_10 _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_9 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_11 (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11)))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u4, u4, u4, u4, u3, u1} R R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_5 _inst_6 _inst_10 _inst_11 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Module.toDistribMulAction.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11) (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))) (smulCommClass_self.{u4, u1} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} P (AddCommMonoid.toAddMonoid.{u1} P _inst_6)) (Module.toMulActionWithZero.{u4, u1} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_6 _inst_11))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, u4, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{u4, u4, max (max u2 u3) u1, max (max u2 u3) u1} 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))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, max u3 u2, u1} 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, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u2, u3} R 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_inst_1) _inst_6 _inst_11)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u3) u1} R (LinearMap.{u4, u4, max u3 u2, u1} 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, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (TensorProduct.addCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_6 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) _inst_11) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, max u2 u3, u1} R R (TensorProduct.{u4, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, 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+Case conversion may be inaccurate. Consider using '#align tensor_product.lift.equiv_symm_apply TensorProduct.lift.equiv_symm_applyₓ'. -/
 @[simp]
 theorem lift.equiv_symm_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) :
     (lift.equiv R M N P).symm f m n = f (m ⊗ₜ n) :=
   rfl
 #align tensor_product.lift.equiv_symm_apply TensorProduct.lift.equiv_symm_apply
 
+/- warning: tensor_product.lcurry -> TensorProduct.lcurry is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.lcurry TensorProduct.lcurryₓ'. -/
 /-- Given a linear map `M ⊗ N → P`, compose it with the canonical bilinear map `M → N → M ⊗ N` to
 form a bilinear map `M → N → P`. -/
 def lcurry : (M ⊗[R] N →ₗ[R] P) →ₗ[R] M →ₗ[R] N →ₗ[R] P :=
@@ -597,26 +879,56 @@ def lcurry : (M ⊗[R] N →ₗ[R] P) →ₗ[R] M →ₗ[R] N →ₗ[R] P :=
 
 variable {R M N P}
 
+/- warning: tensor_product.lcurry_apply -> TensorProduct.lcurry_apply is a dubious translation:
+lean 3 declaration is
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 @[simp]
 theorem lcurry_apply (f : M ⊗[R] N →ₗ[R] P) (m : M) (n : N) : lcurry R M N P f m n = f (m ⊗ₜ n) :=
   rfl
 #align tensor_product.lcurry_apply TensorProduct.lcurry_apply
 
+/- warning: tensor_product.curry -> TensorProduct.curry is a dubious translation:
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 /-- Given a linear map `M ⊗ N → P`, compose it with the canonical bilinear map `M → N → M ⊗ N` to
 form a bilinear map `M → N → P`. -/
 def curry (f : M ⊗ N →ₗ[R] P) : M →ₗ[R] N →ₗ[R] P :=
   lcurry R M N P f
 #align tensor_product.curry TensorProduct.curry
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.curry_apply TensorProduct.curry_applyₓ'. -/
 @[simp]
 theorem curry_apply (f : M ⊗ N →ₗ[R] P) (m : M) (n : N) : curry f m n = f (m ⊗ₜ n) :=
   rfl
 #align tensor_product.curry_apply TensorProduct.curry_apply
 
+/- warning: tensor_product.curry_injective -> TensorProduct.curry_injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.curry_injective TensorProduct.curry_injectiveₓ'. -/
 theorem curry_injective : Function.Injective (curry : (M ⊗[R] N →ₗ[R] P) → M →ₗ[R] N →ₗ[R] P) :=
   fun g h H => ext H
 #align tensor_product.curry_injective TensorProduct.curry_injective
 
+/- warning: tensor_product.ext_threefold -> TensorProduct.ext_threefold is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.ext_threefold TensorProduct.ext_threefoldₓ'. -/
 theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
     (H : ∀ x y z, g (x ⊗ₜ y ⊗ₜ z) = h (x ⊗ₜ y ⊗ₜ z)) : g = h :=
   by
@@ -624,6 +936,12 @@ theorem ext_threefold {g h : (M ⊗[R] N) ⊗[R] P →ₗ[R] Q}
   exact H x y z
 #align tensor_product.ext_threefold TensorProduct.ext_threefold
 
+/- warning: tensor_product.ext_fourfold -> TensorProduct.ext_fourfold is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align tensor_product.ext_fourfold TensorProduct.ext_fourfoldₓ'. -/
 -- We'll need this one for checking the pentagon identity!
 theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
     (H : ∀ w x y z, g (w ⊗ₜ x ⊗ₜ y ⊗ₜ z) = h (w ⊗ₜ x ⊗ₜ y ⊗ₜ z)) : g = h :=
@@ -632,6 +950,12 @@ theorem ext_fourfold {g h : ((M ⊗[R] N) ⊗[R] P) ⊗[R] Q →ₗ[R] S}
   exact H w x y z
 #align tensor_product.ext_fourfold TensorProduct.ext_fourfold
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.ext_fourfold' TensorProduct.ext_fourfold'ₓ'. -/
 /-- Two linear maps (M ⊗ N) ⊗ (P ⊗ Q) → S which agree on all elements of the
 form (m ⊗ₜ n) ⊗ₜ (p ⊗ₜ q) are equal. -/
 theorem ext_fourfold' {φ ψ : (M ⊗[R] N) ⊗[R] P ⊗[R] Q →ₗ[R] S}
@@ -649,6 +973,12 @@ section
 
 variable (R M)
 
+/- warning: tensor_product.lid -> TensorProduct.lid is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.lid TensorProduct.lidₓ'. -/
 /-- The base ring is a left identity for the tensor product of modules, up to linear equivalence.
 -/
 protected def lid : R ⊗ M ≃ₗ[R] M :=
@@ -658,6 +988,12 @@ protected def lid : R ⊗ M ≃ₗ[R] M :=
 
 end
 
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u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_9)))) r m)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.lid_tmul TensorProduct.lid_tmulₓ'. -/
 @[simp]
 theorem lid_tmul (m : M) (r : R) : (TensorProduct.lid R M : R ⊗ M → M) (r ⊗ₜ m) = r • m :=
   by
@@ -665,6 +1001,12 @@ theorem lid_tmul (m : M) (r : R) : (TensorProduct.lid R M : R ⊗ M → M) (r 
   simp
 #align tensor_product.lid_tmul TensorProduct.lid_tmul
 
+/- warning: tensor_product.lid_symm_apply -> TensorProduct.lid_symm_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.lid_symm_apply TensorProduct.lid_symm_applyₓ'. -/
 @[simp]
 theorem lid_symm_apply (m : M) : (TensorProduct.lid R M).symm m = 1 ⊗ₜ m :=
   rfl
@@ -674,6 +1016,12 @@ section
 
 variable (R M N)
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.comm TensorProduct.commₓ'. -/
 /-- The tensor product of modules is commutative, up to linear equivalence.
 -/
 protected def comm : M ⊗ N ≃ₗ[R] N ⊗ M :=
@@ -681,11 +1029,23 @@ protected def comm : M ⊗ N ≃ₗ[R] N ⊗ M :=
     (ext' fun m n => rfl)
 #align tensor_product.comm TensorProduct.comm
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.comm_tmul TensorProduct.comm_tmulₓ'. -/
 @[simp]
 theorem comm_tmul (m : M) (n : N) : (TensorProduct.comm R M N) (m ⊗ₜ n) = n ⊗ₜ m :=
   rfl
 #align tensor_product.comm_tmul TensorProduct.comm_tmul
 
+/- warning: tensor_product.comm_symm_tmul -> TensorProduct.comm_symm_tmul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.comm_symm_tmul TensorProduct.comm_symm_tmulₓ'. -/
 @[simp]
 theorem comm_symm_tmul (m : M) (n : N) : (TensorProduct.comm R M N).symm (n ⊗ₜ m) = m ⊗ₜ n :=
   rfl
@@ -697,6 +1057,12 @@ section
 
 variable (R M)
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.rid TensorProduct.ridₓ'. -/
 /-- The base ring is a right identity for the tensor product of modules, up to linear equivalence.
 -/
 protected def rid : M ⊗[R] R ≃ₗ[R] M :=
@@ -705,6 +1071,12 @@ protected def rid : M ⊗[R] R ≃ₗ[R] M :=
 
 end
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.rid_tmul TensorProduct.rid_tmulₓ'. -/
 @[simp]
 theorem rid_tmul (m : M) (r : R) : (TensorProduct.rid R M) (m ⊗ₜ r) = r • m :=
   by
@@ -712,6 +1084,12 @@ theorem rid_tmul (m : M) (r : R) : (TensorProduct.rid R M) (m ⊗ₜ r) = r •
   simp
 #align tensor_product.rid_tmul TensorProduct.rid_tmul
 
+/- warning: tensor_product.rid_symm_apply -> TensorProduct.rid_symm_apply is a dubious translation:
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(CommSemiring.toSemiring.{u2} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align tensor_product.rid_symm_apply TensorProduct.rid_symm_applyₓ'. -/
 @[simp]
 theorem rid_symm_apply (m : M) : (TensorProduct.rid R M).symm m = m ⊗ₜ 1 :=
   rfl
@@ -723,6 +1101,12 @@ section
 
 variable (R M N P)
 
+/- warning: tensor_product.assoc -> TensorProduct.assoc is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.assoc TensorProduct.assocₓ'. -/
 /-- The associator for tensor product of R-modules, as a linear equivalence. -/
 protected def assoc : (M ⊗[R] N) ⊗[R] P ≃ₗ[R] M ⊗[R] N ⊗[R] P := by
   refine'
@@ -737,28 +1121,58 @@ protected def assoc : (M ⊗[R] N) ⊗[R] P ≃ₗ[R] M ⊗[R] N ⊗[R] P := by
 
 end
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.assoc_tmul TensorProduct.assoc_tmulₓ'. -/
 @[simp]
 theorem assoc_tmul (m : M) (n : N) (p : P) :
     (TensorProduct.assoc R M N P) (m ⊗ₜ n ⊗ₜ p) = m ⊗ₜ (n ⊗ₜ p) :=
   rfl
 #align tensor_product.assoc_tmul TensorProduct.assoc_tmul
 
+/- warning: tensor_product.assoc_symm_tmul -> TensorProduct.assoc_symm_tmul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.assoc_symm_tmul TensorProduct.assoc_symm_tmulₓ'. -/
 @[simp]
 theorem assoc_symm_tmul (m : M) (n : N) (p : P) :
     (TensorProduct.assoc R M N P).symm (m ⊗ₜ (n ⊗ₜ p)) = m ⊗ₜ n ⊗ₜ p :=
   rfl
 #align tensor_product.assoc_symm_tmul TensorProduct.assoc_symm_tmul
 
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 /-- The tensor product of a pair of linear maps between modules. -/
 def map (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : M ⊗ N →ₗ[R] P ⊗ Q :=
   lift <| comp (compl₂ (mk _ _ _) g) f
 #align tensor_product.map TensorProduct.map
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_tmul TensorProduct.map_tmulₓ'. -/
 @[simp]
 theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f g (m ⊗ₜ n) = f m ⊗ₜ g n :=
   rfl
 #align tensor_product.map_tmul TensorProduct.map_tmul
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_range_eq_span_tmul TensorProduct.map_range_eq_span_tmulₓ'. -/
 theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (map f g).range = Submodule.span R { t | ∃ m n, f m ⊗ₜ g n = t } :=
   by
@@ -774,6 +1188,12 @@ theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     simp only [map_tmul]
 #align tensor_product.map_range_eq_span_tmul TensorProduct.map_range_eq_span_tmul
 
+/- warning: tensor_product.map_incl -> TensorProduct.mapIncl is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_incl TensorProduct.mapInclₓ'. -/
 /-- Given submodules `p ⊆ P` and `q ⊆ Q`, this is the natural map: `p ⊗ q → P ⊗ Q`. -/
 @[simp]
 def mapIncl (p : Submodule R P) (q : Submodule R Q) : p ⊗[R] q →ₗ[R] P ⊗[R] Q :=
@@ -788,11 +1208,23 @@ variable [AddCommMonoid P'] [Module R P']
 
 variable [AddCommMonoid Q'] [Module R Q']
 
+/- warning: tensor_product.map_comp -> TensorProduct.map_comp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_comp TensorProduct.map_compₓ'. -/
 theorem map_comp (f₂ : P →ₗ[R] P') (f₁ : M →ₗ[R] P) (g₂ : Q →ₗ[R] Q') (g₁ : N →ₗ[R] Q) :
     map (f₂.comp f₁) (g₂.comp g₁) = (map f₂ g₂).comp (map f₁ g₁) :=
   ext' fun _ _ => rfl
 #align tensor_product.map_comp TensorProduct.map_comp
 
+/- warning: tensor_product.lift_comp_map -> TensorProduct.lift_comp_map is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.lift_comp_map TensorProduct.lift_comp_mapₓ'. -/
 theorem lift_comp_map (i : P →ₗ[R] Q →ₗ[R] Q') (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (lift i).comp (map f g) = lift ((i.comp f).compl₂ g) :=
   ext' fun _ _ => rfl
@@ -800,6 +1232,12 @@ theorem lift_comp_map (i : P →ₗ[R] Q →ₗ[R] Q') (f : M →ₗ[R] P) (g :
 
 attribute [local ext] ext
 
+/- warning: tensor_product.map_id -> TensorProduct.map_id is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_id TensorProduct.map_idₓ'. -/
 @[simp]
 theorem map_id : map (id : M →ₗ[R] M) (id : N →ₗ[R] N) = id :=
   by
@@ -807,16 +1245,34 @@ theorem map_id : map (id : M →ₗ[R] M) (id : N →ₗ[R] N) = id :=
   simp only [mk_apply, id_coe, compr₂_apply, id.def, map_tmul]
 #align tensor_product.map_id TensorProduct.map_id
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_one TensorProduct.map_oneₓ'. -/
 @[simp]
 theorem map_one : map (1 : M →ₗ[R] M) (1 : N →ₗ[R] N) = 1 :=
   map_id
 #align tensor_product.map_one TensorProduct.map_one
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_mul TensorProduct.map_mulₓ'. -/
 theorem map_mul (f₁ f₂ : M →ₗ[R] M) (g₁ g₂ : N →ₗ[R] N) :
     map (f₁ * f₂) (g₁ * g₂) = map f₁ g₁ * map f₂ g₂ :=
   map_comp f₁ f₂ g₁ g₂
 #align tensor_product.map_mul TensorProduct.map_mul
 
+/- warning: tensor_product.map_pow -> TensorProduct.map_pow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_pow TensorProduct.map_powₓ'. -/
 @[simp]
 protected theorem map_pow (f : M →ₗ[R] M) (g : N →ₗ[R] N) (n : ℕ) :
     map f g ^ n = map (f ^ n) (g ^ n) :=
@@ -826,24 +1282,48 @@ protected theorem map_pow (f : M →ₗ[R] M) (g : N →ₗ[R] N) (n : ℕ) :
   · simp only [pow_succ', ih, map_mul]
 #align tensor_product.map_pow TensorProduct.map_pow
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_add_left TensorProduct.map_add_leftₓ'. -/
 theorem map_add_left (f₁ f₂ : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (f₁ + f₂) g = map f₁ g + map f₂ g :=
   by
   ext
   simp only [add_tmul, compr₂_apply, mk_apply, map_tmul, add_apply]
 #align tensor_product.map_add_left TensorProduct.map_add_left
 
+/- warning: tensor_product.map_add_right -> TensorProduct.map_add_right is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_add_right TensorProduct.map_add_rightₓ'. -/
 theorem map_add_right (f : M →ₗ[R] P) (g₁ g₂ : N →ₗ[R] Q) : map f (g₁ + g₂) = map f g₁ + map f g₂ :=
   by
   ext
   simp only [tmul_add, compr₂_apply, mk_apply, map_tmul, add_apply]
 #align tensor_product.map_add_right TensorProduct.map_add_right
 
+/- warning: tensor_product.map_smul_left -> TensorProduct.map_smul_left is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_smul_left TensorProduct.map_smul_leftₓ'. -/
 theorem map_smul_left (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map (r • f) g = r • map f g :=
   by
   ext
   simp only [smul_tmul, compr₂_apply, mk_apply, map_tmul, smul_apply, tmul_smul]
 #align tensor_product.map_smul_left TensorProduct.map_smul_left
 
+/- warning: tensor_product.map_smul_right -> TensorProduct.map_smul_right is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_smul_right TensorProduct.map_smul_rightₓ'. -/
 theorem map_smul_right (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map f (r • g) = r • map f g :=
   by
   ext
@@ -852,46 +1332,82 @@ theorem map_smul_right (r : R) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : map f (
 
 variable (R M N P Q)
 
+/- warning: tensor_product.map_bilinear -> TensorProduct.mapBilinear is a dubious translation:
+lean 3 declaration is
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_inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.mapBilinear._proof_2.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u4} R R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _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 (TensorProduct.mapBilinear._proof_3.{u1, u4} R _inst_1 P _inst_6 _inst_11)) (LinearMap.module.{u1, u1, u1, max u3 u5, max (max u2 u3) u4 u5} R R R (LinearMap.{u1, u1, u3, 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 Q _inst_5 _inst_7 _inst_10 _inst_12) (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u5} R R N Q (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, max u4 u5} R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u5} R R R N Q (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_12 (TensorProduct.mapBilinear._proof_1.{u1, u5} R _inst_1 Q _inst_7 _inst_12)) (LinearMap.module.{u1, u1, u1, max u2 u3, max u4 u5} R R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.mapBilinear._proof_2.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.module.{u1, u1, u1, max u2 u3, max u4 u5} R R R (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.module.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.mapBilinear._proof_2.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12)) (TensorProduct.mapBilinear._proof_4.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) (N : Type.{u3}) (P : Type.{u4}) (Q : Type.{u5}) [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7], LinearMap.{u1, u1, max u4 u2, max (max (max u5 u4) u3 u2) u5 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))) (LinearMap.{u1, u1, u2, 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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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_bilinear TensorProduct.mapBilinearₓ'. -/
 /-- The tensor product of a pair of linear maps between modules, bilinear in both maps. -/
 def mapBilinear : (M →ₗ[R] P) →ₗ[R] (N →ₗ[R] Q) →ₗ[R] M ⊗[R] N →ₗ[R] P ⊗[R] Q :=
   LinearMap.mk₂ R map map_add_left map_smul_left map_add_right map_smul_right
 #align tensor_product.map_bilinear TensorProduct.mapBilinear
 
+#print TensorProduct.ltensorHomToHomLtensor /-
 /-- The canonical linear map from `P ⊗[R] (M →ₗ[R] Q)` to `(M →ₗ[R] P ⊗[R] Q)` -/
 def ltensorHomToHomLtensor : P ⊗[R] (M →ₗ[R] Q) →ₗ[R] M →ₗ[R] P ⊗[R] Q :=
   TensorProduct.lift (llcomp R M Q _ ∘ₗ mk R P Q)
 #align tensor_product.ltensor_hom_to_hom_ltensor TensorProduct.ltensorHomToHomLtensor
+-/
 
+#print TensorProduct.rtensorHomToHomRtensor /-
 /-- The canonical linear map from `(M →ₗ[R] P) ⊗[R] Q` to `(M →ₗ[R] P ⊗[R] Q)` -/
 def rtensorHomToHomRtensor : (M →ₗ[R] P) ⊗[R] Q →ₗ[R] M →ₗ[R] P ⊗[R] Q :=
   TensorProduct.lift (llcomp R M P _ ∘ₗ (mk R P Q).flip).flip
 #align tensor_product.rtensor_hom_to_hom_rtensor TensorProduct.rtensorHomToHomRtensor
+-/
 
+#print TensorProduct.homTensorHomMap /-
 /-- The linear map from `(M →ₗ P) ⊗ (N →ₗ Q)` to `(M ⊗ N →ₗ P ⊗ Q)` sending `f ⊗ₜ g` to
 the `tensor_product.map f g`, the tensor product of the two maps. -/
 def homTensorHomMap : (M →ₗ[R] P) ⊗[R] (N →ₗ[R] Q) →ₗ[R] M ⊗[R] N →ₗ[R] P ⊗[R] Q :=
   lift (mapBilinear R M N P Q)
 #align tensor_product.hom_tensor_hom_map TensorProduct.homTensorHomMap
+-/
 
 variable {R M N P Q}
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.map_bilinear_apply TensorProduct.mapBilinear_applyₓ'. -/
 @[simp]
 theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear R M N P Q f g = map f g :=
   rfl
 #align tensor_product.map_bilinear_apply TensorProduct.mapBilinear_apply
 
+/- warning: tensor_product.ltensor_hom_to_hom_ltensor_apply -> TensorProduct.ltensorHomToHomLtensor_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.ltensorHomToHomLtensor_applyₓ'. -/
 @[simp]
 theorem ltensorHomToHomLtensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
     ltensorHomToHomLtensor R M P Q (p ⊗ₜ f) m = p ⊗ₜ f m :=
   rfl
 #align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.ltensorHomToHomLtensor_apply
 
+/- warning: tensor_product.rtensor_hom_to_hom_rtensor_apply -> TensorProduct.rtensorHomToHomRtensor_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rtensorHomToHomRtensor_applyₓ'. -/
 @[simp]
 theorem rtensorHomToHomRtensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
     rtensorHomToHomRtensor R M P Q (f ⊗ₜ q) m = f m ⊗ₜ q :=
   rfl
 #align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rtensorHomToHomRtensor_apply
 
+/- warning: tensor_product.hom_tensor_hom_map_apply -> TensorProduct.homTensorHomMap_apply is a dubious translation:
+lean 3 declaration is
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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u4} R R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_6 _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 (TensorProduct.homTensorHomMap._proof_1.{u1, u4} R _inst_1 P _inst_6 _inst_11)) (LinearMap.module.{u1, u1, u1, u3, u5} R R R N Q (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_7 _inst_10 _inst_12 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_12 (TensorProduct.homTensorHomMap._proof_2.{u1, u5} R _inst_1 Q _inst_7 _inst_12)) f g)) (TensorProduct.map.{u1, u2, u3, u4, u5} R _inst_1 M N P Q _inst_4 _inst_5 _inst_6 _inst_7 _inst_9 _inst_10 _inst_11 _inst_12 f g)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.hom_tensor_hom_map_apply TensorProduct.homTensorHomMap_applyₓ'. -/
 @[simp]
 theorem homTensorHomMap_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     homTensorHomMap R M N P Q (f ⊗ₜ g) = map f g :=
@@ -900,6 +1416,12 @@ theorem homTensorHomMap_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
 
 end
 
+/- warning: tensor_product.congr -> TensorProduct.congr is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} {Q : Type.{u5}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_7 : AddCommMonoid.{u5} Q] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_12 : Module.{u1, u5} R Q (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7], (LinearEquiv.{u1, u1, 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)) M P _inst_4 _inst_6 _inst_9 _inst_11) -> (LinearEquiv.{u1, u1, u3, 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)) N Q _inst_5 _inst_7 _inst_10 _inst_12) -> (LinearEquiv.{u1, u1, max u3 u2, max u5 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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u5} R _inst_1 P Q _inst_6 _inst_7 _inst_11 _inst_12))
+Case conversion may be inaccurate. Consider using '#align tensor_product.congr TensorProduct.congrₓ'. -/
 /-- If `M` and `P` are linearly equivalent and `N` and `Q` are linearly equivalent
 then `M ⊗ N` and `P ⊗ Q` are linearly equivalent. -/
 def congr (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) : M ⊗ N ≃ₗ[R] P ⊗ Q :=
@@ -908,12 +1430,24 @@ def congr (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) : M ⊗ N ≃ₗ[R] P ⊗ Q :=
     (ext' fun m n => by simp <;> simp only [LinearEquiv.symm_apply_apply])
 #align tensor_product.congr TensorProduct.congr
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.congr_tmul TensorProduct.congr_tmulₓ'. -/
 @[simp]
 theorem congr_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (m : M) (n : N) :
     congr f g (m ⊗ₜ n) = f m ⊗ₜ g n :=
   rfl
 #align tensor_product.congr_tmul TensorProduct.congr_tmul
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.congr_symm_tmul TensorProduct.congr_symm_tmulₓ'. -/
 @[simp]
 theorem congr_symm_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (p : P) (q : Q) :
     (congr f g).symm (p ⊗ₜ q) = f.symm p ⊗ₜ g.symm q :=
@@ -922,6 +1456,12 @@ theorem congr_symm_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (p : P) (q : Q)
 
 variable (R M N P Q)
 
+/- warning: tensor_product.left_comm -> TensorProduct.leftComm is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align tensor_product.left_comm TensorProduct.leftCommₓ'. -/
 /-- A tensor product analogue of `mul_left_comm`. -/
 def leftComm : M ⊗[R] N ⊗[R] P ≃ₗ[R] N ⊗[R] M ⊗[R] P :=
   let e₁ := (TensorProduct.assoc R M N P).symm
@@ -932,11 +1472,23 @@ def leftComm : M ⊗[R] N ⊗[R] P ≃ₗ[R] N ⊗[R] M ⊗[R] P :=
 
 variable {M N P Q}
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.left_comm_tmul TensorProduct.leftComm_tmulₓ'. -/
 @[simp]
 theorem leftComm_tmul (m : M) (n : N) (p : P) : leftComm R M N P (m ⊗ₜ (n ⊗ₜ p)) = n ⊗ₜ (m ⊗ₜ p) :=
   rfl
 #align tensor_product.left_comm_tmul TensorProduct.leftComm_tmul
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.left_comm_symm_tmul TensorProduct.leftComm_symm_tmulₓ'. -/
 @[simp]
 theorem leftComm_symm_tmul (m : M) (n : N) (p : P) :
     (leftComm R M N P).symm (n ⊗ₜ (m ⊗ₜ p)) = m ⊗ₜ (n ⊗ₜ p) :=
@@ -945,6 +1497,12 @@ theorem leftComm_symm_tmul (m : M) (n : N) (p : P) :
 
 variable (M N P Q)
 
+/- warning: tensor_product.tensor_tensor_tensor_comm -> TensorProduct.tensorTensorTensorComm is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_comm TensorProduct.tensorTensorTensorCommₓ'. -/
 /-- This special case is worth defining explicitly since it is useful for defining multiplication
 on tensor products of modules carrying multiplications (e.g., associative rings, Lie rings, ...).
 
@@ -964,12 +1522,24 @@ def tensorTensorTensorComm : (M ⊗[R] N) ⊗[R] P ⊗[R] Q ≃ₗ[R] (M ⊗[R]
 
 variable {M N P Q}
 
+/- warning: tensor_product.tensor_tensor_tensor_comm_tmul -> TensorProduct.tensorTensorTensorComm_tmul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_comm_tmul TensorProduct.tensorTensorTensorComm_tmulₓ'. -/
 @[simp]
 theorem tensorTensorTensorComm_tmul (m : M) (n : N) (p : P) (q : Q) :
     tensorTensorTensorComm R M N P Q (m ⊗ₜ n ⊗ₜ (p ⊗ₜ q)) = m ⊗ₜ p ⊗ₜ (n ⊗ₜ q) :=
   rfl
 #align tensor_product.tensor_tensor_tensor_comm_tmul TensorProduct.tensorTensorTensorComm_tmul
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_comm_symm TensorProduct.tensorTensorTensorComm_symmₓ'. -/
 @[simp]
 theorem tensorTensorTensorComm_symm :
     (tensorTensorTensorComm R M N P Q).symm = tensorTensorTensorComm R M P N Q :=
@@ -978,6 +1548,12 @@ theorem tensorTensorTensorComm_symm :
 
 variable (M N P Q)
 
+/- warning: tensor_product.tensor_tensor_tensor_assoc -> TensorProduct.tensorTensorTensorAssoc is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_assoc TensorProduct.tensorTensorTensorAssocₓ'. -/
 /-- This special case is useful for describing the interplay between `dual_tensor_hom_equiv` and
 composition of linear maps.
 
@@ -993,12 +1569,24 @@ def tensorTensorTensorAssoc : (M ⊗[R] N) ⊗[R] P ⊗[R] Q ≃ₗ[R] (M ⊗[R]
 
 variable {M N P Q}
 
+/- warning: tensor_product.tensor_tensor_tensor_assoc_tmul -> TensorProduct.tensorTensorTensorAssoc_tmul is a dubious translation:
+lean 3 declaration is
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N P _inst_5 _inst_6 _inst_10 _inst_11) m (TensorProduct.tmul.{u1, u4, u3} R _inst_1 N P _inst_5 _inst_6 _inst_10 _inst_11 n p)) q)
+Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_assoc_tmul TensorProduct.tensorTensorTensorAssoc_tmulₓ'. -/
 @[simp]
 theorem tensorTensorTensorAssoc_tmul (m : M) (n : N) (p : P) (q : Q) :
     tensorTensorTensorAssoc R M N P Q (m ⊗ₜ n ⊗ₜ (p ⊗ₜ q)) = m ⊗ₜ (n ⊗ₜ p) ⊗ₜ q :=
   rfl
 #align tensor_product.tensor_tensor_tensor_assoc_tmul TensorProduct.tensorTensorTensorAssoc_tmul
 
+/- warning: tensor_product.tensor_tensor_tensor_assoc_symm_tmul -> TensorProduct.tensorTensorTensorAssoc_symm_tmul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.tensor_tensor_tensor_assoc_symm_tmul TensorProduct.tensorTensorTensorAssoc_symm_tmulₓ'. -/
 @[simp]
 theorem tensorTensorTensorAssoc_symm_tmul (m : M) (n : N) (p : P) (q : Q) :
     (tensorTensorTensorAssoc R M N P Q).symm (m ⊗ₜ (n ⊗ₜ p) ⊗ₜ q) = m ⊗ₜ n ⊗ₜ (p ⊗ₜ q) :=
@@ -1011,11 +1599,23 @@ namespace LinearMap
 
 variable {R} (M) {N P Q}
 
+/- warning: linear_map.ltensor -> LinearMap.ltensor is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) -> (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.module.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.module.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) -> (LinearMap.{u1, u1, max u3 u2, max u4 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 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 M N _inst_4 _inst_5 _inst_9 _inst_10) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u4} R _inst_1 M P _inst_4 _inst_6 _inst_9 _inst_11))
+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor LinearMap.ltensorₓ'. -/
 /-- `ltensor M f : M ⊗ N →ₗ M ⊗ P` is the natural linear map induced by `f : N →ₗ P`. -/
 def ltensor (f : N →ₗ[R] P) : M ⊗ N →ₗ[R] M ⊗ P :=
   TensorProduct.map id f
 #align linear_map.ltensor LinearMap.ltensor
 
+/- warning: linear_map.rtensor -> LinearMap.rtensor is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Type.{u2}) {N : Type.{u3}} {P : Type.{u4}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : AddCommMonoid.{u4} P] [_inst_9 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_10 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5] [_inst_11 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], (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))) N P _inst_5 _inst_6 _inst_10 _inst_11) -> (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u2} R _inst_1 N M _inst_5 _inst_4 _inst_10 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 P M _inst_6 _inst_4 _inst_11 _inst_9))
+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor LinearMap.rtensorₓ'. -/
 /-- `rtensor f M : N₁ ⊗ M →ₗ N₂ ⊗ M` is the natural linear map induced by `f : N₁ →ₗ N₂`. -/
 def rtensor (f : N →ₗ[R] P) : N ⊗ M →ₗ[R] P ⊗ M :=
   TensorProduct.map f id
@@ -1023,11 +1623,23 @@ def rtensor (f : N →ₗ[R] P) : N ⊗ M →ₗ[R] P ⊗ M :=
 
 variable (g : P →ₗ[R] Q) (f : N →ₗ[R] P)
 
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 @[simp]
 theorem ltensor_tmul (m : M) (n : N) : f.ltensor M (m ⊗ₜ n) = m ⊗ₜ f n :=
   rfl
 #align linear_map.ltensor_tmul LinearMap.ltensor_tmul
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_tmul LinearMap.rtensor_tmulₓ'. -/
 @[simp]
 theorem rtensor_tmul (m : M) (n : N) : f.rtensor M (n ⊗ₜ m) = f n ⊗ₜ m :=
   rfl
@@ -1037,6 +1649,12 @@ open TensorProduct
 
 attribute [local ext] TensorProduct.ext
 
+/- warning: linear_map.ltensor_hom -> LinearMap.ltensorHom is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_hom LinearMap.ltensorHomₓ'. -/
 /-- `ltensor_hom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
 def ltensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
     where
@@ -1050,6 +1668,12 @@ def ltensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P
     simp only [compr₂_apply, mk_apply, tmul_smul, smul_apply, ltensor_tmul]
 #align linear_map.ltensor_hom LinearMap.ltensorHom
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_hom LinearMap.rtensorHomₓ'. -/
 /-- `rtensor_hom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
 def rtensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
     where
@@ -1063,91 +1687,199 @@ def rtensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M
     simp only [compr₂_apply, mk_apply, smul_tmul, tmul_smul, smul_apply, rtensor_tmul]
 #align linear_map.rtensor_hom LinearMap.rtensorHom
 
+/- warning: linear_map.coe_ltensor_hom -> LinearMap.coe_ltensorHom is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.coe_ltensor_hom LinearMap.coe_ltensorHomₓ'. -/
 @[simp]
 theorem coe_ltensorHom : (ltensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R] M ⊗[R] P) = ltensor M :=
   rfl
 #align linear_map.coe_ltensor_hom LinearMap.coe_ltensorHom
 
+/- warning: linear_map.coe_rtensor_hom -> LinearMap.coe_rtensorHom is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.coe_rtensor_hom LinearMap.coe_rtensorHomₓ'. -/
 @[simp]
 theorem coe_rtensorHom : (rtensorHom M : (N →ₗ[R] P) → N ⊗[R] M →ₗ[R] P ⊗[R] M) = rtensor M :=
   rfl
 #align linear_map.coe_rtensor_hom LinearMap.coe_rtensorHom
 
+/- warning: linear_map.ltensor_add -> LinearMap.ltensor_add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_add LinearMap.ltensor_addₓ'. -/
 @[simp]
 theorem ltensor_add (f g : N →ₗ[R] P) : (f + g).ltensor M = f.ltensor M + g.ltensor M :=
   (ltensorHom M).map_add f g
 #align linear_map.ltensor_add LinearMap.ltensor_add
 
+/- warning: linear_map.rtensor_add -> LinearMap.rtensor_add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_add LinearMap.rtensor_addₓ'. -/
 @[simp]
 theorem rtensor_add (f g : N →ₗ[R] P) : (f + g).rtensor M = f.rtensor M + g.rtensor M :=
   (rtensorHom M).map_add f g
 #align linear_map.rtensor_add LinearMap.rtensor_add
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_zero LinearMap.ltensor_zeroₓ'. -/
 @[simp]
 theorem ltensor_zero : ltensor M (0 : N →ₗ[R] P) = 0 :=
   (ltensorHom M).map_zero
 #align linear_map.ltensor_zero LinearMap.ltensor_zero
 
+/- warning: linear_map.rtensor_zero -> LinearMap.rtensor_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_zero LinearMap.rtensor_zeroₓ'. -/
 @[simp]
 theorem rtensor_zero : rtensor M (0 : N →ₗ[R] P) = 0 :=
   (rtensorHom M).map_zero
 #align linear_map.rtensor_zero LinearMap.rtensor_zero
 
+/- warning: linear_map.ltensor_smul -> LinearMap.ltensor_smul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_smul LinearMap.ltensor_smulₓ'. -/
 @[simp]
 theorem ltensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).ltensor M = r • f.ltensor M :=
   (ltensorHom M).map_smul r f
 #align linear_map.ltensor_smul LinearMap.ltensor_smul
 
+/- warning: linear_map.rtensor_smul -> LinearMap.rtensor_smul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_smul LinearMap.rtensor_smulₓ'. -/
 @[simp]
 theorem rtensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).rtensor M = r • f.rtensor M :=
   (rtensorHom M).map_smul r f
 #align linear_map.rtensor_smul LinearMap.rtensor_smul
 
+/- warning: linear_map.ltensor_comp -> LinearMap.ltensor_comp is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp LinearMap.ltensor_compₓ'. -/
 theorem ltensor_comp : (g.comp f).ltensor M = (g.ltensor M).comp (f.ltensor M) :=
   by
   ext (m n)
   simp only [compr₂_apply, mk_apply, comp_apply, ltensor_tmul]
 #align linear_map.ltensor_comp LinearMap.ltensor_comp
 
+/- warning: linear_map.ltensor_comp_apply -> LinearMap.ltensor_comp_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_apply LinearMap.ltensor_comp_applyₓ'. -/
 theorem ltensor_comp_apply (x : M ⊗[R] N) :
     (g.comp f).ltensor M x = (g.ltensor M) ((f.ltensor M) x) := by rw [ltensor_comp, coe_comp]
 #align linear_map.ltensor_comp_apply LinearMap.ltensor_comp_apply
 
+/- warning: linear_map.rtensor_comp -> LinearMap.rtensor_comp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp LinearMap.rtensor_compₓ'. -/
 theorem rtensor_comp : (g.comp f).rtensor M = (g.rtensor M).comp (f.rtensor M) :=
   by
   ext (m n)
   simp only [compr₂_apply, mk_apply, comp_apply, rtensor_tmul]
 #align linear_map.rtensor_comp LinearMap.rtensor_comp
 
+/- warning: linear_map.rtensor_comp_apply -> LinearMap.rtensor_comp_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_apply LinearMap.rtensor_comp_applyₓ'. -/
 theorem rtensor_comp_apply (x : N ⊗[R] M) :
     (g.comp f).rtensor M x = (g.rtensor M) ((f.rtensor M) x) := by rw [rtensor_comp, coe_comp]
 #align linear_map.rtensor_comp_apply LinearMap.rtensor_comp_apply
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_mul LinearMap.ltensor_mulₓ'. -/
 theorem ltensor_mul (f g : Module.End R N) : (f * g).ltensor M = f.ltensor M * g.ltensor M :=
   ltensor_comp M f g
 #align linear_map.ltensor_mul LinearMap.ltensor_mul
 
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 theorem rtensor_mul (f g : Module.End R N) : (f * g).rtensor M = f.rtensor M * g.rtensor M :=
   rtensor_comp M f g
 #align linear_map.rtensor_mul LinearMap.rtensor_mul
 
 variable (N)
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_id LinearMap.ltensor_idₓ'. -/
 @[simp]
 theorem ltensor_id : (id : N →ₗ[R] N).ltensor M = id :=
   map_id
 #align linear_map.ltensor_id LinearMap.ltensor_id
 
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 -- `simp` can prove this.
 theorem ltensor_id_apply (x : M ⊗[R] N) : (LinearMap.id : N →ₗ[R] N).ltensor M x = x := by
   rw [ltensor_id, id_coe, id.def]
 #align linear_map.ltensor_id_apply LinearMap.ltensor_id_apply
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_id LinearMap.rtensor_idₓ'. -/
 @[simp]
 theorem rtensor_id : (id : N →ₗ[R] N).rtensor M = id :=
   map_id
 #align linear_map.rtensor_id LinearMap.rtensor_id
 
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 -- `simp` can prove this.
 theorem rtensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rtensor M x = x := by
   rw [rtensor_id, id_coe, id.def]
@@ -1155,36 +1887,72 @@ theorem rtensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rtens
 
 variable {N}
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_rtensor LinearMap.ltensor_comp_rtensorₓ'. -/
 @[simp]
 theorem ltensor_comp_rtensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (g.ltensor P).comp (f.rtensor N) = map f g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.ltensor_comp_rtensor LinearMap.ltensor_comp_rtensor
 
+/- warning: linear_map.rtensor_comp_ltensor -> LinearMap.rtensor_comp_ltensor is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_ltensor LinearMap.rtensor_comp_ltensorₓ'. -/
 @[simp]
 theorem rtensor_comp_ltensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (f.rtensor Q).comp (g.ltensor M) = map f g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.rtensor_comp_ltensor LinearMap.rtensor_comp_ltensor
 
+/- warning: linear_map.map_comp_rtensor -> LinearMap.map_comp_rtensor is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.map_comp_rtensor LinearMap.map_comp_rtensorₓ'. -/
 @[simp]
 theorem map_comp_rtensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (f' : S →ₗ[R] M) :
     (map f g).comp (f'.rtensor _) = map (f.comp f') g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.map_comp_rtensor LinearMap.map_comp_rtensor
 
+/- warning: linear_map.map_comp_ltensor -> LinearMap.map_comp_ltensor is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.map_comp_ltensor LinearMap.map_comp_ltensorₓ'. -/
 @[simp]
 theorem map_comp_ltensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (g' : S →ₗ[R] N) :
     (map f g).comp (g'.ltensor _) = map f (g.comp g') := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.map_comp_ltensor LinearMap.map_comp_ltensor
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_comp_map LinearMap.rtensor_comp_mapₓ'. -/
 @[simp]
 theorem rtensor_comp_map (f' : P →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (f'.rtensor _).comp (map f g) = map (f'.comp f) g := by
   simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
 #align linear_map.rtensor_comp_map LinearMap.rtensor_comp_map
 
+/- warning: linear_map.ltensor_comp_map -> LinearMap.ltensor_comp_map is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_comp_map LinearMap.ltensor_comp_mapₓ'. -/
 @[simp]
 theorem ltensor_comp_map (g' : Q →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (g'.ltensor _).comp (map f g) = map f (g'.comp g) := by
@@ -1193,6 +1961,12 @@ theorem ltensor_comp_map (g' : Q →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[
 
 variable {M}
 
+/- warning: linear_map.rtensor_pow -> LinearMap.rtensor_pow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_pow LinearMap.rtensor_powₓ'. -/
 @[simp]
 theorem rtensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rtensor N ^ n = (f ^ n).rtensor N :=
   by
@@ -1200,6 +1974,12 @@ theorem rtensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rtensor N ^ n = (f ^ n).rt
   rwa [id_pow] at h
 #align linear_map.rtensor_pow LinearMap.rtensor_pow
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_pow LinearMap.ltensor_powₓ'. -/
 @[simp]
 theorem ltensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.ltensor M ^ n = (f ^ n).ltensor M :=
   by
@@ -1229,6 +2009,12 @@ open LinearMap
 
 variable (R)
 
+/- warning: tensor_product.neg.aux -> TensorProduct.Neg.aux is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.neg.aux TensorProduct.Neg.auxₓ'. -/
 /-- Auxiliary function to defining negation multiplication on tensor product. -/
 def Neg.aux : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
   FreeAddMonoid.lift fun p : M × N => (-p.1) ⊗ₜ p.2
@@ -1236,6 +2022,12 @@ def Neg.aux : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
 
 variable {R}
 
+/- warning: tensor_product.neg.aux_of -> TensorProduct.Neg.aux_of is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.neg.aux_of TensorProduct.Neg.aux_ofₓ'. -/
 theorem Neg.aux_of (m : M) (n : N) : Neg.aux R (FreeAddMonoid.of (m, n)) = (-m) ⊗ₜ[R] n :=
   rfl
 #align tensor_product.neg.aux_of TensorProduct.Neg.aux_of
@@ -1259,6 +2051,12 @@ instance : Neg (M ⊗[R] N)
         | _, _, eqv.add_comm x y =>
           (AddCon.ker_rel _).2 <| by simp_rw [AddMonoidHom.map_add, add_comm]
 
+/- warning: tensor_product.add_left_neg -> TensorProduct.add_left_neg is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tensor_product.add_left_neg TensorProduct.add_left_negₓ'. -/
 protected theorem add_left_neg (x : M ⊗[R] N) : -x + x = 0 :=
   TensorProduct.induction_on x
     (by
@@ -1290,22 +2088,52 @@ instance : AddCommGroup (M ⊗[R] N) :=
         add_smul, ← sub_eq_add_neg, sub_self, zero_smul, add_zero]
       rfl }
 
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+Case conversion may be inaccurate. Consider using '#align tensor_product.neg_tmul TensorProduct.neg_tmulₓ'. -/
 theorem neg_tmul (m : M) (n : N) : (-m) ⊗ₜ n = -m ⊗ₜ[R] n :=
   rfl
 #align tensor_product.neg_tmul TensorProduct.neg_tmul
 
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 theorem tmul_neg (m : M) (n : N) : m ⊗ₜ (-n) = -m ⊗ₜ[R] n :=
   (mk R M N _).map_neg _
 #align tensor_product.tmul_neg TensorProduct.tmul_neg
 
+/- warning: tensor_product.tmul_sub -> TensorProduct.tmul_sub is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.tmul_sub TensorProduct.tmul_subₓ'. -/
 theorem tmul_sub (m : M) (n₁ n₂ : N) : m ⊗ₜ (n₁ - n₂) = m ⊗ₜ[R] n₁ - m ⊗ₜ[R] n₂ :=
   (mk R M N _).map_sub _ _
 #align tensor_product.tmul_sub TensorProduct.tmul_sub
 
+/- warning: tensor_product.sub_tmul -> TensorProduct.sub_tmul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align tensor_product.sub_tmul TensorProduct.sub_tmulₓ'. -/
 theorem sub_tmul (m₁ m₂ : M) (n : N) : (m₁ - m₂) ⊗ₜ n = m₁ ⊗ₜ[R] n - m₂ ⊗ₜ[R] n :=
   (mk R M N).map_sub₂ _ _ _
 #align tensor_product.sub_tmul TensorProduct.sub_tmul
 
+/- warning: tensor_product.compatible_smul.int -> TensorProduct.CompatibleSMul.int is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)], TensorProduct.CompatibleSMul.{u1, 0, u2, u3} R _inst_1 Int Int.monoid M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8 (Module.toDistribMulAction.{0, u2} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.intModule.{u2} M _inst_2)) (Module.toDistribMulAction.{0, u3} Int N Int.semiring (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.intModule.{u3} N _inst_3))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)], TensorProduct.CompatibleSMul.{u1, 0, u2, u3} R _inst_1 Int Int.instMonoidInt M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8 (Module.toDistribMulAction.{0, u2} Int M (Ring.toSemiring.{0} Int (CommRing.toRing.{0} Int Int.instCommRingInt)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.intModule.{u2} M _inst_2)) (Module.toDistribMulAction.{0, u3} Int N (Ring.toSemiring.{0} Int (CommRing.toRing.{0} Int Int.instCommRingInt)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.intModule.{u3} N _inst_3))
+Case conversion may be inaccurate. Consider using '#align tensor_product.compatible_smul.int TensorProduct.CompatibleSMul.intₓ'. -/
 /-- While the tensor product will automatically inherit a ℤ-module structure from
 `add_comm_group.int_module`, that structure won't be compatible with lemmas like `tmul_smul` unless
 we use a `ℤ-module` instance provided by `tensor_product.left_module`.
@@ -1314,36 +2142,66 @@ When `R` is a `ring` we get the required `tensor_product.compatible_smul` instan
 `is_scalar_tower`, but when it is only a `semiring` we need to build it from scratch.
 The instance diamond in `compatible_smul` doesn't matter because it's in `Prop`.
 -/
-instance CompatibleSmul.int : CompatibleSmul R ℤ M N :=
+instance CompatibleSMul.int : CompatibleSMul R ℤ M N :=
   ⟨fun r m n =>
     Int.induction_on r (by simp) (fun r ih => by simpa [add_smul, tmul_add, add_tmul] using ih)
       fun r ih => by simpa [sub_smul, tmul_sub, sub_tmul] using ih⟩
-#align tensor_product.compatible_smul.int TensorProduct.CompatibleSmul.int
-
-instance CompatibleSmul.unit {S} [Monoid S] [DistribMulAction S M] [DistribMulAction S N]
-    [CompatibleSmul R S M N] : CompatibleSmul R Sˣ M N :=
-  ⟨fun s m n => (CompatibleSmul.smul_tmul (s : S) m n : _)⟩
-#align tensor_product.compatible_smul.unit TensorProduct.CompatibleSmul.unit
+#align tensor_product.compatible_smul.int TensorProduct.CompatibleSMul.int
+
+/- warning: tensor_product.compatible_smul.unit -> TensorProduct.CompatibleSMul.unit is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] {S : Type.{u4}} [_inst_12 : Monoid.{u4} S] [_inst_13 : DistribMulAction.{u4, u2} S M _inst_12 (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))] [_inst_14 : DistribMulAction.{u4, u3} S N _inst_12 (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_3)))] [_inst_15 : TensorProduct.CompatibleSMul.{u1, u4, u2, u3} R _inst_1 S _inst_12 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8 _inst_13 _inst_14], TensorProduct.CompatibleSMul.{u1, u4, u2, u3} R _inst_1 (Units.{u4} S _inst_12) (DivInvMonoid.toMonoid.{u4} (Units.{u4} S _inst_12) (Group.toDivInvMonoid.{u4} (Units.{u4} S _inst_12) (Units.group.{u4} S _inst_12))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8 (Units.distribMulAction.{u4, u2} S M _inst_12 (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) _inst_13) (Units.distribMulAction.{u4, u3} S N _inst_12 (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)) _inst_14)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] {S : Type.{u4}} [_inst_12 : Monoid.{u4} S] [_inst_13 : DistribMulAction.{u4, u2} S M _inst_12 (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))] [_inst_14 : DistribMulAction.{u4, u3} S N _inst_12 (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_3)))] [_inst_15 : TensorProduct.CompatibleSMul.{u1, u4, u2, u3} R _inst_1 S _inst_12 M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8 _inst_13 _inst_14], TensorProduct.CompatibleSMul.{u1, u4, u2, u3} R _inst_1 (Units.{u4} S _inst_12) (DivInvMonoid.toMonoid.{u4} (Units.{u4} S _inst_12) (Group.toDivInvMonoid.{u4} (Units.{u4} S _inst_12) (Units.instGroupUnits.{u4} S _inst_12))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_7 _inst_8 (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u4, u2} S M _inst_12 (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) _inst_13) (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u4, u3} S N _inst_12 (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)) _inst_14)
+Case conversion may be inaccurate. Consider using '#align tensor_product.compatible_smul.unit TensorProduct.CompatibleSMul.unitₓ'. -/
+instance CompatibleSMul.unit {S} [Monoid S] [DistribMulAction S M] [DistribMulAction S N]
+    [CompatibleSMul R S M N] : CompatibleSMul R Sˣ M N :=
+  ⟨fun s m n => (CompatibleSMul.smul_tmul (s : S) m n : _)⟩
+#align tensor_product.compatible_smul.unit TensorProduct.CompatibleSMul.unit
 
 end TensorProduct
 
 namespace LinearMap
 
+/- warning: linear_map.ltensor_sub -> LinearMap.ltensor_sub is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : AddCommGroup.{u4} P] [_inst_7 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] [_inst_9 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4)] (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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_8 _inst_9) (g : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_sub LinearMap.ltensor_subₓ'. -/
 @[simp]
 theorem ltensor_sub (f g : N →ₗ[R] P) : (f - g).ltensor M = f.ltensor M - g.ltensor M := by
   simp only [← coe_ltensor_hom, map_sub]
 #align linear_map.ltensor_sub LinearMap.ltensor_sub
 
+/- warning: linear_map.rtensor_sub -> LinearMap.rtensor_sub is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_sub LinearMap.rtensor_subₓ'. -/
 @[simp]
 theorem rtensor_sub (f g : N →ₗ[R] P) : (f - g).rtensor M = f.rtensor M - g.rtensor M := by
   simp only [← coe_rtensor_hom, map_sub]
 #align linear_map.rtensor_sub LinearMap.rtensor_sub
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.ltensor_neg LinearMap.ltensor_negₓ'. -/
 @[simp]
 theorem ltensor_neg (f : N →ₗ[R] P) : (-f).ltensor M = -f.ltensor M := by
   simp only [← coe_ltensor_hom, map_neg]
 #align linear_map.ltensor_neg LinearMap.ltensor_neg
 
+/- warning: linear_map.rtensor_neg -> LinearMap.rtensor_neg is a dubious translation:
+lean 3 declaration is
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u2} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 _inst_7)) (LinearMap.rtensor.{u1, u2, u3, u4} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_8 _inst_9 (Neg.neg.{max u3 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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_8 _inst_9) (LinearMap.hasNeg.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_4 _inst_8 _inst_9 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f)) (Neg.neg.{max 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_8 _inst_7) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 _inst_7)) (LinearMap.hasNeg.{u1, u1, max u3 u2, max u4 u2} R R (TensorProduct.{u1, u3, u2} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_8 _inst_7) (TensorProduct.{u1, u4, u2} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u2} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_8 _inst_7) (TensorProduct.addCommGroup.{u1, u4, u2} R _inst_1 P M _inst_4 _inst_2 _inst_9 _inst_7) (TensorProduct.module.{u1, u3, u2} R _inst_1 N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_8 _inst_7) (TensorProduct.module.{u1, u4, u2} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 _inst_7) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.rtensor.{u1, u2, u3, u4} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u4} P _inst_4) _inst_7 _inst_8 _inst_9 f))
+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Type.{u1}} {N : Type.{u3}} {P : Type.{u2}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : AddCommGroup.{u2} P] [_inst_7 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Module.{u4, u3} R N (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] [_inst_9 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4)] (f : LinearMap.{u4, u4, u3, u2} 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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_8 _inst_9), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u1 u3, max u1 u2} R R 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_inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R _inst_1 P M (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_9 _inst_7)) (LinearMap.rtensor.{u4, u1, u3, u2} R _inst_1 M N P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_7 _inst_8 _inst_9 (Neg.neg.{max u3 u2} (LinearMap.{u4, u4, u3, u2} 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))) N P (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) (AddCommGroup.toAddCommMonoid.{u2} P _inst_4) _inst_8 _inst_9) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u4, u3, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_4 _inst_8 _inst_9 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+Case conversion may be inaccurate. Consider using '#align linear_map.rtensor_neg LinearMap.rtensor_negₓ'. -/
 @[simp]
 theorem rtensor_neg (f : N →ₗ[R] P) : (-f).rtensor M = -f.rtensor M := by
   simp only [← coe_rtensor_hom, map_neg]

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

• add LinearMap.(l|r)Tensor and their properties
• add congr_symm, congr_refl_refl, congr_trans, congr_mul, congr_pow and congr_zpow

@@ -1032,6 +1032,30 @@ theorem congr_symm_tmul (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (p : P) (q : Q)
   rfl
 #align tensor_product.congr_symm_tmul TensorProduct.congr_symm_tmul
 
+theorem congr_symm (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) : (congr f g).symm = congr f.symm g.symm := rfl
+
+@[simp] theorem congr_refl_refl : congr (.refl R M) (.refl R N) = .refl R _ :=
+  LinearEquiv.toLinearMap_injective <| ext' fun _ _ ↦ rfl
+
+theorem congr_trans (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (f' : P ≃ₗ[R] S) (g' : Q ≃ₗ[R] T) :
+    congr (f ≪≫ₗ f') (g ≪≫ₗ g') = congr f g ≪≫ₗ congr f' g' :=
+  LinearEquiv.toLinearMap_injective <| map_comp _ _ _ _
+
+theorem congr_mul (f : M ≃ₗ[R] M) (g : N ≃ₗ[R] N) (f' : M ≃ₗ[R] M) (g' : N ≃ₗ[R] N) :
+    congr (f * f') (g * g') = congr f g * congr f' g' := congr_trans _ _ _ _
+
+@[simp] theorem congr_pow (f : M ≃ₗ[R] M) (g : N ≃ₗ[R] N) (n : ℕ) :
+    congr f g ^ n = congr (f ^ n) (g ^ n) := by
+  induction n with
+  | zero => exact congr_refl_refl.symm
+  | succ n ih => simp_rw [pow_succ, ih, congr_mul]
+
+@[simp] theorem congr_zpow (f : M ≃ₗ[R] M) (g : N ≃ₗ[R] N) (n : ℤ) :
+    congr f g ^ n = congr (f ^ n) (g ^ n) := by
+  induction n with
+  | ofNat n => exact congr_pow _ _ _
+  | negSucc n => simp_rw [zpow_negSucc, congr_pow]; exact congr_symm _ _
+
 variable (R M N P Q)
 
 /-- A tensor product analogue of `mul_left_comm`. -/
@@ -1121,16 +1145,19 @@ theorem tensorTensorTensorAssoc_symm_tmul (m : M) (n : N) (p : P) (q : Q) :
 end TensorProduct
 
 open scoped TensorProduct
+
 namespace LinearMap
 
 variable {N}
 
-/-- `lTensor M f : M ⊗ N →ₗ M ⊗ P` is the natural linear map induced by `f : N →ₗ P`. -/
+/-- `LinearMap.lTensor M f : M ⊗ N →ₗ M ⊗ P` is the natural linear map
+induced by `f : N →ₗ P`. -/
 def lTensor (f : N →ₗ[R] P) : M ⊗[R] N →ₗ[R] M ⊗[R] P :=
   TensorProduct.map id f
 #align linear_map.ltensor LinearMap.lTensor
 
-/-- `rTensor f M : N₁ ⊗ M →ₗ N₂ ⊗ M` is the natural linear map induced by `f : N₁ →ₗ N₂`. -/
+/-- `LinearMap.rTensor M f : N₁ ⊗ M →ₗ N₂ ⊗ M` is the natural linear map
+induced by `f : N₁ →ₗ N₂`. -/
 def rTensor (f : N →ₗ[R] P) : N ⊗[R] M →ₗ[R] P ⊗[R] M :=
   TensorProduct.map f id
 #align linear_map.rtensor LinearMap.rTensor
@@ -1355,6 +1382,114 @@ theorem lTensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.lTensor M ^ n = (f ^ n).lT
 
 end LinearMap
 
+namespace LinearEquiv
+
+variable {N}
+
+/-- `LinearEquiv.lTensor M f : M ⊗ N ≃ₗ M ⊗ P` is the natural linear equivalence
+induced by `f : N ≃ₗ P`. -/
+def lTensor (f : N ≃ₗ[R] P) : M ⊗[R] N ≃ₗ[R] M ⊗[R] P := TensorProduct.congr (refl R M) f
+
+/-- `LinearEquiv.rTensor M f : N₁ ⊗ M ≃ₗ N₂ ⊗ M` is the natural linear equivalence
+induced by `f : N₁ ≃ₗ N₂`. -/
+def rTensor (f : N ≃ₗ[R] P) : N ⊗[R] M ≃ₗ[R] P ⊗[R] M := TensorProduct.congr f (refl R M)
+
+variable (g : P ≃ₗ[R] Q) (f : N ≃ₗ[R] P) (m : M) (n : N) (p : P) (x : M ⊗[R] N) (y : N ⊗[R] M)
+
+@[simp] theorem coe_lTensor : lTensor M f = (f : N →ₗ[R] P).lTensor M := rfl
+
+@[simp] theorem coe_lTensor_symm : (lTensor M f).symm = (f.symm : P →ₗ[R] N).lTensor M := rfl
+
+@[simp] theorem coe_rTensor : rTensor M f = (f : N →ₗ[R] P).rTensor M := rfl
+
+@[simp] theorem coe_rTensor_symm : (rTensor M f).symm = (f.symm : P →ₗ[R] N).rTensor M := rfl
+
+@[simp] theorem lTensor_tmul : f.lTensor M (m ⊗ₜ n) = m ⊗ₜ f n := rfl
+
+@[simp] theorem lTensor_symm_tmul : (f.lTensor M).symm (m ⊗ₜ p) = m ⊗ₜ f.symm p := rfl
+
+@[simp] theorem rTensor_tmul : f.rTensor M (n ⊗ₜ m) = f n ⊗ₜ m := rfl
+
+@[simp] theorem rTensor_symm_tmul : (f.rTensor M).symm (p ⊗ₜ m) = f.symm p ⊗ₜ m := rfl
+
+lemma comm_trans_rTensor_trans_comm_eq (g : N ≃ₗ[R] P) :
+    TensorProduct.comm R Q N ≪≫ₗ rTensor Q g ≪≫ₗ TensorProduct.comm R P Q = lTensor Q g :=
+  toLinearMap_injective <| TensorProduct.ext rfl
+
+lemma comm_trans_lTensor_trans_comm_eq (g : N ≃ₗ[R] P) :
+    TensorProduct.comm R N Q ≪≫ₗ lTensor Q g ≪≫ₗ TensorProduct.comm R Q P = rTensor Q g :=
+  toLinearMap_injective <| TensorProduct.ext rfl
+
+theorem lTensor_trans : (f ≪≫ₗ g).lTensor M = f.lTensor M ≪≫ₗ g.lTensor M :=
+  toLinearMap_injective <| LinearMap.lTensor_comp M _ _
+
+theorem lTensor_trans_apply : (f ≪≫ₗ g).lTensor M x = g.lTensor M (f.lTensor M x) :=
+  LinearMap.lTensor_comp_apply M _ _ x
+
+theorem rTensor_trans : (f ≪≫ₗ g).rTensor M = f.rTensor M ≪≫ₗ g.rTensor M :=
+  toLinearMap_injective <| LinearMap.rTensor_comp M _ _
+
+theorem rTensor_trans_apply : (f ≪≫ₗ g).rTensor M y = g.rTensor M (f.rTensor M y) :=
+  LinearMap.rTensor_comp_apply M _ _ y
+
+theorem lTensor_mul (f g : N ≃ₗ[R] N) : (f * g).lTensor M = f.lTensor M * g.lTensor M :=
+  lTensor_trans M f g
+
+theorem rTensor_mul (f g : N ≃ₗ[R] N) : (f * g).rTensor M = f.rTensor M * g.rTensor M :=
+  rTensor_trans M f g
+
+variable (N)
+
+@[simp] theorem lTensor_refl : (refl R N).lTensor M = refl R _ := TensorProduct.congr_refl_refl
+
+theorem lTensor_refl_apply : (refl R N).lTensor M x = x := by rw [lTensor_refl, refl_apply]
+
+@[simp] theorem rTensor_refl : (refl R N).rTensor M = refl R _ := TensorProduct.congr_refl_refl
+
+theorem rTensor_refl_apply : (refl R N).rTensor M y = y := by rw [rTensor_refl, refl_apply]
+
+variable {N}
+
+@[simp] theorem rTensor_trans_lTensor (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) :
+    f.rTensor N ≪≫ₗ g.lTensor P = TensorProduct.congr f g :=
+  toLinearMap_injective <| LinearMap.lTensor_comp_rTensor M _ _
+
+@[simp] theorem lTensor_trans_rTensor (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) :
+    g.lTensor M ≪≫ₗ f.rTensor Q = TensorProduct.congr f g :=
+  toLinearMap_injective <| LinearMap.rTensor_comp_lTensor M _ _
+
+@[simp] theorem rTensor_trans_congr (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (f' : S ≃ₗ[R] M) :
+    f'.rTensor _ ≪≫ₗ TensorProduct.congr f g = TensorProduct.congr (f' ≪≫ₗ f) g :=
+  toLinearMap_injective <| LinearMap.map_comp_rTensor M _ _ _
+
+@[simp] theorem lTensor_trans_congr (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) (g' : S ≃ₗ[R] N) :
+    g'.lTensor _ ≪≫ₗ TensorProduct.congr f g = TensorProduct.congr f (g' ≪≫ₗ g) :=
+  toLinearMap_injective <| LinearMap.map_comp_lTensor M _ _ _
+
+@[simp] theorem congr_trans_rTensor (f' : P ≃ₗ[R] S) (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) :
+    TensorProduct.congr f g ≪≫ₗ f'.rTensor _ = TensorProduct.congr (f ≪≫ₗ f') g :=
+  toLinearMap_injective <| LinearMap.rTensor_comp_map M _ _ _
+
+@[simp] theorem congr_trans_lTensor (g' : Q ≃ₗ[R] S) (f : M ≃ₗ[R] P) (g : N ≃ₗ[R] Q) :
+    TensorProduct.congr f g ≪≫ₗ g'.lTensor _ = TensorProduct.congr f (g ≪≫ₗ g') :=
+  toLinearMap_injective <| LinearMap.lTensor_comp_map M _ _ _
+
+variable {M}
+
+@[simp] theorem rTensor_pow (f : M ≃ₗ[R] M) (n : ℕ) : f.rTensor N ^ n = (f ^ n).rTensor N := by
+  simpa only [one_pow] using TensorProduct.congr_pow f (1 : N ≃ₗ[R] N) n
+
+@[simp] theorem rTensor_zpow (f : M ≃ₗ[R] M) (n : ℤ) : f.rTensor N ^ n = (f ^ n).rTensor N := by
+  simpa only [one_zpow] using TensorProduct.congr_zpow f (1 : N ≃ₗ[R] N) n
+
+@[simp] theorem lTensor_pow (f : N ≃ₗ[R] N) (n : ℕ) : f.lTensor M ^ n = (f ^ n).lTensor M := by
+  simpa only [one_pow] using TensorProduct.congr_pow (1 : M ≃ₗ[R] M) f n
+
+@[simp] theorem lTensor_zpow (f : N ≃ₗ[R] N) (n : ℤ) : f.lTensor M ^ n = (f ^ n).lTensor M := by
+  simpa only [one_zpow] using TensorProduct.congr_zpow (1 : M ≃ₗ[R] M) f n
+
+end LinearEquiv
+
 end Semiring
 
 section Ring

Switch M ⊗ f to f ⊗ M in rTensorHom M docstring.

@@ -1198,7 +1198,7 @@ def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P where
     simp only [compr₂_apply, mk_apply, tmul_smul, smul_apply, lTensor_tmul]
 #align linear_map.ltensor_hom LinearMap.lTensorHom
 
-/-- `rTensorHom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
+/-- `rTensorHom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `f ⊗ M`. -/
 def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M where
   toFun f := f.rTensor M
   map_add' f g := by

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -1285,7 +1285,7 @@ theorem lTensor_id : (id : N →ₗ[R] N).lTensor M = id :=
 
 -- `simp` can prove this.
 theorem lTensor_id_apply (x : M ⊗[R] N) : (LinearMap.id : N →ₗ[R] N).lTensor M x = x := by
-  rw [lTensor_id, id_coe, id.def]
+  rw [lTensor_id, id_coe, _root_.id]
 #align linear_map.ltensor_id_apply LinearMap.lTensor_id_apply
 
 @[simp]
@@ -1295,7 +1295,7 @@ theorem rTensor_id : (id : N →ₗ[R] N).rTensor M = id :=
 
 -- `simp` can prove this.
 theorem rTensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rTensor M x = x := by
-  rw [rTensor_id, id_coe, id.def]
+  rw [rTensor_id, id_coe, _root_.id]
 #align linear_map.rtensor_id_apply LinearMap.rTensor_id_apply
 
 variable {N}

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -894,7 +894,7 @@ attribute [local ext high] ext
 @[simp]
 theorem map_id : map (id : M →ₗ[R] M) (id : N →ₗ[R] N) = .id := by
   ext
-  simp only [mk_apply, id_coe, compr₂_apply, id.def, map_tmul]
+  simp only [mk_apply, id_coe, compr₂_apply, _root_.id, map_tmul]
 #align tensor_product.map_id TensorProduct.map_id
 
 @[simp]

• TensorProduct.exists_multiset, TensorProduct.exists_finsupp_left, TensorProduct.exists_finsupp_right, TensorProduct.exists_finset: any element of M ⊗[R] N can be written as a finite sum of pure tensors. See also TensorProduct.span_tmul_eq_top.

• TensorProduct.exists_finite_submodule_left_of_finite, TensorProduct.exists_finite_submodule_right_of_finite, TensorProduct.exists_finite_submodule_of_finite and 3 more: any finite subset of M ⊗[R] N is contained in M' ⊗[R] N' for some finitely generated submodules M' and N' of M and N, respectively. Each of these 3 functions has 2 variants.

@@ -863,6 +863,11 @@ def mapIncl (p : Submodule R P) (q : Submodule R Q) : p ⊗[R] q →ₗ[R] P ⊗
   map p.subtype q.subtype
 #align tensor_product.map_incl TensorProduct.mapIncl
 
+lemma range_mapIncl (p : Submodule R P) (q : Submodule R Q) :
+    LinearMap.range (mapIncl p q) = Submodule.span R (Set.image2 (· ⊗ₜ ·) p q) := by
+  rw [mapIncl, map_range_eq_span_tmul]
+  congr; ext; simp
+
 section
 
 variable {P' Q' : Type*}
@@ -874,6 +879,11 @@ theorem map_comp (f₂ : P →ₗ[R] P') (f₁ : M →ₗ[R] P) (g₂ : Q →ₗ
   ext' fun _ _ => rfl
 #align tensor_product.map_comp TensorProduct.map_comp
 
+lemma range_mapIncl_mono {p p' : Submodule R P} {q q' : Submodule R Q} (hp : p ≤ p') (hq : q ≤ q') :
+    LinearMap.range (mapIncl p q) ≤ LinearMap.range (mapIncl p' q') := by
+  simp_rw [range_mapIncl]
+  exact Submodule.span_mono (Set.image2_subset hp hq)
+
 theorem lift_comp_map (i : P →ₗ[R] Q →ₗ[R] Q') (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (lift i).comp (map f g) = lift ((i.comp f).compl₂ g) :=
   ext' fun _ _ => rfl

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -245,7 +245,7 @@ instance (priority := 100) CompatibleSMul.isScalarTower [SMul R' R] [IsScalarTow
     exact Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_smul _ _ _⟩
 #align tensor_product.compatible_smul.is_scalar_tower TensorProduct.CompatibleSMul.isScalarTower
 
-/-- `smul` can be moved from one side of the product to the other .-/
+/-- `smul` can be moved from one side of the product to the other . -/
 theorem smul_tmul [DistribMulAction R' N] [CompatibleSMul R R' M N] (r : R') (m : M) (n : N) :
     (r • m) ⊗ₜ n = m ⊗ₜ[R] (r • n) :=
   CompatibleSMul.smul_tmul _ _ _

@@ -334,13 +334,13 @@ protected theorem add_smul (r s : R'') (x : M ⊗[R] N) : (r + s) • x = r •
 #align tensor_product.add_smul TensorProduct.add_smul
 
 instance addMonoid : AddMonoid (M ⊗[R] N) :=
-{ TensorProduct.addZeroClass _ _ with
-  toAddSemigroup := TensorProduct.addSemigroup _ _
-  toZero := (TensorProduct.addZeroClass _ _).toZero
-  nsmul := fun n v => n • v
-  nsmul_zero := by simp [TensorProduct.zero_smul]
-  nsmul_succ := by simp only [TensorProduct.one_smul, TensorProduct.add_smul, add_comm,
-    forall_const] }
+  { TensorProduct.addZeroClass _ _ with
+    toAddSemigroup := TensorProduct.addSemigroup _ _
+    toZero := (TensorProduct.addZeroClass _ _).toZero
+    nsmul := fun n v => n • v
+    nsmul_zero := by simp [TensorProduct.zero_smul]
+    nsmul_succ := by simp only [TensorProduct.one_smul, TensorProduct.add_smul, add_comm,
+      forall_const] }
 
 instance addCommMonoid : AddCommMonoid (M ⊗[R] N) :=
   { TensorProduct.addCommSemigroup _ _ with

also move lTensor_inj_iff_rTensor_inj to LinearMap

@@ -1157,6 +1157,21 @@ lemma comm_comp_lTensor_comp_comm_eq (g : N →ₗ[R] P) :
       rTensor Q g :=
   TensorProduct.ext rfl
 
+/-- Given a linear map `f : N → P`, `f ⊗ M` is injective if and only if `M ⊗ f` is injective. -/
+theorem lTensor_inj_iff_rTensor_inj :
+    Function.Injective (lTensor M f) ↔ Function.Injective (rTensor M f) := by
+  simp [← comm_comp_rTensor_comp_comm_eq]
+
+/-- Given a linear map `f : N → P`, `f ⊗ M` is surjective if and only if `M ⊗ f` is surjective. -/
+theorem lTensor_surj_iff_rTensor_surj :
+    Function.Surjective (lTensor M f) ↔ Function.Surjective (rTensor M f) := by
+  simp [← comm_comp_rTensor_comp_comm_eq]
+
+/-- Given a linear map `f : N → P`, `f ⊗ M` is bijective if and only if `M ⊗ f` is bijective. -/
+theorem lTensor_bij_iff_rTensor_bij :
+    Function.Bijective (lTensor M f) ↔ Function.Bijective (rTensor M f) := by
+  simp [← comm_comp_rTensor_comp_comm_eq]
+
 open TensorProduct
 
 attribute [local ext high] TensorProduct.ext

• add finsuppTensorFinsuppLid, finsuppTensorFinsuppRid as well as their simp lemmas
• make finsuppTensorFinsupp' a special case of finsuppTensorFinsuppLid
• add TensorProduct.lid_eq_rid

@@ -760,6 +760,10 @@ theorem rid_symm_apply (m : M) : (TensorProduct.rid R M).symm m = m ⊗ₜ 1 :=
   rfl
 #align tensor_product.rid_symm_apply TensorProduct.rid_symm_apply
 
+variable (R) in
+theorem lid_eq_rid : TensorProduct.lid R R = TensorProduct.rid R R :=
+  LinearEquiv.toLinearMap_injective <| ext' mul_comm
+
 open LinearMap
 
 section

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -1377,7 +1377,7 @@ instance addCommGroup : AddCommGroup (M ⊗[R] N) :=
     add_left_neg := fun x => TensorProduct.add_left_neg x
     zsmul := fun n v => n • v
     zsmul_zero' := by simp [TensorProduct.zero_smul]
-    zsmul_succ' := by simp [Nat.succ_eq_one_add, TensorProduct.one_smul, TensorProduct.add_smul]
+    zsmul_succ' := by simp [Nat.succ_eq_add_one, TensorProduct.one_smul, TensorProduct.add_smul]
     zsmul_neg' := fun n x => by
       change (-n.succ : ℤ) • x = -(((n : ℤ) + 1) • x)
       rw [← zero_add (_ • x), ← TensorProduct.add_left_neg ((n.succ : ℤ) • x), add_assoc,

We define TensorProduct.addCommMonoid in terms of TensorProduct.addMonoid to reduce unfolding.

@@ -333,15 +333,18 @@ protected theorem add_smul (r s : R'') (x : M ⊗[R] N) : (r + s) • x = r •
     rw [ihx, ihy, add_add_add_comm]
 #align tensor_product.add_smul TensorProduct.add_smul
 
+instance addMonoid : AddMonoid (M ⊗[R] N) :=
+{ TensorProduct.addZeroClass _ _ with
+  toAddSemigroup := TensorProduct.addSemigroup _ _
+  toZero := (TensorProduct.addZeroClass _ _).toZero
+  nsmul := fun n v => n • v
+  nsmul_zero := by simp [TensorProduct.zero_smul]
+  nsmul_succ := by simp only [TensorProduct.one_smul, TensorProduct.add_smul, add_comm,
+    forall_const] }
+
 instance addCommMonoid : AddCommMonoid (M ⊗[R] N) :=
-  { TensorProduct.addCommSemigroup _ _,
-    TensorProduct.addZeroClass _ _ with
-    toAddSemigroup := TensorProduct.addSemigroup _ _
-    toZero := (TensorProduct.addZeroClass _ _).toZero
-    nsmul := fun n v => n • v
-    nsmul_zero := by simp [TensorProduct.zero_smul]
-    nsmul_succ := by simp only [TensorProduct.one_smul, TensorProduct.add_smul, add_comm,
-      forall_const] }
+  { TensorProduct.addCommSemigroup _ _ with
+    toAddMonoid := TensorProduct.addMonoid }
 
 instance leftDistribMulAction : DistribMulAction R' (M ⊗[R] N) :=
   have : ∀ (r : R') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -130,7 +130,7 @@ infixl:100 " ⊗ₜ " => tmul _
 /-- The canonical function `M → N → M ⊗ N`. -/
 notation:100 x " ⊗ₜ[" R "] " y:100 => tmul R x y
 
--- porting note: make the arguments of induction_on explicit
+-- Porting note: make the arguments of induction_on explicit
 @[elab_as_elim]
 protected theorem induction_on {motive : M ⊗[R] N → Prop} (z : M ⊗[R] N)
     (zero : motive 0)
@@ -251,7 +251,7 @@ theorem smul_tmul [DistribMulAction R' N] [CompatibleSMul R R' M N] (r : R') (m
   CompatibleSMul.smul_tmul _ _ _
 #align tensor_product.smul_tmul TensorProduct.smul_tmul
 
--- porting note: This is added as a local instance for `SMul.aux`.
+-- Porting note: This is added as a local instance for `SMul.aux`.
 -- For some reason type-class inference in Lean 3 unfolded this definition.
 private def addMonoidWithWrongNSMul : AddMonoid (M ⊗[R] N) :=
   { (addConGen (TensorProduct.Eqv R M N)).addMonoid with }
@@ -1065,7 +1065,7 @@ theorem tensorTensorTensorComm_tmul (m : M) (n : N) (p : P) (q : Q) :
   rfl
 #align tensor_product.tensor_tensor_tensor_comm_tmul TensorProduct.tensorTensorTensorComm_tmul
 
--- porting note: the proof here was `rfl` but that caused a timeout.
+-- Porting note: the proof here was `rfl` but that caused a timeout.
 @[simp]
 theorem tensorTensorTensorComm_symm :
     (tensorTensorTensorComm R M N P Q).symm = tensorTensorTensorComm R M P N Q :=

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

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

@@ -1268,6 +1268,9 @@ theorem rTensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rTens
 
 variable {N}
 
+theorem lid_comp_rTensor (f : N →ₗ[R] R) :
+    (TensorProduct.lid R M).comp (rTensor M f) = lift ((lsmul R M).comp f) := ext' fun _ _ ↦ rfl
+
 @[simp]
 theorem lTensor_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     (g.lTensor P).comp (f.rTensor N) = map f g := by

@@ -945,6 +945,19 @@ def homTensorHomMap : (M →ₗ[R] P) ⊗[R] (N →ₗ[R] Q) →ₗ[R] M ⊗[R]
 
 variable {R M N P Q}
 
+/--
+This is a binary version of `TensorProduct.map`: Given a bilinear map `f : M ⟶ P ⟶ Q` and a
+bilinear map `g : N ⟶ S ⟶ T`, if we think `f` and `g` as linear maps with two inputs, then
+`map₂ f g` is a bilinear map taking two inputs `M ⊗ N → P ⊗ S → Q ⊗ S` defined by
+`map₂ f g (m ⊗ n) (p ⊗ s) = f m p ⊗ g n s`.
+
+Mathematically, `TensorProduct.map₂` is defined as the composition
+`M ⊗ N -map→ Hom(P, Q) ⊗ Hom(S, T) -homTensorHomMap→ Hom(P ⊗ S, Q ⊗ T)`.
+-/
+def map₂ (f : M →ₗ[R] P →ₗ[R] Q) (g : N →ₗ[R] S →ₗ[R] T) :
+    M ⊗[R] N →ₗ[R] P ⊗[R] S →ₗ[R] Q ⊗[R] T :=
+  homTensorHomMap R _ _ _ _ ∘ₗ map f g
+
 @[simp]
 theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear R M N P Q f g = map f g :=
   rfl
@@ -968,6 +981,10 @@ theorem homTensorHomMap_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
   rfl
 #align tensor_product.hom_tensor_hom_map_apply TensorProduct.homTensorHomMap_apply
 
+@[simp]
+theorem map₂_apply_tmul (f : M →ₗ[R] P →ₗ[R] Q) (g : N →ₗ[R] S →ₗ[R] T) (m : M) (n : N) :
+    map₂ f g (m ⊗ₜ n) = map (f m) (g n) := rfl
+
 @[simp]
 theorem map_zero_left (g : N →ₗ[R] Q) : map (0 : M →ₗ[R] P) g = 0 :=
   (mapBilinear R M N P Q).map_zero₂ _

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

This follows on from #6964.

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

@@ -1337,8 +1337,8 @@ protected theorem add_left_neg (x : M ⊗[R] N) : -x + x = 0 :=
     (by rw [add_zero]; apply (Neg.aux R).map_zero)
     (fun x y => by convert (add_tmul (R := R) (-x) x y).symm; rw [add_left_neg, zero_tmul])
     fun x y hx hy => by
-    suffices : -x + x + (-y + y) = 0
-    · rw [← this]
+    suffices -x + x + (-y + y) = 0 by
+      rw [← this]
       unfold Neg.neg neg
       simp only
       rw [map_add]

This shortens Mathlib.LinearAlgebra.Basic, which is both longer than we like and doesn't have a clear scope.

@@ -3,8 +3,9 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro
 -/
-import Mathlib.GroupTheory.Congruence
 import Mathlib.Algebra.Module.Submodule.Bilinear
+import Mathlib.GroupTheory.Congruence
+import Mathlib.LinearAlgebra.Basic
 import Mathlib.Tactic.SuppressCompilation
 
 #align_import linear_algebra.tensor_product from "leanprover-community/mathlib"@"88fcdc3da43943f5b01925deddaa5bf0c0e85e4e"

Make all the notations that unambiguously should inherit the docstring of their definition actually inherit it.

Also write a few docstrings by hand. I only wrote the ones I was competent to write and which I was sure of. Some docstrings come from mathlib3 as they were lost during the early port.

This PR is only intended as a first pass There are many more docstrings to add.

@@ -81,9 +81,9 @@ def TensorProduct : Type _ :=
 variable {R}
 
 set_option quotPrecheck false in
-scoped[TensorProduct] infixl:100 " ⊗ " => TensorProduct _
+@[inherit_doc TensorProduct] scoped[TensorProduct] infixl:100 " ⊗ " => TensorProduct _
 
-scoped[TensorProduct] notation:100 M " ⊗[" R "] " N:100 => TensorProduct R M N
+@[inherit_doc] scoped[TensorProduct] notation:100 M " ⊗[" R "] " N:100 => TensorProduct R M N
 
 namespace TensorProduct
 
@@ -123,8 +123,10 @@ def tmul (m : M) (n : N) : M ⊗[R] N :=
 
 variable {R}
 
+/-- The canonical function `M → N → M ⊗ N`. -/
 infixl:100 " ⊗ₜ " => tmul _
 
+/-- The canonical function `M → N → M ⊗ N`. -/
 notation:100 x " ⊗ₜ[" R "] " y:100 => tmul R x y
 
 -- porting note: make the arguments of induction_on explicit

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

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

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

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

@@ -805,7 +805,7 @@ lemma map_comp_comm_eq (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
 
 lemma map_comm (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (x : N ⊗[R] M):
     map f g (TensorProduct.comm R N M x) = TensorProduct.comm R Q P (map g f x) :=
-  FunLike.congr_fun (map_comp_comm_eq _ _) _
+  DFunLike.congr_fun (map_comp_comm_eq _ _) _
 
 /-- Given linear maps `f : M → Q`, `g : N → S`, and `h : P → T`, if we identify `(M ⊗ N) ⊗ P`
 with `M ⊗ (N ⊗ P)` and `(Q ⊗ S) ⊗ T` with `Q ⊗ (S ⊗ T)`, then this lemma states that
@@ -818,7 +818,7 @@ lemma map_map_comp_assoc_eq (f : M →ₗ[R] Q) (g : N →ₗ[R] S) (h : P →
 lemma map_map_assoc (f : M →ₗ[R] Q) (g : N →ₗ[R] S) (h : P →ₗ[R] T) (x : (M ⊗[R] N) ⊗[R] P) :
     map f (map g h) (TensorProduct.assoc R M N P x) =
       TensorProduct.assoc R Q S T (map (map f g) h x) :=
-  FunLike.congr_fun (map_map_comp_assoc_eq _ _ _) _
+  DFunLike.congr_fun (map_map_comp_assoc_eq _ _ _) _
 
 /-- Given linear maps `f : M → Q`, `g : N → S`, and `h : P → T`, if we identify `M ⊗ (N ⊗ P)`
 with `(M ⊗ N) ⊗ P` and `Q ⊗ (S ⊗ T)` with `(Q ⊗ S) ⊗ T`, then this lemma states that
@@ -831,7 +831,7 @@ lemma map_map_comp_assoc_symm_eq (f : M →ₗ[R] Q) (g : N →ₗ[R] S) (h : P
 lemma map_map_assoc_symm (f : M →ₗ[R] Q) (g : N →ₗ[R] S) (h : P →ₗ[R] T) (x : M ⊗[R] (N ⊗[R] P)) :
     map (map f g) h ((TensorProduct.assoc R M N P).symm x) =
       (TensorProduct.assoc R Q S T).symm (map f (map g h) x) :=
-  FunLike.congr_fun (map_map_comp_assoc_symm_eq _ _ _) _
+  DFunLike.congr_fun (map_map_comp_assoc_symm_eq _ _ _) _
 
 theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     range (map f g) = Submodule.span R { t | ∃ m n, f m ⊗ₜ g n = t } := by

• Redefine Set.image2 to use ∃ a ∈ s, ∃ b ∈ t, f a b = c instead of ∃ a b, a ∈ s ∧ b ∈ t ∧ f a b = c.
• Redefine Set.seq as Set.image2. The new definition is equal to the old one but rw [Set.seq] gives a different result.
• Redefine Filter.map₂ to use ∃ u ∈ f, ∃ v ∈ g, image2 m u v ⊆ s instead of ∃ u v, u ∈ f ∧ v ∈ g ∧ ...
• Update lemmas like Set.mem_image2, Finset.mem_image₂, Set.mem_mul, Finset.mem_div etc

The two reasons to make the change are:

• ∃ a ∈ s, ∃ b ∈ t, _ is a simp-normal form, and
• it looks a bit nicer.

@@ -489,7 +489,7 @@ theorem span_tmul_eq_top : Submodule.span R { t : M ⊗[R] N | ∃ m n, m ⊗ₜ
 @[simp]
 theorem map₂_mk_top_top_eq_top : Submodule.map₂ (mk R M N) ⊤ ⊤ = ⊤ := by
   rw [← top_le_iff, ← span_tmul_eq_top, Submodule.map₂_eq_span_image2]
-  exact Submodule.span_mono fun _ ⟨m, n, h⟩ => ⟨m, n, trivial, trivial, h⟩
+  exact Submodule.span_mono fun _ ⟨m, n, h⟩ => ⟨m, trivial, n, trivial, h⟩
 #align tensor_product.map₂_mk_top_top_eq_top TensorProduct.map₂_mk_top_top_eq_top
 
 theorem exists_eq_tmul_of_forall (x : TensorProduct R M N)

This also splits out a CoalgebraStruct typeclass, to allow defining the operators and their definitional properties before committing to proving coassociativity.

These proofs are extremely painful, as you're fighting associativity all the time (and LinearMap.comp is very verbose in the goal view)

@@ -41,9 +41,10 @@ section Semiring
 variable {R : Type*} [CommSemiring R]
 variable {R' : Type*} [Monoid R']
 variable {R'' : Type*} [Semiring R'']
-variable {M : Type*} {N : Type*} {P : Type*} {Q : Type*} {S : Type*}
-variable [AddCommMonoid M] [AddCommMonoid N] [AddCommMonoid P] [AddCommMonoid Q] [AddCommMonoid S]
-variable [Module R M] [Module R N] [Module R P] [Module R Q] [Module R S]
+variable {M : Type*} {N : Type*} {P : Type*} {Q : Type*} {S : Type*} {T : Type*}
+variable [AddCommMonoid M] [AddCommMonoid N] [AddCommMonoid P]
+variable [AddCommMonoid Q] [AddCommMonoid S] [AddCommMonoid T]
+variable [Module R M] [Module R N] [Module R P] [Module R Q] [Module R S] [Module R T]
 variable [DistribMulAction R' M]
 variable [Module R'' M]
 variable (M N)
@@ -796,11 +797,42 @@ theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f
   rfl
 #align tensor_product.map_tmul TensorProduct.map_tmul
 
+/-- Given linear maps `f : M → P`, `g : N → Q`, if we identify `M ⊗ N` with `N ⊗ M` and `P ⊗ Q`
+with `Q ⊗ P`, then this lemma states that `f ⊗ g = g ⊗ f`. -/
 lemma map_comp_comm_eq (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
-    map f g ∘ₗ TensorProduct.comm R N M =
-      TensorProduct.comm R Q P ∘ₗ map g f :=
+    map f g ∘ₗ TensorProduct.comm R N M = TensorProduct.comm R Q P ∘ₗ map g f :=
   ext rfl
 
+lemma map_comm (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (x : N ⊗[R] M):
+    map f g (TensorProduct.comm R N M x) = TensorProduct.comm R Q P (map g f x) :=
+  FunLike.congr_fun (map_comp_comm_eq _ _) _
+
+/-- Given linear maps `f : M → Q`, `g : N → S`, and `h : P → T`, if we identify `(M ⊗ N) ⊗ P`
+with `M ⊗ (N ⊗ P)` and `(Q ⊗ S) ⊗ T` with `Q ⊗ (S ⊗ T)`, then this lemma states that
+`f ⊗ (g ⊗ h) = (f ⊗ g) ⊗ h`. -/
+lemma map_map_comp_assoc_eq (f : M →ₗ[R] Q) (g : N →ₗ[R] S) (h : P →ₗ[R] T) :
+    map f (map g h) ∘ₗ TensorProduct.assoc R M N P =
+      TensorProduct.assoc R Q S T ∘ₗ map (map f g) h :=
+  ext <| ext <| LinearMap.ext fun _ => LinearMap.ext fun _ => LinearMap.ext fun _ => rfl
+
+lemma map_map_assoc (f : M →ₗ[R] Q) (g : N →ₗ[R] S) (h : P →ₗ[R] T) (x : (M ⊗[R] N) ⊗[R] P) :
+    map f (map g h) (TensorProduct.assoc R M N P x) =
+      TensorProduct.assoc R Q S T (map (map f g) h x) :=
+  FunLike.congr_fun (map_map_comp_assoc_eq _ _ _) _
+
+/-- Given linear maps `f : M → Q`, `g : N → S`, and `h : P → T`, if we identify `M ⊗ (N ⊗ P)`
+with `(M ⊗ N) ⊗ P` and `Q ⊗ (S ⊗ T)` with `(Q ⊗ S) ⊗ T`, then this lemma states that
+`(f ⊗ g) ⊗ h = f ⊗ (g ⊗ h)`. -/
+lemma map_map_comp_assoc_symm_eq (f : M →ₗ[R] Q) (g : N →ₗ[R] S) (h : P →ₗ[R] T) :
+    map (map f g) h ∘ₗ (TensorProduct.assoc R M N P).symm =
+      (TensorProduct.assoc R Q S T).symm ∘ₗ map f (map g h) :=
+  ext <| LinearMap.ext fun _ => ext <| LinearMap.ext fun _ => LinearMap.ext fun _ => rfl
+
+lemma map_map_assoc_symm (f : M →ₗ[R] Q) (g : N →ₗ[R] S) (h : P →ₗ[R] T) (x : M ⊗[R] (N ⊗[R] P)) :
+    map (map f g) h ((TensorProduct.assoc R M N P).symm x) =
+      (TensorProduct.assoc R Q S T).symm (map f (map g h) x) :=
+  FunLike.congr_fun (map_map_comp_assoc_symm_eq _ _ _) _
+
 theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     range (map f g) = Submodule.span R { t | ∃ m n, f m ⊗ₜ g n = t } := by
   simp only [← Submodule.map_top, ← span_tmul_eq_top, Submodule.map_span, Set.mem_image,
@@ -933,6 +965,14 @@ theorem homTensorHomMap_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
   rfl
 #align tensor_product.hom_tensor_hom_map_apply TensorProduct.homTensorHomMap_apply
 
+@[simp]
+theorem map_zero_left (g : N →ₗ[R] Q) : map (0 : M →ₗ[R] P) g = 0 :=
+  (mapBilinear R M N P Q).map_zero₂ _
+
+@[simp]
+theorem map_zero_right (f : M →ₗ[R] P) : map f (0 : N →ₗ[R] Q) = 0 :=
+  (mapBilinear R M N P Q _).map_zero
+
 end
 
 /-- If `M` and `P` are linearly equivalent and `N` and `Q` are linearly equivalent
@@ -1070,6 +1110,16 @@ theorem rTensor_tmul (m : M) (n : N) : f.rTensor M (n ⊗ₜ m) = f n ⊗ₜ m :
   rfl
 #align linear_map.rtensor_tmul LinearMap.rTensor_tmul
 
+@[simp]
+theorem lTensor_comp_mk (m : M) :
+    f.lTensor M ∘ₗ TensorProduct.mk R M N m = TensorProduct.mk R M P m ∘ₗ f :=
+  rfl
+
+@[simp]
+theorem rTensor_comp_flip_mk (m : M) :
+    f.rTensor M ∘ₗ (TensorProduct.mk R N M).flip m = (TensorProduct.mk R P M).flip m ∘ₗ f :=
+  rfl
+
 lemma comm_comp_rTensor_comp_comm_eq (g : N →ₗ[R] P) :
     TensorProduct.comm R P Q ∘ₗ rTensor Q g ∘ₗ TensorProduct.comm R Q N =
       lTensor Q g :=

This incurs a very slight performance hit globally.

@@ -515,21 +515,8 @@ variable (f : M →ₗ[R] N →ₗ[R] P)
 with the property that its composition with the canonical bilinear map `M → N → M ⊗ N` is
 the given bilinear map `M → N → P`. -/
 def liftAux : M ⊗[R] N →+ P :=
-  (addConGen (TensorProduct.Eqv R M N)).lift (FreeAddMonoid.lift fun p : M × N => f p.1 p.2) <|
-    AddCon.addConGen_le fun x y hxy =>
-      match x, y, hxy with
-      | _, _, Eqv.of_zero_left n =>
-        (AddCon.ker_rel _).2 <| by simp_rw [map_zero, FreeAddMonoid.lift_eval_of, f.map_zero₂]
-      | _, _, Eqv.of_zero_right m =>
-        (AddCon.ker_rel _).2 <| by simp_rw [map_zero, FreeAddMonoid.lift_eval_of, (f m).map_zero]
-      | _, _, Eqv.of_add_left m₁ m₂ n =>
-        (AddCon.ker_rel _).2 <| by simp_rw [map_add, FreeAddMonoid.lift_eval_of, f.map_add₂]
-      | _, _, Eqv.of_add_right m n₁ n₂ =>
-        (AddCon.ker_rel _).2 <| by simp_rw [map_add, FreeAddMonoid.lift_eval_of, (f m).map_add]
-      | _, _, Eqv.of_smul r m n =>
-        (AddCon.ker_rel _).2 <| by simp_rw [FreeAddMonoid.lift_eval_of, f.map_smul₂, (f m).map_smul]
-      | _, _, Eqv.add_comm x y =>
-        (AddCon.ker_rel _).2 <| by simp_rw [map_add, add_comm]
+  liftAddHom (LinearMap.toAddMonoidHom'.comp <| f.toAddMonoidHom)
+    fun r m n => by dsimp; rw [LinearMap.map_smul₂, map_smul]
 #align tensor_product.lift_aux TensorProduct.liftAux
 
 theorem liftAux_tmul (m n) : liftAux f (m ⊗ₜ n) = f m n :=

Mention R-balanced maps in liftAddHom docstring.

The terminology "R-balanced" and "middle linear with respect to R" is used in Dummit and Foote (top of p.365 in section 10.4)

@@ -138,8 +138,10 @@ protected theorem induction_on {motive : M ⊗[R] N → Prop} (z : M ⊗[R] N)
       exact add _ _ (tmul ..) ih
 #align tensor_product.induction_on TensorProduct.induction_on
 
-/-- Lift a map that is additive in both arguments to the tensor product, provided scalar
-multiplication in either argument is equivalent.
+/-- Lift an `R`-balanced map to the tensor product.
+
+A map `f : M →+ N →+ P` additive in both components is `R`-balanced, or middle linear with respect
+to `R`, if scalar multiplication in either argument is equivalent, `f (r • m) n = f m (r • n)`.
 
 Note that strictly the first action should be a right-action by `R`, but for now `R` is commutative
 so it doesn't matter. -/

This new TensorProduct.liftAddHom doesn't require bilinearity, only that scalar multiplication can be moved between the arguments.

In theory this could be used to golf some later definitions, but in practice this resulted in performance regressions (#8519). For now we just leave a TODO, so that the performance/deduplication tradeoff doesn't hold up further mathematics.

@@ -138,6 +138,40 @@ protected theorem induction_on {motive : M ⊗[R] N → Prop} (z : M ⊗[R] N)
       exact add _ _ (tmul ..) ih
 #align tensor_product.induction_on TensorProduct.induction_on
 
+/-- Lift a map that is additive in both arguments to the tensor product, provided scalar
+multiplication in either argument is equivalent.
+
+Note that strictly the first action should be a right-action by `R`, but for now `R` is commutative
+so it doesn't matter. -/
+-- TODO: use this to implement `lift` and `SMul.aux`. For now we do not do this as it causes
+-- performance issues elsewhere.
+def liftAddHom (f : M →+ N →+ P)
+    (hf : ∀ (r : R) (m : M) (n : N), f (r • m) n = f m (r • n)) :
+    M ⊗[R] N →+ P :=
+  (addConGen (TensorProduct.Eqv R M N)).lift (FreeAddMonoid.lift (fun mn : M × N => f mn.1 mn.2)) <|
+    AddCon.addConGen_le fun x y hxy =>
+      match x, y, hxy with
+      | _, _, .of_zero_left n =>
+        (AddCon.ker_rel _).2 <| by simp_rw [map_zero, FreeAddMonoid.lift_eval_of, map_zero,
+          AddMonoidHom.zero_apply]
+      | _, _, .of_zero_right m =>
+        (AddCon.ker_rel _).2 <| by simp_rw [map_zero, FreeAddMonoid.lift_eval_of, map_zero]
+      | _, _, .of_add_left m₁ m₂ n =>
+        (AddCon.ker_rel _).2 <| by simp_rw [map_add, FreeAddMonoid.lift_eval_of, map_add,
+          AddMonoidHom.add_apply]
+      | _, _, .of_add_right m n₁ n₂ =>
+        (AddCon.ker_rel _).2 <| by simp_rw [map_add, FreeAddMonoid.lift_eval_of, map_add]
+      | _, _, .of_smul s m n =>
+        (AddCon.ker_rel _).2 <| by rw [FreeAddMonoid.lift_eval_of, FreeAddMonoid.lift_eval_of, hf]
+      | _, _, .add_comm x y =>
+        (AddCon.ker_rel _).2 <| by simp_rw [map_add, add_comm]
+
+@[simp]
+theorem liftAddHom_tmul (f : M →+ N →+ P)
+    (hf : ∀ (r : R) (m : M) (n : N), f (r • m) n = f m (r • n)) (m : M) (n : N) :
+    liftAddHom f hf (m ⊗ₜ n) = f m n :=
+  rfl
+
 variable (M)
 
 @[simp]

This instance is needed to set things up, but then should never be used again. To ensure this, it is made private and given a scary name.

@@ -88,11 +88,6 @@ namespace TensorProduct
 
 section Module
 
--- porting note: This is added as a local instance for `SMul.aux`.
--- For some reason type-class inference in Lean 3 unfolded this definition.
-def addMonoid : AddMonoid (M ⊗[R] N) :=
-  { (addConGen (TensorProduct.Eqv R M N)).addMonoid with }
-
 protected instance add : Add (M ⊗[R] N) :=
   (addConGen (TensorProduct.Eqv R M N)).hasAdd
 
@@ -216,12 +211,16 @@ theorem smul_tmul [DistribMulAction R' N] [CompatibleSMul R R' M N] (r : R') (m
   CompatibleSMul.smul_tmul _ _ _
 #align tensor_product.smul_tmul TensorProduct.smul_tmul
 
-attribute [local instance] addMonoid
+-- porting note: This is added as a local instance for `SMul.aux`.
+-- For some reason type-class inference in Lean 3 unfolded this definition.
+private def addMonoidWithWrongNSMul : AddMonoid (M ⊗[R] N) :=
+  { (addConGen (TensorProduct.Eqv R M N)).addMonoid with }
+
+attribute [local instance] addMonoidWithWrongNSMul in
 /-- Auxiliary function to defining scalar multiplication on tensor product. -/
 def SMul.aux {R' : Type*} [SMul R' M] (r : R') : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
   FreeAddMonoid.lift fun p : M × N => (r • p.1) ⊗ₜ p.2
 #align tensor_product.smul.aux TensorProduct.SMul.aux
-attribute [-instance] addMonoid
 
 theorem SMul.aux_of {R' : Type*} [SMul R' M] (r : R') (m : M) (n : N) :
     SMul.aux r (.of (m, n)) = (r • m) ⊗ₜ[R] n :=

The aim is to remove some extraneous Nonempty assumptions in Algebra/DirectLimit.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com>

@@ -169,6 +169,16 @@ theorem tmul_add (m : M) (n₁ n₂ : N) : m ⊗ₜ (n₁ + n₂) = m ⊗ₜ n
   Eq.symm <| Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.of_add_right _ _ _
 #align tensor_product.tmul_add TensorProduct.tmul_add
 
+instance uniqueLeft [Subsingleton M] : Unique (M ⊗[R] N) where
+  default := 0
+  uniq z := z.induction_on rfl (fun x y ↦ by rw [Subsingleton.elim x 0, zero_tmul]; rfl) <| by
+    rintro _ _ rfl rfl; apply add_zero
+
+instance uniqueRight [Subsingleton N] : Unique (M ⊗[R] N) where
+  default := 0
+  uniq z := z.induction_on rfl (fun x y ↦ by rw [Subsingleton.elim y 0, tmul_zero]; rfl) <| by
+    rintro _ _ rfl rfl; apply add_zero
+
 section
 
 variable (R R' M N)

More principled version of #7281.

@@ -5,6 +5,7 @@ Authors: Kenny Lau, Mario Carneiro
 -/
 import Mathlib.GroupTheory.Congruence
 import Mathlib.Algebra.Module.Submodule.Bilinear
+import Mathlib.Tactic.SuppressCompilation
 
 #align_import linear_algebra.tensor_product from "leanprover-community/mathlib"@"88fcdc3da43943f5b01925deddaa5bf0c0e85e4e"
 
@@ -33,6 +34,7 @@ as `m ⊗ₜ n` and `m ⊗ₜ[R] n` for `TensorProduct.tmul R m n`.
 bilinear, tensor, tensor product
 -/
 
+suppress_compilation
 
 section Semiring
 

@@ -1234,33 +1234,16 @@ open LinearMap
 variable (R)
 
 /-- Auxiliary function to defining negation multiplication on tensor product. -/
-def Neg.aux : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
-  FreeAddMonoid.lift fun p : M × N => (-p.1) ⊗ₜ p.2
-#align tensor_product.neg.aux TensorProduct.Neg.aux
+def Neg.aux : M ⊗[R] N →ₗ[R] M ⊗[R] N :=
+  lift <| (mk R M N).comp (-LinearMap.id)
+#noalign tensor_product.neg.aux
 
 variable {R}
 
-theorem Neg.aux_of (m : M) (n : N) : Neg.aux R (FreeAddMonoid.of (m, n)) = (-m) ⊗ₜ[R] n :=
-  rfl
-#align tensor_product.neg.aux_of TensorProduct.Neg.aux_of
+#noalign tensor_product.neg.aux_of
 
 instance neg : Neg (M ⊗[R] N) where
-  neg :=
-    (addConGen (TensorProduct.Eqv R M N)).lift (Neg.aux R) <|
-      AddCon.addConGen_le fun x y hxy =>
-        match x, y, hxy with
-        | _, _, Eqv.of_zero_left n =>
-          (AddCon.ker_rel _).2 <| by simp_rw [map_zero, Neg.aux_of, neg_zero, zero_tmul]
-        | _, _, Eqv.of_zero_right m =>
-          (AddCon.ker_rel _).2 <| by simp_rw [map_zero, Neg.aux_of, tmul_zero]
-        | _, _, Eqv.of_add_left m₁ m₂ n =>
-          (AddCon.ker_rel _).2 <| by simp_rw [map_add, Neg.aux_of, neg_add, add_tmul]
-        | _, _, Eqv.of_add_right m n₁ n₂ =>
-          (AddCon.ker_rel _).2 <| by simp_rw [map_add, Neg.aux_of, tmul_add]
-        | _, _, Eqv.of_smul s m n =>
-          (AddCon.ker_rel _).2 <| by simp_rw [Neg.aux_of, ← smul_neg, ← smul_tmul]
-        | _, _, Eqv.add_comm x y =>
-          (AddCon.ker_rel _).2 <| by simp_rw [map_add, add_comm]
+  neg := Neg.aux R
 
 protected theorem add_left_neg (x : M ⊗[R] N) : -x + x = 0 :=
   x.induction_on
@@ -1271,7 +1254,7 @@ protected theorem add_left_neg (x : M ⊗[R] N) : -x + x = 0 :=
     · rw [← this]
       unfold Neg.neg neg
       simp only
-      rw [AddMonoidHom.map_add]
+      rw [map_add]
       abel
     rw [hx, hy, add_zero]
 #align tensor_product.add_left_neg TensorProduct.add_left_neg

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk>

@@ -692,6 +692,9 @@ theorem comm_symm_tmul (m : M) (n : N) : (TensorProduct.comm R M N).symm (n ⊗
   rfl
 #align tensor_product.comm_symm_tmul TensorProduct.comm_symm_tmul
 
+lemma lift_comp_comm_eq  (f : M →ₗ[R] N →ₗ[R] P) :
+    lift f ∘ₗ TensorProduct.comm R N M = lift f.flip :=
+  ext rfl
 end
 
 section
@@ -759,6 +762,11 @@ theorem map_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (m : M) (n : N) : map f
   rfl
 #align tensor_product.map_tmul TensorProduct.map_tmul
 
+lemma map_comp_comm_eq (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
+    map f g ∘ₗ TensorProduct.comm R N M =
+      TensorProduct.comm R Q P ∘ₗ map g f :=
+  ext rfl
+
 theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     range (map f g) = Submodule.span R { t | ∃ m n, f m ⊗ₜ g n = t } := by
   simp only [← Submodule.map_top, ← span_tmul_eq_top, Submodule.map_span, Set.mem_image,
@@ -1028,6 +1036,16 @@ theorem rTensor_tmul (m : M) (n : N) : f.rTensor M (n ⊗ₜ m) = f n ⊗ₜ m :
   rfl
 #align linear_map.rtensor_tmul LinearMap.rTensor_tmul
 
+lemma comm_comp_rTensor_comp_comm_eq (g : N →ₗ[R] P) :
+    TensorProduct.comm R P Q ∘ₗ rTensor Q g ∘ₗ TensorProduct.comm R Q N =
+      lTensor Q g :=
+  TensorProduct.ext rfl
+
+lemma comm_comp_lTensor_comp_comm_eq (g : N →ₗ[R] P) :
+    TensorProduct.comm R Q P ∘ₗ lTensor Q g ∘ₗ TensorProduct.comm R N Q =
+      rTensor Q g :=
+  TensorProduct.ext rfl
+
 open TensorProduct
 
 attribute [local ext high] TensorProduct.ext

Purely cosmetic PR

@@ -1315,25 +1315,25 @@ namespace LinearMap
 @[simp]
 theorem lTensor_sub (f g : N →ₗ[R] P) : (f - g).lTensor M = f.lTensor M - g.lTensor M := by
   simp_rw [← coe_lTensorHom]
-  exact (lTensorHom (R:=R) (N:=N) (P:=P) M).map_sub f g
+  exact (lTensorHom (R := R) (N := N) (P := P) M).map_sub f g
 #align linear_map.ltensor_sub LinearMap.lTensor_sub
 
 @[simp]
 theorem rTensor_sub (f g : N →ₗ[R] P) : (f - g).rTensor M = f.rTensor M - g.rTensor M := by
   simp only [← coe_rTensorHom]
-  exact (rTensorHom (R:=R) (N:=N) (P:=P) M).map_sub f g
+  exact (rTensorHom (R := R) (N := N) (P := P) M).map_sub f g
 #align linear_map.rtensor_sub LinearMap.rTensor_sub
 
 @[simp]
 theorem lTensor_neg (f : N →ₗ[R] P) : (-f).lTensor M = -f.lTensor M := by
   simp only [← coe_lTensorHom]
-  exact (lTensorHom (R:=R) (N:=N) (P:=P) M).map_neg f
+  exact (lTensorHom (R := R) (N := N) (P := P) M).map_neg f
 #align linear_map.ltensor_neg LinearMap.lTensor_neg
 
 @[simp]
 theorem rTensor_neg (f : N →ₗ[R] P) : (-f).rTensor M = -f.rTensor M := by
   simp only [← coe_rTensorHom]
-  exact (rTensorHom (R:=R) (N:=N) (P:=P) M).map_neg f
+  exact (rTensorHom (R := R) (N := N) (P := P) M).map_neg f
 #align linear_map.rtensor_neg LinearMap.rTensor_neg
 
 end LinearMap

Co-authored-by: Chris Hughes <33847686+ChrisHughes24@users.noreply.github.com>

@@ -91,11 +91,23 @@ section Module
 def addMonoid : AddMonoid (M ⊗[R] N) :=
   { (addConGen (TensorProduct.Eqv R M N)).addMonoid with }
 
+protected instance add : Add (M ⊗[R] N) :=
+  (addConGen (TensorProduct.Eqv R M N)).hasAdd
+
 instance addZeroClass : AddZeroClass (M ⊗[R] N) :=
-  { (addConGen (TensorProduct.Eqv R M N)).addMonoid with }
+  { (addConGen (TensorProduct.Eqv R M N)).addMonoid with
+    /- The `toAdd` field is given explicitly as `TensorProduct.add` for performance reasons.
+    This avoids any need to unfold `Con.addMonoid` when the type checker is checking
+    that instance diagrams commute -/
+    toAdd := TensorProduct.add _ _ }
+
+instance addSemigroup : AddSemigroup (M ⊗[R] N) :=
+  { (addConGen (TensorProduct.Eqv R M N)).addMonoid with
+    toAdd := TensorProduct.add _ _ }
 
 instance addCommSemigroup : AddCommSemigroup (M ⊗[R] N) :=
   { (addConGen (TensorProduct.Eqv R M N)).addMonoid with
+    toAddSemigroup := TensorProduct.addSemigroup _ _
     add_comm := fun x y =>
       AddCon.induction_on₂ x y fun _ _ =>
         Quotient.sound' <| AddConGen.Rel.of _ _ <| Eqv.add_comm _ _ }
@@ -273,6 +285,8 @@ protected theorem add_smul (r s : R'') (x : M ⊗[R] N) : (r + s) • x = r •
 instance addCommMonoid : AddCommMonoid (M ⊗[R] N) :=
   { TensorProduct.addCommSemigroup _ _,
     TensorProduct.addZeroClass _ _ with
+    toAddSemigroup := TensorProduct.addSemigroup _ _
+    toZero := (TensorProduct.addZeroClass _ _).toZero
     nsmul := fun n v => n • v
     nsmul_zero := by simp [TensorProduct.zero_smul]
     nsmul_succ := by simp only [TensorProduct.one_smul, TensorProduct.add_smul, add_comm,
@@ -280,8 +294,7 @@ instance addCommMonoid : AddCommMonoid (M ⊗[R] N) :=
 
 instance leftDistribMulAction : DistribMulAction R' (M ⊗[R] N) :=
   have : ∀ (r : R') (m : M) (n : N), r • m ⊗ₜ[R] n = (r • m) ⊗ₜ n := fun _ _ _ => rfl
-  { smul := (· • ·)
-    smul_add := fun r x y => TensorProduct.smul_add r x y
+  { smul_add := fun r x y => TensorProduct.smul_add r x y
     mul_smul := fun r s x =>
       x.induction_on (by simp_rw [TensorProduct.smul_zero])
         (fun m n => by simp_rw [this, mul_smul]) fun x y ihx ihy => by
@@ -309,8 +322,7 @@ theorem smul_tmul_smul (r s : R) (m : M) (n : N) : (r • m) ⊗ₜ[R] (s • n)
 #align tensor_product.smul_tmul_smul TensorProduct.smul_tmul_smul
 
 instance leftModule : Module R'' (M ⊗[R] N) :=
-  { TensorProduct.leftDistribMulAction with
-    add_smul := TensorProduct.add_smul
+  { add_smul := TensorProduct.add_smul
     zero_smul := TensorProduct.zero_smul }
 #align tensor_product.left_module TensorProduct.leftModule
 

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -810,13 +810,13 @@ protected theorem map_pow (f : M →ₗ[R] M) (g : N →ₗ[R] N) (n : ℕ) :
 #align tensor_product.map_pow TensorProduct.map_pow
 
 theorem map_add_left (f₁ f₂ : M →ₗ[R] P) (g : N →ₗ[R] Q) :
-  map (f₁ + f₂) g = map f₁ g + map f₂ g := by
+    map (f₁ + f₂) g = map f₁ g + map f₂ g := by
   ext
   simp only [add_tmul, compr₂_apply, mk_apply, map_tmul, add_apply]
 #align tensor_product.map_add_left TensorProduct.map_add_left
 
 theorem map_add_right (f : M →ₗ[R] P) (g₁ g₂ : N →ₗ[R] Q) :
-  map f (g₁ + g₂) = map f g₁ + map f g₂ := by
+    map f (g₁ + g₂) = map f g₁ + map f g₂ := by
   ext
   simp only [tmul_add, compr₂_apply, mk_apply, map_tmul, add_apply]
 #align tensor_product.map_add_right TensorProduct.map_add_right

This removes redundant field values of the form add := add for smaller terms and less unfolding during unification.

A list of all files containing a structure instance of the form { a1, ... with x1 := val, ... } where some xi is a field of some aj was generated by modifying the structure instance elaboration algorithm to print such overlaps to stdout in a custom toolchain.

Using that toolchain, I went through each file on the list and attempted to remove algebraic fields that overlapped and were redundant, eg add := add and not toFun (though some other ones did creep in). If things broke (which was the case in a couple of cases), I did not push further and reverted.

It is possible that pushing harder and trying to remove all redundant overlaps will yield further improvements.

@@ -310,7 +310,6 @@ theorem smul_tmul_smul (r s : R) (m : M) (n : N) : (r • m) ⊗ₜ[R] (s • n)
 
 instance leftModule : Module R'' (M ⊗[R] N) :=
   { TensorProduct.leftDistribMulAction with
-    smul := (· • ·)
     add_smul := TensorProduct.add_smul
     zero_smul := TensorProduct.zero_smul }
 #align tensor_product.left_module TensorProduct.leftModule

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

This has nice performance benefits.

@@ -36,10 +36,10 @@ bilinear, tensor, tensor product
 
 section Semiring
 
-variable {R : Type _} [CommSemiring R]
-variable {R' : Type _} [Monoid R']
-variable {R'' : Type _} [Semiring R'']
-variable {M : Type _} {N : Type _} {P : Type _} {Q : Type _} {S : Type _}
+variable {R : Type*} [CommSemiring R]
+variable {R' : Type*} [Monoid R']
+variable {R'' : Type*} [Semiring R'']
+variable {M : Type*} {N : Type*} {P : Type*} {Q : Type*} {S : Type*}
 variable [AddCommMonoid M] [AddCommMonoid N] [AddCommMonoid P] [AddCommMonoid Q] [AddCommMonoid S]
 variable [Module R M] [Module R N] [Module R P] [Module R Q] [Module R S]
 variable [DistribMulAction R' M]
@@ -194,12 +194,12 @@ theorem smul_tmul [DistribMulAction R' N] [CompatibleSMul R R' M N] (r : R') (m
 
 attribute [local instance] addMonoid
 /-- Auxiliary function to defining scalar multiplication on tensor product. -/
-def SMul.aux {R' : Type _} [SMul R' M] (r : R') : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
+def SMul.aux {R' : Type*} [SMul R' M] (r : R') : FreeAddMonoid (M × N) →+ M ⊗[R] N :=
   FreeAddMonoid.lift fun p : M × N => (r • p.1) ⊗ₜ p.2
 #align tensor_product.smul.aux TensorProduct.SMul.aux
 attribute [-instance] addMonoid
 
-theorem SMul.aux_of {R' : Type _} [SMul R' M] (r : R') (m : M) (n : N) :
+theorem SMul.aux_of {R' : Type*} [SMul R' M] (r : R') (m : M) (n : N) :
     SMul.aux r (.of (m, n)) = (r • m) ⊗ₜ[R] n :=
   rfl
 #align tensor_product.smul.aux_of TensorProduct.SMul.aux_of
@@ -327,7 +327,7 @@ instance [Module R''ᵐᵒᵖ M] [IsCentralScalar R'' M] : IsCentralScalar R'' (
 section
 
 -- Like `R'`, `R'₂` provides a `DistribMulAction R'₂ (M ⊗[R] N)`
-variable {R'₂ : Type _} [Monoid R'₂] [DistribMulAction R'₂ M]
+variable {R'₂ : Type*} [Monoid R'₂] [DistribMulAction R'₂ M]
 variable [SMulCommClass R R'₂ M]
 
 /-- `SMulCommClass R' R'₂ M` implies `SMulCommClass R' R'₂ (M ⊗[R] N)` -/
@@ -395,7 +395,7 @@ section
 
 open BigOperators
 
-theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
+theorem sum_tmul {α : Type*} (s : Finset α) (m : α → M) (n : N) :
     (∑ a in s, m a) ⊗ₜ[R] n = ∑ a in s, m a ⊗ₜ[R] n := by
   classical
     induction' s using Finset.induction with a s has ih h
@@ -403,7 +403,7 @@ theorem sum_tmul {α : Type _} (s : Finset α) (m : α → M) (n : N) :
     · simp [Finset.sum_insert has, add_tmul, ih]
 #align tensor_product.sum_tmul TensorProduct.sum_tmul
 
-theorem tmul_sum (m : M) {α : Type _} (s : Finset α) (n : α → N) :
+theorem tmul_sum (m : M) {α : Type*} (s : Finset α) (n : α → N) :
     (m ⊗ₜ[R] ∑ a in s, n a) = ∑ a in s, m ⊗ₜ[R] n a := by
   classical
     induction' s using Finset.induction with a s has ih h
@@ -770,7 +770,7 @@ def mapIncl (p : Submodule R P) (q : Submodule R Q) : p ⊗[R] q →ₗ[R] P ⊗
 
 section
 
-variable {P' Q' : Type _}
+variable {P' Q' : Type*}
 variable [AddCommMonoid P'] [Module R P']
 variable [AddCommMonoid Q'] [Module R Q']
 
@@ -1191,8 +1191,8 @@ end Semiring
 
 section Ring
 
-variable {R : Type _} [CommSemiring R]
-variable {M : Type _} {N : Type _} {P : Type _} {Q : Type _} {S : Type _}
+variable {R : Type*} [CommSemiring R]
+variable {M : Type*} {N : Type*} {P : Type*} {Q : Type*} {S : Type*}
 variable [AddCommGroup M] [AddCommGroup N] [AddCommGroup P] [AddCommGroup Q] [AddCommGroup S]
 variable [Module R M] [Module R N] [Module R P] [Module R Q] [Module R S]
 

This also makes some proofs more verbose to make it clearer which goal is which.

@@ -119,12 +119,14 @@ notation:100 x " ⊗ₜ[" R "] " y:100 => tmul R x y
 
 -- porting note: make the arguments of induction_on explicit
 @[elab_as_elim]
-protected theorem induction_on {C : M ⊗[R] N → Prop} (z : M ⊗[R] N) (C0 : C 0)
-    (C1 : ∀ x y, C <| x ⊗ₜ[R] y) (Cp : ∀ x y, C x → C y → C (x + y)) : C z :=
+protected theorem induction_on {motive : M ⊗[R] N → Prop} (z : M ⊗[R] N)
+    (zero : motive 0)
+    (tmul : ∀ x y, motive <| x ⊗ₜ[R] y)
+    (add : ∀ x y, motive x → motive y → motive (x + y)) : motive z :=
   AddCon.induction_on z fun x =>
-    FreeAddMonoid.recOn x C0 fun ⟨m, n⟩ y ih => by
+    FreeAddMonoid.recOn x zero fun ⟨m, n⟩ y ih => by
       rw [AddCon.coe_add]
-      exact Cp _ _ (C1 ..) ih
+      exact add _ _ (tmul ..) ih
 #align tensor_product.induction_on TensorProduct.induction_on
 
 variable (M)
@@ -434,11 +436,13 @@ theorem map₂_mk_top_top_eq_top : Submodule.map₂ (mk R M N) ⊤ ⊤ = ⊤ :=
 theorem exists_eq_tmul_of_forall (x : TensorProduct R M N)
     (h : ∀ (m₁ m₂ : M) (n₁ n₂ : N), ∃ m n, m₁ ⊗ₜ n₁ + m₂ ⊗ₜ n₂ = m ⊗ₜ[R] n) :
     ∃ m n, x = m ⊗ₜ n := by
-  induction' x using TensorProduct.induction_on with m n x y h₁ h₂
-  · use 0, 0
+  induction x using TensorProduct.induction_on with
+  | zero =>
+    use 0, 0
     rw [TensorProduct.zero_tmul]
-  · use m, n
-  · obtain ⟨m₁, n₁, rfl⟩ := h₁
+  | tmul m n => use m, n
+  | add x y h₁ h₂ =>
+    obtain ⟨m₁, n₁, rfl⟩ := h₁
     obtain ⟨m₂, n₂, rfl⟩ := h₂
     apply h
 

Port of leanprover-community/mathlib#17973

Follow up work:

• add IsPushout when M is a CommRing.

Co-authored-by: Calvin Lee <calvins.lee@utah.edu> Co-authored-by: Calvin Lee <pounce@integraldoma.in>

@@ -431,6 +431,17 @@ theorem map₂_mk_top_top_eq_top : Submodule.map₂ (mk R M N) ⊤ ⊤ = ⊤ :=
   exact Submodule.span_mono fun _ ⟨m, n, h⟩ => ⟨m, n, trivial, trivial, h⟩
 #align tensor_product.map₂_mk_top_top_eq_top TensorProduct.map₂_mk_top_top_eq_top
 
+theorem exists_eq_tmul_of_forall (x : TensorProduct R M N)
+    (h : ∀ (m₁ m₂ : M) (n₁ n₂ : N), ∃ m n, m₁ ⊗ₜ n₁ + m₂ ⊗ₜ n₂ = m ⊗ₜ[R] n) :
+    ∃ m n, x = m ⊗ₜ n := by
+  induction' x using TensorProduct.induction_on with m n x y h₁ h₂
+  · use 0, 0
+    rw [TensorProduct.zero_tmul]
+  · use m, n
+  · obtain ⟨m₁, n₁, rfl⟩ := h₁
+    obtain ⟨m₂, n₂, rfl⟩ := h₂
+    apply h
+
 end Module
 
 section UMP

@@ -167,7 +167,7 @@ Note that `Module R' (M ⊗[R] N)` is available even without this typeclass on `
 needed if `TensorProduct.smul_tmul`, `TensorProduct.smul_tmul'`, or `TensorProduct.tmul_smul` is
 used.
 -/
-class CompatibleSMul [DistribMulAction R' N] where
+class CompatibleSMul [DistribMulAction R' N] : Prop where
   smul_tmul : ∀ (r : R') (m : M) (n : N), (r • m) ⊗ₜ n = m ⊗ₜ[R] (r • n)
 #align tensor_product.compatible_smul TensorProduct.CompatibleSMul
 

@@ -6,7 +6,7 @@ Authors: Kenny Lau, Mario Carneiro
 import Mathlib.GroupTheory.Congruence
 import Mathlib.Algebra.Module.Submodule.Bilinear
 
-#align_import linear_algebra.tensor_product from "leanprover-community/mathlib"@"b0c712376e4ef44c53c3b872157ef44dfe9f9599"
+#align_import linear_algebra.tensor_product from "leanprover-community/mathlib"@"88fcdc3da43943f5b01925deddaa5bf0c0e85e4e"
 
 /-!
 # Tensor product of modules over commutative semirings.
@@ -326,7 +326,17 @@ section
 
 -- Like `R'`, `R'₂` provides a `DistribMulAction R'₂ (M ⊗[R] N)`
 variable {R'₂ : Type _} [Monoid R'₂] [DistribMulAction R'₂ M]
-variable [SMulCommClass R R'₂ M] [SMul R'₂ R']
+variable [SMulCommClass R R'₂ M]
+
+/-- `SMulCommClass R' R'₂ M` implies `SMulCommClass R' R'₂ (M ⊗[R] N)` -/
+instance smulCommClass_left [SMulCommClass R' R'₂ M] : SMulCommClass R' R'₂ (M ⊗[R] N) where
+  smul_comm r' r'₂ x :=
+    TensorProduct.induction_on x (by simp_rw [TensorProduct.smul_zero])
+      (fun m n => by simp_rw [smul_tmul', smul_comm]) fun x y ihx ihy => by
+      simp_rw [TensorProduct.smul_add]; rw [ihx, ihy]
+#align tensor_product.smul_comm_class_left TensorProduct.smulCommClass_left
+
+variable [SMul R'₂ R']
 
 /-- `IsScalarTower R'₂ R' M` implies `IsScalarTower R'₂ R' (M ⊗[R] N)` -/
 instance isScalarTower_left [IsScalarTower R'₂ R' M] : IsScalarTower R'₂ R' (M ⊗[R] N) :=

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro
-
-! This file was ported from Lean 3 source module linear_algebra.tensor_product
-! leanprover-community/mathlib commit b0c712376e4ef44c53c3b872157ef44dfe9f9599
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.GroupTheory.Congruence
 import Mathlib.Algebra.Module.Submodule.Bilinear
 
+#align_import linear_algebra.tensor_product from "leanprover-community/mathlib"@"b0c712376e4ef44c53c3b872157ef44dfe9f9599"
+
 /-!
 # Tensor product of modules over commutative semirings.
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -730,7 +730,7 @@ theorem map_range_eq_span_tmul (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
     range (map f g) = Submodule.span R { t | ∃ m n, f m ⊗ₜ g n = t } := by
   simp only [← Submodule.map_top, ← span_tmul_eq_top, Submodule.map_span, Set.mem_image,
     Set.mem_setOf_eq]
-  congr ; ext t
+  congr; ext t
   constructor
   · rintro ⟨_, ⟨⟨m, n, rfl⟩, rfl⟩⟩
     use m, n

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -1015,11 +1015,11 @@ def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P where
 def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M where
   toFun f := f.rTensor M
   map_add' f g := by
-    ext (x y)
+    ext x y
     simp only [compr₂_apply, mk_apply, add_apply, rTensor_tmul, add_tmul]
   map_smul' r f := by
     dsimp
-    ext (x y)
+    ext x y
     simp only [compr₂_apply, mk_apply, smul_tmul, tmul_smul, smul_apply, rTensor_tmul]
 #align linear_map.rtensor_hom LinearMap.rTensorHom
 
@@ -1064,7 +1064,7 @@ theorem rTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).rTensor M = r • f
 #align linear_map.rtensor_smul LinearMap.rTensor_smul
 
 theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) := by
-  ext (m n)
+  ext m n
   simp only [compr₂_apply, mk_apply, comp_apply, lTensor_tmul]
 #align linear_map.ltensor_comp LinearMap.lTensor_comp
 
@@ -1073,7 +1073,7 @@ theorem lTensor_comp_apply (x : M ⊗[R] N) :
 #align linear_map.ltensor_comp_apply LinearMap.lTensor_comp_apply
 
 theorem rTensor_comp : (g.comp f).rTensor M = (g.rTensor M).comp (f.rTensor M) := by
-  ext (m n)
+  ext m n
   simp only [compr₂_apply, mk_apply, comp_apply, rTensor_tmul]
 #align linear_map.rtensor_comp LinearMap.rTensor_comp
 

Part 2 of #5001

@@ -162,7 +162,7 @@ variable (R R' M N)
 
 /-- A typeclass for `SMul` structures which can be moved across a tensor product.
 
-This typeclass is generated automatically from a `IsScalarTower` instance, but exists so that
+This typeclass is generated automatically from an `IsScalarTower` instance, but exists so that
 we can also add an instance for `AddCommGroup.intModule`, allowing `z •` to be moved even if
 `R` does not support negation.
 

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

@@ -939,12 +939,12 @@ theorem tensorTensorTensorComm_symm :
 
 variable (M N P Q)
 
-/-- This special case is useful for describing the interplay between `dual_tensor_hom_equiv` and
+/-- This special case is useful for describing the interplay between `dualTensorHomEquiv` and
 composition of linear maps.
 
 E.g., composition of linear maps gives a map `(M → N) ⊗ (N → P) → (M → P)`, and applying
 `dual_tensor_hom_equiv.symm` to the three hom-modules gives a map
-`(M.dual ⊗ N) ⊗ (N.dual ⊗ P) → (M.dual ⊗ P)`, which agrees with the application of `contract_right`
+`(M.dual ⊗ N) ⊗ (N.dual ⊗ P) → (M.dual ⊗ P)`, which agrees with the application of `contractRight`
 on `N ⊗ N.dual` after the suitable rebracketting.
 -/
 def tensorTensorTensorAssoc : (M ⊗[R] N) ⊗[R] P ⊗[R] Q ≃ₗ[R] (M ⊗[R] N ⊗[R] P) ⊗[R] Q :=

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com>

@@ -818,14 +818,14 @@ def mapBilinear : (M →ₗ[R] P) →ₗ[R] (N →ₗ[R] Q) →ₗ[R] M ⊗[R] N
 #align tensor_product.map_bilinear TensorProduct.mapBilinear
 
 /-- The canonical linear map from `P ⊗[R] (M →ₗ[R] Q)` to `(M →ₗ[R] P ⊗[R] Q)` -/
-def ltensorHomToHomLtensor : P ⊗[R] (M →ₗ[R] Q) →ₗ[R] M →ₗ[R] P ⊗[R] Q :=
+def lTensorHomToHomLTensor : P ⊗[R] (M →ₗ[R] Q) →ₗ[R] M →ₗ[R] P ⊗[R] Q :=
   TensorProduct.lift (llcomp R M Q _ ∘ₗ mk R P Q)
-#align tensor_product.ltensor_hom_to_hom_ltensor TensorProduct.ltensorHomToHomLtensor
+#align tensor_product.ltensor_hom_to_hom_ltensor TensorProduct.lTensorHomToHomLTensor
 
 /-- The canonical linear map from `(M →ₗ[R] P) ⊗[R] Q` to `(M →ₗ[R] P ⊗[R] Q)` -/
-def rtensorHomToHomRtensor : (M →ₗ[R] P) ⊗[R] Q →ₗ[R] M →ₗ[R] P ⊗[R] Q :=
+def rTensorHomToHomRTensor : (M →ₗ[R] P) ⊗[R] Q →ₗ[R] M →ₗ[R] P ⊗[R] Q :=
   TensorProduct.lift (llcomp R M P _ ∘ₗ (mk R P Q).flip).flip
-#align tensor_product.rtensor_hom_to_hom_rtensor TensorProduct.rtensorHomToHomRtensor
+#align tensor_product.rtensor_hom_to_hom_rtensor TensorProduct.rTensorHomToHomRTensor
 
 /-- The linear map from `(M →ₗ P) ⊗ (N →ₗ Q)` to `(M ⊗ N →ₗ P ⊗ Q)` sending `f ⊗ₜ g` to
 the `TensorProduct.map f g`, the tensor product of the two maps. -/
@@ -841,16 +841,16 @@ theorem mapBilinear_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) : mapBilinear
 #align tensor_product.map_bilinear_apply TensorProduct.mapBilinear_apply
 
 @[simp]
-theorem ltensorHomToHomLtensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
-    ltensorHomToHomLtensor R M P Q (p ⊗ₜ f) m = p ⊗ₜ f m :=
+theorem lTensorHomToHomLTensor_apply (p : P) (f : M →ₗ[R] Q) (m : M) :
+    lTensorHomToHomLTensor R M P Q (p ⊗ₜ f) m = p ⊗ₜ f m :=
   rfl
-#align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.ltensorHomToHomLtensor_apply
+#align tensor_product.ltensor_hom_to_hom_ltensor_apply TensorProduct.lTensorHomToHomLTensor_apply
 
 @[simp]
-theorem rtensorHomToHomRtensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
-    rtensorHomToHomRtensor R M P Q (f ⊗ₜ q) m = f m ⊗ₜ q :=
+theorem rTensorHomToHomRTensor_apply (f : M →ₗ[R] P) (q : Q) (m : M) :
+    rTensorHomToHomRTensor R M P Q (f ⊗ₜ q) m = f m ⊗ₜ q :=
   rfl
-#align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rtensorHomToHomRtensor_apply
+#align tensor_product.rtensor_hom_to_hom_rtensor_apply TensorProduct.rTensorHomToHomRTensor_apply
 
 @[simp]
 theorem homTensorHomMap_apply (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
@@ -973,195 +973,195 @@ namespace LinearMap
 
 variable {N}
 
-/-- `ltensor M f : M ⊗ N →ₗ M ⊗ P` is the natural linear map induced by `f : N →ₗ P`. -/
-def ltensor (f : N →ₗ[R] P) : M ⊗[R] N →ₗ[R] M ⊗[R] P :=
+/-- `lTensor M f : M ⊗ N →ₗ M ⊗ P` is the natural linear map induced by `f : N →ₗ P`. -/
+def lTensor (f : N →ₗ[R] P) : M ⊗[R] N →ₗ[R] M ⊗[R] P :=
   TensorProduct.map id f
-#align linear_map.ltensor LinearMap.ltensor
+#align linear_map.ltensor LinearMap.lTensor
 
-/-- `rtensor f M : N₁ ⊗ M →ₗ N₂ ⊗ M` is the natural linear map induced by `f : N₁ →ₗ N₂`. -/
-def rtensor (f : N →ₗ[R] P) : N ⊗[R] M →ₗ[R] P ⊗[R] M :=
+/-- `rTensor f M : N₁ ⊗ M →ₗ N₂ ⊗ M` is the natural linear map induced by `f : N₁ →ₗ N₂`. -/
+def rTensor (f : N →ₗ[R] P) : N ⊗[R] M →ₗ[R] P ⊗[R] M :=
   TensorProduct.map f id
-#align linear_map.rtensor LinearMap.rtensor
+#align linear_map.rtensor LinearMap.rTensor
 
 variable (g : P →ₗ[R] Q) (f : N →ₗ[R] P)
 
 @[simp]
-theorem ltensor_tmul (m : M) (n : N) : f.ltensor M (m ⊗ₜ n) = m ⊗ₜ f n :=
+theorem lTensor_tmul (m : M) (n : N) : f.lTensor M (m ⊗ₜ n) = m ⊗ₜ f n :=
   rfl
-#align linear_map.ltensor_tmul LinearMap.ltensor_tmul
+#align linear_map.ltensor_tmul LinearMap.lTensor_tmul
 
 @[simp]
-theorem rtensor_tmul (m : M) (n : N) : f.rtensor M (n ⊗ₜ m) = f n ⊗ₜ m :=
+theorem rTensor_tmul (m : M) (n : N) : f.rTensor M (n ⊗ₜ m) = f n ⊗ₜ m :=
   rfl
-#align linear_map.rtensor_tmul LinearMap.rtensor_tmul
+#align linear_map.rtensor_tmul LinearMap.rTensor_tmul
 
 open TensorProduct
 
 attribute [local ext high] TensorProduct.ext
 
-/-- `ltensor_hom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
-def ltensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P where
-  toFun := ltensor M
+/-- `lTensorHom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
+def lTensorHom : (N →ₗ[R] P) →ₗ[R] M ⊗[R] N →ₗ[R] M ⊗[R] P where
+  toFun := lTensor M
   map_add' f g := by
     ext x y
-    simp only [compr₂_apply, mk_apply, add_apply, ltensor_tmul, tmul_add]
+    simp only [compr₂_apply, mk_apply, add_apply, lTensor_tmul, tmul_add]
   map_smul' r f := by
     dsimp
     ext x y
-    simp only [compr₂_apply, mk_apply, tmul_smul, smul_apply, ltensor_tmul]
-#align linear_map.ltensor_hom LinearMap.ltensorHom
+    simp only [compr₂_apply, mk_apply, tmul_smul, smul_apply, lTensor_tmul]
+#align linear_map.ltensor_hom LinearMap.lTensorHom
 
-/-- `rtensor_hom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
-def rtensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M where
-  toFun f := f.rtensor M
+/-- `rTensorHom M` is the natural linear map that sends a linear map `f : N →ₗ P` to `M ⊗ f`. -/
+def rTensorHom : (N →ₗ[R] P) →ₗ[R] N ⊗[R] M →ₗ[R] P ⊗[R] M where
+  toFun f := f.rTensor M
   map_add' f g := by
     ext (x y)
-    simp only [compr₂_apply, mk_apply, add_apply, rtensor_tmul, add_tmul]
+    simp only [compr₂_apply, mk_apply, add_apply, rTensor_tmul, add_tmul]
   map_smul' r f := by
     dsimp
     ext (x y)
-    simp only [compr₂_apply, mk_apply, smul_tmul, tmul_smul, smul_apply, rtensor_tmul]
-#align linear_map.rtensor_hom LinearMap.rtensorHom
+    simp only [compr₂_apply, mk_apply, smul_tmul, tmul_smul, smul_apply, rTensor_tmul]
+#align linear_map.rtensor_hom LinearMap.rTensorHom
 
 @[simp]
-theorem coe_ltensorHom : (ltensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R] M ⊗[R] P) = ltensor M :=
+theorem coe_lTensorHom : (lTensorHom M : (N →ₗ[R] P) → M ⊗[R] N →ₗ[R] M ⊗[R] P) = lTensor M :=
   rfl
-#align linear_map.coe_ltensor_hom LinearMap.coe_ltensorHom
+#align linear_map.coe_ltensor_hom LinearMap.coe_lTensorHom
 
 @[simp]
-theorem coe_rtensorHom : (rtensorHom M : (N →ₗ[R] P) → N ⊗[R] M →ₗ[R] P ⊗[R] M) = rtensor M :=
+theorem coe_rTensorHom : (rTensorHom M : (N →ₗ[R] P) → N ⊗[R] M →ₗ[R] P ⊗[R] M) = rTensor M :=
   rfl
-#align linear_map.coe_rtensor_hom LinearMap.coe_rtensorHom
+#align linear_map.coe_rtensor_hom LinearMap.coe_rTensorHom
 
 @[simp]
-theorem ltensor_add (f g : N →ₗ[R] P) : (f + g).ltensor M = f.ltensor M + g.ltensor M :=
-  (ltensorHom M).map_add f g
-#align linear_map.ltensor_add LinearMap.ltensor_add
+theorem lTensor_add (f g : N →ₗ[R] P) : (f + g).lTensor M = f.lTensor M + g.lTensor M :=
+  (lTensorHom M).map_add f g
+#align linear_map.ltensor_add LinearMap.lTensor_add
 
 @[simp]
-theorem rtensor_add (f g : N →ₗ[R] P) : (f + g).rtensor M = f.rtensor M + g.rtensor M :=
-  (rtensorHom M).map_add f g
-#align linear_map.rtensor_add LinearMap.rtensor_add
+theorem rTensor_add (f g : N →ₗ[R] P) : (f + g).rTensor M = f.rTensor M + g.rTensor M :=
+  (rTensorHom M).map_add f g
+#align linear_map.rtensor_add LinearMap.rTensor_add
 
 @[simp]
-theorem ltensor_zero : ltensor M (0 : N →ₗ[R] P) = 0 :=
-  (ltensorHom M).map_zero
-#align linear_map.ltensor_zero LinearMap.ltensor_zero
+theorem lTensor_zero : lTensor M (0 : N →ₗ[R] P) = 0 :=
+  (lTensorHom M).map_zero
+#align linear_map.ltensor_zero LinearMap.lTensor_zero
 
 @[simp]
-theorem rtensor_zero : rtensor M (0 : N →ₗ[R] P) = 0 :=
-  (rtensorHom M).map_zero
-#align linear_map.rtensor_zero LinearMap.rtensor_zero
+theorem rTensor_zero : rTensor M (0 : N →ₗ[R] P) = 0 :=
+  (rTensorHom M).map_zero
+#align linear_map.rtensor_zero LinearMap.rTensor_zero
 
 @[simp]
-theorem ltensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).ltensor M = r • f.ltensor M :=
-  (ltensorHom M).map_smul r f
-#align linear_map.ltensor_smul LinearMap.ltensor_smul
+theorem lTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).lTensor M = r • f.lTensor M :=
+  (lTensorHom M).map_smul r f
+#align linear_map.ltensor_smul LinearMap.lTensor_smul
 
 @[simp]
-theorem rtensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).rtensor M = r • f.rtensor M :=
-  (rtensorHom M).map_smul r f
-#align linear_map.rtensor_smul LinearMap.rtensor_smul
+theorem rTensor_smul (r : R) (f : N →ₗ[R] P) : (r • f).rTensor M = r • f.rTensor M :=
+  (rTensorHom M).map_smul r f
+#align linear_map.rtensor_smul LinearMap.rTensor_smul
 
-theorem ltensor_comp : (g.comp f).ltensor M = (g.ltensor M).comp (f.ltensor M) := by
+theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) := by
   ext (m n)
-  simp only [compr₂_apply, mk_apply, comp_apply, ltensor_tmul]
-#align linear_map.ltensor_comp LinearMap.ltensor_comp
+  simp only [compr₂_apply, mk_apply, comp_apply, lTensor_tmul]
+#align linear_map.ltensor_comp LinearMap.lTensor_comp
 
-theorem ltensor_comp_apply (x : M ⊗[R] N) :
-    (g.comp f).ltensor M x = (g.ltensor M) ((f.ltensor M) x) := by rw [ltensor_comp, coe_comp]; rfl
-#align linear_map.ltensor_comp_apply LinearMap.ltensor_comp_apply
+theorem lTensor_comp_apply (x : M ⊗[R] N) :
+    (g.comp f).lTensor M x = (g.lTensor M) ((f.lTensor M) x) := by rw [lTensor_comp, coe_comp]; rfl
+#align linear_map.ltensor_comp_apply LinearMap.lTensor_comp_apply
 
-theorem rtensor_comp : (g.comp f).rtensor M = (g.rtensor M).comp (f.rtensor M) := by
+theorem rTensor_comp : (g.comp f).rTensor M = (g.rTensor M).comp (f.rTensor M) := by
   ext (m n)
-  simp only [compr₂_apply, mk_apply, comp_apply, rtensor_tmul]
-#align linear_map.rtensor_comp LinearMap.rtensor_comp
+  simp only [compr₂_apply, mk_apply, comp_apply, rTensor_tmul]
+#align linear_map.rtensor_comp LinearMap.rTensor_comp
 
-theorem rtensor_comp_apply (x : N ⊗[R] M) :
-    (g.comp f).rtensor M x = (g.rtensor M) ((f.rtensor M) x) := by rw [rtensor_comp, coe_comp]; rfl
-#align linear_map.rtensor_comp_apply LinearMap.rtensor_comp_apply
+theorem rTensor_comp_apply (x : N ⊗[R] M) :
+    (g.comp f).rTensor M x = (g.rTensor M) ((f.rTensor M) x) := by rw [rTensor_comp, coe_comp]; rfl
+#align linear_map.rtensor_comp_apply LinearMap.rTensor_comp_apply
 
-theorem ltensor_mul (f g : Module.End R N) : (f * g).ltensor M = f.ltensor M * g.ltensor M :=
-  ltensor_comp M f g
-#align linear_map.ltensor_mul LinearMap.ltensor_mul
+theorem lTensor_mul (f g : Module.End R N) : (f * g).lTensor M = f.lTensor M * g.lTensor M :=
+  lTensor_comp M f g
+#align linear_map.ltensor_mul LinearMap.lTensor_mul
 
-theorem rtensor_mul (f g : Module.End R N) : (f * g).rtensor M = f.rtensor M * g.rtensor M :=
-  rtensor_comp M f g
-#align linear_map.rtensor_mul LinearMap.rtensor_mul
+theorem rTensor_mul (f g : Module.End R N) : (f * g).rTensor M = f.rTensor M * g.rTensor M :=
+  rTensor_comp M f g
+#align linear_map.rtensor_mul LinearMap.rTensor_mul
 
 variable (N)
 
 @[simp]
-theorem ltensor_id : (id : N →ₗ[R] N).ltensor M = id :=
+theorem lTensor_id : (id : N →ₗ[R] N).lTensor M = id :=
   map_id
-#align linear_map.ltensor_id LinearMap.ltensor_id
+#align linear_map.ltensor_id LinearMap.lTensor_id
 
 -- `simp` can prove this.
-theorem ltensor_id_apply (x : M ⊗[R] N) : (LinearMap.id : N →ₗ[R] N).ltensor M x = x := by
-  rw [ltensor_id, id_coe, id.def]
-#align linear_map.ltensor_id_apply LinearMap.ltensor_id_apply
+theorem lTensor_id_apply (x : M ⊗[R] N) : (LinearMap.id : N →ₗ[R] N).lTensor M x = x := by
+  rw [lTensor_id, id_coe, id.def]
+#align linear_map.ltensor_id_apply LinearMap.lTensor_id_apply
 
 @[simp]
-theorem rtensor_id : (id : N →ₗ[R] N).rtensor M = id :=
+theorem rTensor_id : (id : N →ₗ[R] N).rTensor M = id :=
   map_id
-#align linear_map.rtensor_id LinearMap.rtensor_id
+#align linear_map.rtensor_id LinearMap.rTensor_id
 
 -- `simp` can prove this.
-theorem rtensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rtensor M x = x := by
-  rw [rtensor_id, id_coe, id.def]
-#align linear_map.rtensor_id_apply LinearMap.rtensor_id_apply
+theorem rTensor_id_apply (x : N ⊗[R] M) : (LinearMap.id : N →ₗ[R] N).rTensor M x = x := by
+  rw [rTensor_id, id_coe, id.def]
+#align linear_map.rtensor_id_apply LinearMap.rTensor_id_apply
 
 variable {N}
 
 @[simp]
-theorem ltensor_comp_rtensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
-    (g.ltensor P).comp (f.rtensor N) = map f g := by
-  simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
-#align linear_map.ltensor_comp_rtensor LinearMap.ltensor_comp_rtensor
+theorem lTensor_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
+    (g.lTensor P).comp (f.rTensor N) = map f g := by
+  simp only [lTensor, rTensor, ← map_comp, id_comp, comp_id]
+#align linear_map.ltensor_comp_rtensor LinearMap.lTensor_comp_rTensor
 
 @[simp]
-theorem rtensor_comp_ltensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
-    (f.rtensor Q).comp (g.ltensor M) = map f g := by
-  simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
-#align linear_map.rtensor_comp_ltensor LinearMap.rtensor_comp_ltensor
+theorem rTensor_comp_lTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
+    (f.rTensor Q).comp (g.lTensor M) = map f g := by
+  simp only [lTensor, rTensor, ← map_comp, id_comp, comp_id]
+#align linear_map.rtensor_comp_ltensor LinearMap.rTensor_comp_lTensor
 
 @[simp]
-theorem map_comp_rtensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (f' : S →ₗ[R] M) :
-    (map f g).comp (f'.rtensor _) = map (f.comp f') g := by
-  simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
-#align linear_map.map_comp_rtensor LinearMap.map_comp_rtensor
+theorem map_comp_rTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (f' : S →ₗ[R] M) :
+    (map f g).comp (f'.rTensor _) = map (f.comp f') g := by
+  simp only [lTensor, rTensor, ← map_comp, id_comp, comp_id]
+#align linear_map.map_comp_rtensor LinearMap.map_comp_rTensor
 
 @[simp]
-theorem map_comp_ltensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (g' : S →ₗ[R] N) :
-    (map f g).comp (g'.ltensor _) = map f (g.comp g') := by
-  simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
-#align linear_map.map_comp_ltensor LinearMap.map_comp_ltensor
+theorem map_comp_lTensor (f : M →ₗ[R] P) (g : N →ₗ[R] Q) (g' : S →ₗ[R] N) :
+    (map f g).comp (g'.lTensor _) = map f (g.comp g') := by
+  simp only [lTensor, rTensor, ← map_comp, id_comp, comp_id]
+#align linear_map.map_comp_ltensor LinearMap.map_comp_lTensor
 
 @[simp]
-theorem rtensor_comp_map (f' : P →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
-    (f'.rtensor _).comp (map f g) = map (f'.comp f) g := by
-  simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
-#align linear_map.rtensor_comp_map LinearMap.rtensor_comp_map
+theorem rTensor_comp_map (f' : P →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
+    (f'.rTensor _).comp (map f g) = map (f'.comp f) g := by
+  simp only [lTensor, rTensor, ← map_comp, id_comp, comp_id]
+#align linear_map.rtensor_comp_map LinearMap.rTensor_comp_map
 
 @[simp]
-theorem ltensor_comp_map (g' : Q →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
-    (g'.ltensor _).comp (map f g) = map f (g'.comp g) := by
-  simp only [ltensor, rtensor, ← map_comp, id_comp, comp_id]
-#align linear_map.ltensor_comp_map LinearMap.ltensor_comp_map
+theorem lTensor_comp_map (g' : Q →ₗ[R] S) (f : M →ₗ[R] P) (g : N →ₗ[R] Q) :
+    (g'.lTensor _).comp (map f g) = map f (g'.comp g) := by
+  simp only [lTensor, rTensor, ← map_comp, id_comp, comp_id]
+#align linear_map.ltensor_comp_map LinearMap.lTensor_comp_map
 
 variable {M}
 
 @[simp]
-theorem rtensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rtensor N ^ n = (f ^ n).rtensor N := by
+theorem rTensor_pow (f : M →ₗ[R] M) (n : ℕ) : f.rTensor N ^ n = (f ^ n).rTensor N := by
   have h := TensorProduct.map_pow f (id : N →ₗ[R] N) n
   rwa [id_pow] at h
-#align linear_map.rtensor_pow LinearMap.rtensor_pow
+#align linear_map.rtensor_pow LinearMap.rTensor_pow
 
 @[simp]
-theorem ltensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.ltensor M ^ n = (f ^ n).ltensor M := by
+theorem lTensor_pow (f : N →ₗ[R] N) (n : ℕ) : f.lTensor M ^ n = (f ^ n).lTensor M := by
   have h := TensorProduct.map_pow (id : M →ₗ[R] M) f n
   rwa [id_pow] at h
-#align linear_map.ltensor_pow LinearMap.ltensor_pow
+#align linear_map.ltensor_pow LinearMap.lTensor_pow
 
 end LinearMap
 
@@ -1280,28 +1280,28 @@ end TensorProduct
 namespace LinearMap
 
 @[simp]
-theorem ltensor_sub (f g : N →ₗ[R] P) : (f - g).ltensor M = f.ltensor M - g.ltensor M := by
-  simp_rw [← coe_ltensorHom]
-  exact (ltensorHom (R:=R) (N:=N) (P:=P) M).map_sub f g
-#align linear_map.ltensor_sub LinearMap.ltensor_sub
+theorem lTensor_sub (f g : N →ₗ[R] P) : (f - g).lTensor M = f.lTensor M - g.lTensor M := by
+  simp_rw [← coe_lTensorHom]
+  exact (lTensorHom (R:=R) (N:=N) (P:=P) M).map_sub f g
+#align linear_map.ltensor_sub LinearMap.lTensor_sub
 
 @[simp]
-theorem rtensor_sub (f g : N →ₗ[R] P) : (f - g).rtensor M = f.rtensor M - g.rtensor M := by
-  simp only [← coe_rtensorHom]
-  exact (rtensorHom (R:=R) (N:=N) (P:=P) M).map_sub f g
-#align linear_map.rtensor_sub LinearMap.rtensor_sub
+theorem rTensor_sub (f g : N →ₗ[R] P) : (f - g).rTensor M = f.rTensor M - g.rTensor M := by
+  simp only [← coe_rTensorHom]
+  exact (rTensorHom (R:=R) (N:=N) (P:=P) M).map_sub f g
+#align linear_map.rtensor_sub LinearMap.rTensor_sub
 
 @[simp]
-theorem ltensor_neg (f : N →ₗ[R] P) : (-f).ltensor M = -f.ltensor M := by
-  simp only [← coe_ltensorHom]
-  exact (ltensorHom (R:=R) (N:=N) (P:=P) M).map_neg f
-#align linear_map.ltensor_neg LinearMap.ltensor_neg
+theorem lTensor_neg (f : N →ₗ[R] P) : (-f).lTensor M = -f.lTensor M := by
+  simp only [← coe_lTensorHom]
+  exact (lTensorHom (R:=R) (N:=N) (P:=P) M).map_neg f
+#align linear_map.ltensor_neg LinearMap.lTensor_neg
 
 @[simp]
-theorem rtensor_neg (f : N →ₗ[R] P) : (-f).rtensor M = -f.rtensor M := by
-  simp only [← coe_rtensorHom]
-  exact (rtensorHom (R:=R) (N:=N) (P:=P) M).map_neg f
-#align linear_map.rtensor_neg LinearMap.rtensor_neg
+theorem rTensor_neg (f : N →ₗ[R] P) : (-f).rTensor M = -f.rTensor M := by
+  simp only [← coe_rTensorHom]
+  exact (rTensorHom (R:=R) (N:=N) (P:=P) M).map_neg f
+#align linear_map.rtensor_neg LinearMap.rTensor_neg
 
 end LinearMap
 

@@ -629,9 +629,7 @@ protected def lid : R ⊗[R] M ≃ₗ[R] M :=
 end
 
 @[simp]
-theorem lid_tmul (m : M) (r : R) : (TensorProduct.lid R M : R ⊗ M → M) (r ⊗ₜ m) = r • m := by
-  dsimp [TensorProduct.lid]
-  simp
+theorem lid_tmul (m : M) (r : R) : (TensorProduct.lid R M : R ⊗ M → M) (r ⊗ₜ m) = r • m :=
   rfl
 #align tensor_product.lid_tmul TensorProduct.lid_tmul
 
@@ -676,9 +674,7 @@ protected def rid : M ⊗[R] R ≃ₗ[R] M :=
 end
 
 @[simp]
-theorem rid_tmul (m : M) (r : R) : (TensorProduct.rid R M) (m ⊗ₜ r) = r • m := by
-  dsimp [TensorProduct.rid, TensorProduct.comm, TensorProduct.lid]
-  simp
+theorem rid_tmul (m : M) (r : R) : (TensorProduct.rid R M) (m ⊗ₜ r) = r • m :=
   rfl
 #align tensor_product.rid_tmul TensorProduct.rid_tmul