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

@@ -264,8 +264,8 @@ theorem map_zero [Nonempty ι] : f 0 = 0 :=
 #print AlternatingMap.map_eq_zero_of_not_injective /-
 theorem map_eq_zero_of_not_injective (v : ι → M) (hv : ¬Function.Injective v) : f v = 0 :=
   by
-  rw [Function.Injective] at hv 
-  push_neg at hv 
+  rw [Function.Injective] at hv
+  push_neg at hv
   rcases hv with ⟨i₁, i₂, heq, hne⟩
   exact f.map_eq_zero_of_eq v HEq hne
 #align alternating_map.map_eq_zero_of_not_injective AlternatingMap.map_eq_zero_of_not_injective
@@ -981,11 +981,11 @@ theorem map_linearDependent {K : Type _} [Ring K] {M : Type _} [AddCommGroup M]
   letI := Classical.decEq ι
   suffices f (update v i (g i • v i)) = 0
     by
-    rw [f.map_smul, Function.update_eq_self, smul_eq_zero] at this 
+    rw [f.map_smul, Function.update_eq_self, smul_eq_zero] at this
     exact Or.resolve_left this hz
   conv at h in g _ • v _ => rw [← if_t_t (i = x) (g _ • v _)]
   rw [Finset.sum_ite, Finset.filter_eq, Finset.filter_ne, if_pos hi, Finset.sum_singleton,
-    add_eq_zero_iff_eq_neg] at h 
+    add_eq_zero_iff_eq_neg] at h
   rw [h, f.map_neg, f.map_update_sum, neg_eq_zero, Finset.sum_eq_zero]
   intro j hj
   obtain ⟨hij, _⟩ := finset.mem_erase.mp hj
@@ -1162,7 +1162,7 @@ def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap
       σ.sign •
         (MultilinearMap.domCoprod ↑a ↑b : MultilinearMap R' (fun _ => Mᵢ) (N₁ ⊗ N₂)).domDomCongr σ)
     fun σ₁ σ₂ H => by
-    rw [QuotientGroup.leftRel_apply] at H 
+    rw [QuotientGroup.leftRel_apply] at H
     obtain ⟨⟨sl, sr⟩, h⟩ := H
     ext v
     simp only [MultilinearMap.domDomCongr_apply, MultilinearMap.domCoprod_apply,
@@ -1218,7 +1218,7 @@ theorem domCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ
   dsimp only [Quotient.liftOn'_mk'', Quotient.map'_mk'', MultilinearMap.smul_apply,
     MultilinearMap.domDomCongr_apply, MultilinearMap.domCoprod_apply, dom_coprod.summand]
   intro hσ
-  cases hi : σ⁻¹ i <;> cases hj : σ⁻¹ j <;> rw [perm.inv_eq_iff_eq] at hi hj  <;> substs hi hj <;>
+  cases hi : σ⁻¹ i <;> cases hj : σ⁻¹ j <;> rw [perm.inv_eq_iff_eq] at hi hj <;> substs hi hj <;>
     revert val val_1
   case inl.inr |
     inr.inl =>
@@ -1229,7 +1229,7 @@ theorem domCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ
     on_goal 1 => replace hσ := Equiv.congr_fun hσ (Sum.inl i')
     on_goal 2 => replace hσ := Equiv.congr_fun hσ (Sum.inr i')
     all_goals
-      rw [smul_eq_mul, ← mul_swap_eq_swap_mul, mul_inv_rev, swap_inv, inv_mul_cancel_right] at hσ 
+      rw [smul_eq_mul, ← mul_swap_eq_swap_mul, mul_inv_rev, swap_inv, inv_mul_cancel_right] at hσ
       simpa using hσ
   case inr.inr |
     inl.inl =>

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

@@ -1422,7 +1422,14 @@ variable [Module R' N₁] [Module R' N₂]
 are distinct basis vectors. -/
 theorem Basis.ext_alternating {f g : AlternatingMap R' N₁ N₂ ι} (e : Basis ι₁ R' N₁)
     (h : ∀ v : ι → ι₁, Function.Injective v → (f fun i => e (v i)) = g fun i => e (v i)) : f = g :=
-  by classical
+  by
+  classical
+  refine' AlternatingMap.coe_multilinearMap_injective (Basis.ext_multilinear e fun v => _)
+  by_cases hi : Function.Injective v
+  · exact h v hi
+  · have : ¬Function.Injective fun i => e (v i) := hi.imp Function.Injective.of_comp
+    rw [coe_multilinear_map, coe_multilinear_map, f.map_eq_zero_of_not_injective _ this,
+      g.map_eq_zero_of_not_injective _ this]
 #align basis.ext_alternating Basis.ext_alternating
 -/
 

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

@@ -1422,14 +1422,7 @@ variable [Module R' N₁] [Module R' N₂]
 are distinct basis vectors. -/
 theorem Basis.ext_alternating {f g : AlternatingMap R' N₁ N₂ ι} (e : Basis ι₁ R' N₁)
     (h : ∀ v : ι → ι₁, Function.Injective v → (f fun i => e (v i)) = g fun i => e (v i)) : f = g :=
-  by
-  classical
-  refine' AlternatingMap.coe_multilinearMap_injective (Basis.ext_multilinear e fun v => _)
-  by_cases hi : Function.Injective v
-  · exact h v hi
-  · have : ¬Function.Injective fun i => e (v i) := hi.imp Function.Injective.of_comp
-    rw [coe_multilinear_map, coe_multilinear_map, f.map_eq_zero_of_not_injective _ this,
-      g.map_eq_zero_of_not_injective _ this]
+  by classical
 #align basis.ext_alternating Basis.ext_alternating
 -/
 

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

@@ -99,12 +99,12 @@ open Function
 
 section Coercions
 
-#print AlternatingMap.instDFunLike /-
-instance instDFunLike : DFunLike (AlternatingMap R M N ι) (ι → M) fun _ => N
+#print AlternatingMap.instFunLike /-
+instance instFunLike : DFunLike (AlternatingMap R M N ι) (ι → M) fun _ => N
     where
   coe := AlternatingMap.toFun
   coe_injective' f g h := by cases f; cases g; congr
-#align alternating_map.fun_like AlternatingMap.instDFunLike
+#align alternating_map.fun_like AlternatingMap.instFunLike
 -/
 
 -- shortcut instance

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

@@ -99,17 +99,17 @@ open Function
 
 section Coercions
 
-#print AlternatingMap.funLike /-
-instance funLike : FunLike (AlternatingMap R M N ι) (ι → M) fun _ => N
+#print AlternatingMap.instDFunLike /-
+instance instDFunLike : DFunLike (AlternatingMap R M N ι) (ι → M) fun _ => N
     where
   coe := AlternatingMap.toFun
   coe_injective' f g h := by cases f; cases g; congr
-#align alternating_map.fun_like AlternatingMap.funLike
+#align alternating_map.fun_like AlternatingMap.instDFunLike
 -/
 
 -- shortcut instance
 instance : CoeFun (AlternatingMap R M N ι) fun _ => (ι → M) → N :=
-  ⟨FunLike.coe⟩
+  ⟨DFunLike.coe⟩
 
 initialize_simps_projections AlternatingMap (toFun → apply)
 
@@ -139,7 +139,7 @@ theorem congr_arg (f : AlternatingMap R M N ι) {x y : ι → M} (h : x = y) : f
 
 #print AlternatingMap.coe_injective /-
 theorem coe_injective : Injective (coeFn : AlternatingMap R M N ι → (ι → M) → N) :=
-  FunLike.coe_injective
+  DFunLike.coe_injective
 #align alternating_map.coe_injective AlternatingMap.coe_injective
 -/
 
@@ -153,7 +153,7 @@ theorem coe_inj {f g : AlternatingMap R M N ι} : (f : (ι → M) → N) = g ↔
 #print AlternatingMap.ext /-
 @[ext]
 theorem ext {f f' : AlternatingMap R M N ι} (H : ∀ x, f x = f' x) : f = f' :=
-  FunLike.ext _ _ H
+  DFunLike.ext _ _ H
 #align alternating_map.ext AlternatingMap.ext
 -/
 

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

@@ -1136,13 +1136,13 @@ abbrev ModSumCongr (α β : Type _) :=
 #align equiv.perm.mod_sum_congr Equiv.Perm.ModSumCongr
 -/
 
-#print Equiv.Perm.ModSumCongr.swap_smul_involutive /-
-theorem ModSumCongr.swap_smul_involutive {α β : Type _} [DecidableEq (Sum α β)] (i j : Sum α β) :
+#print Equiv.swap_smul_involutive /-
+theorem Equiv.swap_smul_involutive {α β : Type _} [DecidableEq (Sum α β)] (i j : Sum α β) :
     Function.Involutive (SMul.smul (Equiv.swap i j) : ModSumCongr α β → ModSumCongr α β) := fun σ =>
   by
   apply σ.induction_on' fun σ => _
   exact _root_.congr_arg Quotient.mk'' (Equiv.swap_mul_involutive i j σ)
-#align equiv.perm.mod_sum_congr.swap_smul_involutive Equiv.Perm.ModSumCongr.swap_smul_involutive
+#align equiv.perm.mod_sum_congr.swap_smul_involutive Equiv.swap_smul_involutive
 -/
 
 end Equiv.Perm
@@ -1279,8 +1279,7 @@ def domCoprod (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ
         Finset.sum_involution (fun σ _ => Equiv.swap i j • σ)
           (fun σ _ => dom_coprod.summand_add_swap_smul_eq_zero a b σ hv hij)
           (fun σ _ => mt <| dom_coprod.summand_eq_zero_of_smul_invariant a b σ hv hij)
-          (fun σ _ => Finset.mem_univ _) fun σ _ =>
-          Equiv.Perm.ModSumCongr.swap_smul_involutive i j σ }
+          (fun σ _ => Finset.mem_univ _) fun σ _ => Equiv.swap_smul_involutive i j σ }
 #align alternating_map.dom_coprod AlternatingMap.domCoprod
 -/
 
@@ -1373,8 +1372,7 @@ theorem MultilinearMap.domCoprod_alternization [DecidableEq ιa] [DecidableEq ι
     Finset.sum_image (perm.sum_congr_hom_injective.inj_on _)]
   -- now we're ready to clean up the RHS, pulling out the summation
   rw [dom_coprod.summand_mk', MultilinearMap.domCoprod_alternization_coe, ← Finset.sum_product',
-    Finset.univ_product_univ, ← MultilinearMap.domDomCongrEquiv_apply, AddEquiv.map_sum,
-    Finset.smul_sum]
+    Finset.univ_product_univ, ← MultilinearMap.domDomCongrEquiv_apply, map_sum, Finset.smul_sum]
   congr 1
   ext1 ⟨al, ar⟩
   dsimp only

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

@@ -903,10 +903,10 @@ section DomDomLcongr
 
 variable (S : Type _) [Semiring S] [Module S N] [SMulCommClass R S N]
 
-#print AlternatingMap.domDomLcongr /-
+#print AlternatingMap.domDomCongrₗ /-
 /-- `alternating_map.dom_dom_congr` as a linear equivalence. -/
 @[simps apply symm_apply]
-def domDomLcongr (σ : ι ≃ ι') : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι'
+def domDomCongrₗ (σ : ι ≃ ι') : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι'
     where
   toFun := domDomCongr σ
   invFun := domDomCongr σ.symm
@@ -914,25 +914,25 @@ def domDomLcongr (σ : ι ≃ ι') : AlternatingMap R M N ι ≃ₗ[S] Alternati
   right_inv m := by ext; simp [Function.comp]
   map_add' := domDomCongr_add σ
   map_smul' := domDomCongr_smul σ
-#align alternating_map.dom_dom_lcongr AlternatingMap.domDomLcongr
+#align alternating_map.dom_dom_lcongr AlternatingMap.domDomCongrₗ
 -/
 
-#print AlternatingMap.domDomLcongr_refl /-
+#print AlternatingMap.domDomCongrₗ_refl /-
 @[simp]
-theorem domDomLcongr_refl :
-    (domDomLcongr S (Equiv.refl ι) : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι) =
+theorem domDomCongrₗ_refl :
+    (domDomCongrₗ S (Equiv.refl ι) : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι) =
       LinearEquiv.refl _ _ :=
   LinearEquiv.ext domDomCongr_refl
-#align alternating_map.dom_dom_lcongr_refl AlternatingMap.domDomLcongr_refl
+#align alternating_map.dom_dom_lcongr_refl AlternatingMap.domDomCongrₗ_refl
 -/
 
-#print AlternatingMap.domDomLcongr_toAddEquiv /-
+#print AlternatingMap.domDomCongrₗ_toAddEquiv /-
 @[simp]
-theorem domDomLcongr_toAddEquiv (σ : ι ≃ ι') :
-    (domDomLcongr S σ : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι').toAddEquiv =
+theorem domDomCongrₗ_toAddEquiv (σ : ι ≃ ι') :
+    (domDomCongrₗ S σ : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι').toAddEquiv =
       domDomCongrEquiv σ :=
   rfl
-#align alternating_map.dom_dom_lcongr_to_add_equiv AlternatingMap.domDomLcongr_toAddEquiv
+#align alternating_map.dom_dom_lcongr_to_add_equiv AlternatingMap.domDomCongrₗ_toAddEquiv
 -/
 
 end DomDomLcongr

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

@@ -1340,8 +1340,8 @@ theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableE
         σa.sign • σb.sign • MultilinearMap.domCoprod (a.domDomCongr σa) (b.domDomCongr σb) :=
   by
   simp_rw [← MultilinearMap.domCoprod'_apply, MultilinearMap.alternatization_coe]
-  simp_rw [TensorProduct.sum_tmul, TensorProduct.tmul_sum, LinearMap.map_sum, ←
-    TensorProduct.smul_tmul', TensorProduct.tmul_smul, LinearMap.map_smul_of_tower]
+  simp_rw [TensorProduct.sum_tmul, TensorProduct.tmul_sum, map_sum, ← TensorProduct.smul_tmul',
+    TensorProduct.tmul_smul, LinearMap.map_smul_of_tower]
 #align multilinear_map.dom_coprod_alternization_coe MultilinearMap.domCoprod_alternization_coe
 -/
 

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

@@ -3,12 +3,12 @@ Copyright (c) 2020 Zhangir Azerbayev. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Zhangir Azerbayev
 -/
-import Mathbin.GroupTheory.GroupAction.Quotient
-import Mathbin.GroupTheory.Perm.Sign
-import Mathbin.GroupTheory.Perm.Subgroup
-import Mathbin.LinearAlgebra.LinearIndependent
-import Mathbin.LinearAlgebra.Multilinear.Basis
-import Mathbin.LinearAlgebra.Multilinear.TensorProduct
+import GroupTheory.GroupAction.Quotient
+import GroupTheory.Perm.Sign
+import GroupTheory.Perm.Subgroup
+import LinearAlgebra.LinearIndependent
+import LinearAlgebra.Multilinear.Basis
+import LinearAlgebra.Multilinear.TensorProduct
 
 #align_import linear_algebra.alternating from "leanprover-community/mathlib"@"0c1d80f5a86b36c1db32e021e8d19ae7809d5b79"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

@@ -875,12 +875,14 @@ theorem domDomCongr_add (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
 #align alternating_map.dom_dom_congr_add AlternatingMap.domDomCongr_add
 -/
 
+#print AlternatingMap.domDomCongr_smul /-
 @[simp]
 theorem domDomCongr_smul {S : Type _} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
     (σ : ι ≃ ι') (c : S) (f : AlternatingMap R M N ι) :
     (c • f).domDomCongr σ = c • f.domDomCongr σ :=
   rfl
 #align alternating_map.dom_dom_congr_smul AlternatingMap.domDomCongr_smul
+-/
 
 #print AlternatingMap.domDomCongrEquiv /-
 /-- `alternating_map.dom_dom_congr` as an equivalence.
@@ -901,6 +903,7 @@ section DomDomLcongr
 
 variable (S : Type _) [Semiring S] [Module S N] [SMulCommClass R S N]
 
+#print AlternatingMap.domDomLcongr /-
 /-- `alternating_map.dom_dom_congr` as a linear equivalence. -/
 @[simps apply symm_apply]
 def domDomLcongr (σ : ι ≃ ι') : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι'
@@ -912,20 +915,25 @@ def domDomLcongr (σ : ι ≃ ι') : AlternatingMap R M N ι ≃ₗ[S] Alternati
   map_add' := domDomCongr_add σ
   map_smul' := domDomCongr_smul σ
 #align alternating_map.dom_dom_lcongr AlternatingMap.domDomLcongr
+-/
 
+#print AlternatingMap.domDomLcongr_refl /-
 @[simp]
 theorem domDomLcongr_refl :
     (domDomLcongr S (Equiv.refl ι) : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι) =
       LinearEquiv.refl _ _ :=
   LinearEquiv.ext domDomCongr_refl
 #align alternating_map.dom_dom_lcongr_refl AlternatingMap.domDomLcongr_refl
+-/
 
+#print AlternatingMap.domDomLcongr_toAddEquiv /-
 @[simp]
 theorem domDomLcongr_toAddEquiv (σ : ι ≃ ι') :
     (domDomLcongr S σ : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι').toAddEquiv =
       domDomCongrEquiv σ :=
   rfl
 #align alternating_map.dom_dom_lcongr_to_add_equiv AlternatingMap.domDomLcongr_toAddEquiv
+-/
 
 end DomDomLcongr
 

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

@@ -467,7 +467,7 @@ variable {S : Type _} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
 instance : DistribMulAction S (AlternatingMap R M N ι)
     where
   one_smul f := ext fun x => one_smul _ _
-  mul_smul c₁ c₂ f := ext fun x => mul_smul _ _ _
+  hMul_smul c₁ c₂ f := ext fun x => hMul_smul _ _ _
   smul_zero r := ext fun x => smul_zero _
   smul_add r f₁ f₂ := ext fun x => smul_add _ _ _
 

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

@@ -10,7 +10,7 @@ import Mathbin.LinearAlgebra.LinearIndependent
 import Mathbin.LinearAlgebra.Multilinear.Basis
 import Mathbin.LinearAlgebra.Multilinear.TensorProduct
 
-#align_import linear_algebra.alternating from "leanprover-community/mathlib"@"bd65478311e4dfd41f48bf38c7e3b02fb75d0163"
+#align_import linear_algebra.alternating from "leanprover-community/mathlib"@"0c1d80f5a86b36c1db32e021e8d19ae7809d5b79"
 
 /-!
 # Alternating Maps
@@ -875,6 +875,13 @@ theorem domDomCongr_add (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
 #align alternating_map.dom_dom_congr_add AlternatingMap.domDomCongr_add
 -/
 
+@[simp]
+theorem domDomCongr_smul {S : Type _} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
+    (σ : ι ≃ ι') (c : S) (f : AlternatingMap R M N ι) :
+    (c • f).domDomCongr σ = c • f.domDomCongr σ :=
+  rfl
+#align alternating_map.dom_dom_congr_smul AlternatingMap.domDomCongr_smul
+
 #print AlternatingMap.domDomCongrEquiv /-
 /-- `alternating_map.dom_dom_congr` as an equivalence.
 
@@ -890,6 +897,38 @@ def domDomCongrEquiv (σ : ι ≃ ι') : AlternatingMap R M N ι ≃+ Alternatin
 #align alternating_map.dom_dom_congr_equiv AlternatingMap.domDomCongrEquiv
 -/
 
+section DomDomLcongr
+
+variable (S : Type _) [Semiring S] [Module S N] [SMulCommClass R S N]
+
+/-- `alternating_map.dom_dom_congr` as a linear equivalence. -/
+@[simps apply symm_apply]
+def domDomLcongr (σ : ι ≃ ι') : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι'
+    where
+  toFun := domDomCongr σ
+  invFun := domDomCongr σ.symm
+  left_inv f := by ext; simp [Function.comp]
+  right_inv m := by ext; simp [Function.comp]
+  map_add' := domDomCongr_add σ
+  map_smul' := domDomCongr_smul σ
+#align alternating_map.dom_dom_lcongr AlternatingMap.domDomLcongr
+
+@[simp]
+theorem domDomLcongr_refl :
+    (domDomLcongr S (Equiv.refl ι) : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι) =
+      LinearEquiv.refl _ _ :=
+  LinearEquiv.ext domDomCongr_refl
+#align alternating_map.dom_dom_lcongr_refl AlternatingMap.domDomLcongr_refl
+
+@[simp]
+theorem domDomLcongr_toAddEquiv (σ : ι ≃ ι') :
+    (domDomLcongr S σ : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι').toAddEquiv =
+      domDomCongrEquiv σ :=
+  rfl
+#align alternating_map.dom_dom_lcongr_to_add_equiv AlternatingMap.domDomLcongr_toAddEquiv
+
+end DomDomLcongr
+
 #print AlternatingMap.domDomCongr_eq_iff /-
 /-- The results of applying `dom_dom_congr` to two maps are equal if and only if those maps are. -/
 @[simp]

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Zhangir Azerbayev. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Zhangir Azerbayev
-
-! This file was ported from Lean 3 source module linear_algebra.alternating
-! leanprover-community/mathlib commit bd65478311e4dfd41f48bf38c7e3b02fb75d0163
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.GroupTheory.GroupAction.Quotient
 import Mathbin.GroupTheory.Perm.Sign
@@ -15,6 +10,8 @@ import Mathbin.LinearAlgebra.LinearIndependent
 import Mathbin.LinearAlgebra.Multilinear.Basis
 import Mathbin.LinearAlgebra.Multilinear.TensorProduct
 
+#align_import linear_algebra.alternating from "leanprover-community/mathlib"@"bd65478311e4dfd41f48bf38c7e3b02fb75d0163"
+
 /-!
 # Alternating Maps
 

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

@@ -116,66 +116,86 @@ instance : CoeFun (AlternatingMap R M N ι) fun _ => (ι → M) → N :=
 
 initialize_simps_projections AlternatingMap (toFun → apply)
 
+#print AlternatingMap.toFun_eq_coe /-
 @[simp]
 theorem toFun_eq_coe : f.toFun = f :=
   rfl
 #align alternating_map.to_fun_eq_coe AlternatingMap.toFun_eq_coe
+-/
 
 @[simp]
 theorem coe_mk (f : (ι → M) → N) (h₁ h₂ h₃) : ⇑(⟨f, h₁, h₂, h₃⟩ : AlternatingMap R M N ι) = f :=
   rfl
 #align alternating_map.coe_mk AlternatingMap.coe_mkₓ
 
+#print AlternatingMap.congr_fun /-
 theorem congr_fun {f g : AlternatingMap R M N ι} (h : f = g) (x : ι → M) : f x = g x :=
   congr_arg (fun h : AlternatingMap R M N ι => h x) h
 #align alternating_map.congr_fun AlternatingMap.congr_fun
+-/
 
+#print AlternatingMap.congr_arg /-
 theorem congr_arg (f : AlternatingMap R M N ι) {x y : ι → M} (h : x = y) : f x = f y :=
   congr_arg (fun x : ι → M => f x) h
 #align alternating_map.congr_arg AlternatingMap.congr_arg
+-/
 
+#print AlternatingMap.coe_injective /-
 theorem coe_injective : Injective (coeFn : AlternatingMap R M N ι → (ι → M) → N) :=
   FunLike.coe_injective
 #align alternating_map.coe_injective AlternatingMap.coe_injective
+-/
 
+#print AlternatingMap.coe_inj /-
 @[simp, norm_cast]
 theorem coe_inj {f g : AlternatingMap R M N ι} : (f : (ι → M) → N) = g ↔ f = g :=
   coe_injective.eq_iff
 #align alternating_map.coe_inj AlternatingMap.coe_inj
+-/
 
+#print AlternatingMap.ext /-
 @[ext]
 theorem ext {f f' : AlternatingMap R M N ι} (H : ∀ x, f x = f' x) : f = f' :=
   FunLike.ext _ _ H
 #align alternating_map.ext AlternatingMap.ext
+-/
 
+#print AlternatingMap.ext_iff /-
 theorem ext_iff {f g : AlternatingMap R M N ι} : f = g ↔ ∀ x, f x = g x :=
   ⟨fun h x => h ▸ rfl, fun h => ext h⟩
 #align alternating_map.ext_iff AlternatingMap.ext_iff
+-/
 
 instance : Coe (AlternatingMap R M N ι) (MultilinearMap R (fun i : ι => M) N) :=
   ⟨fun x => x.toMultilinearMap⟩
 
+#print AlternatingMap.coe_multilinearMap /-
 @[simp, norm_cast]
 theorem coe_multilinearMap : ⇑(f : MultilinearMap R (fun i : ι => M) N) = f :=
   rfl
 #align alternating_map.coe_multilinear_map AlternatingMap.coe_multilinearMap
+-/
 
+#print AlternatingMap.coe_multilinearMap_injective /-
 theorem coe_multilinearMap_injective :
     Function.Injective (coe : AlternatingMap R M N ι → MultilinearMap R (fun i : ι => M) N) :=
   fun x y h => ext <| MultilinearMap.congr_fun h
 #align alternating_map.coe_multilinear_map_injective AlternatingMap.coe_multilinearMap_injective
+-/
 
 @[simp]
 theorem toMultilinearMap_eq_coe : f.toMultilinearMap = f :=
   rfl
 #align alternating_map.to_multilinear_map_eq_coe AlternatingMap.toMultilinearMap_eq_coe
 
+#print AlternatingMap.coe_multilinearMap_mk /-
 @[simp]
 theorem coe_multilinearMap_mk (f : (ι → M) → N) (h₁ h₂ h₃) :
     ((⟨f, h₁, h₂, h₃⟩ : AlternatingMap R M N ι) : MultilinearMap R (fun i : ι => M) N) =
       ⟨f, @h₁, @h₂⟩ :=
   rfl
 #align alternating_map.coe_multilinear_map_mk AlternatingMap.coe_multilinearMap_mk
+-/
 
 end Coercions
 
@@ -186,22 +206,28 @@ These are expressed in terms of `⇑f` instead of `f.to_fun`.
 -/
 
 
+#print AlternatingMap.map_add /-
 @[simp]
 theorem map_add [DecidableEq ι] (i : ι) (x y : M) :
     f (update v i (x + y)) = f (update v i x) + f (update v i y) :=
   f.toMultilinearMap.map_add' v i x y
 #align alternating_map.map_add AlternatingMap.map_add
+-/
 
+#print AlternatingMap.map_sub /-
 @[simp]
 theorem map_sub [DecidableEq ι] (i : ι) (x y : M') :
     g' (update v' i (x - y)) = g' (update v' i x) - g' (update v' i y) :=
   g'.toMultilinearMap.map_sub v' i x y
 #align alternating_map.map_sub AlternatingMap.map_sub
+-/
 
+#print AlternatingMap.map_neg /-
 @[simp]
 theorem map_neg [DecidableEq ι] (i : ι) (x : M') : g' (update v' i (-x)) = -g' (update v' i x) :=
   g'.toMultilinearMap.map_neg v' i x
 #align alternating_map.map_neg AlternatingMap.map_neg
+-/
 
 #print AlternatingMap.map_smul /-
 @[simp]
@@ -211,25 +237,34 @@ theorem map_smul [DecidableEq ι] (i : ι) (r : R) (x : M) :
 #align alternating_map.map_smul AlternatingMap.map_smul
 -/
 
+#print AlternatingMap.map_eq_zero_of_eq /-
 @[simp]
 theorem map_eq_zero_of_eq (v : ι → M) {i j : ι} (h : v i = v j) (hij : i ≠ j) : f v = 0 :=
   f.map_eq_zero_of_eq' v i j h hij
 #align alternating_map.map_eq_zero_of_eq AlternatingMap.map_eq_zero_of_eq
+-/
 
+#print AlternatingMap.map_coord_zero /-
 theorem map_coord_zero {m : ι → M} (i : ι) (h : m i = 0) : f m = 0 :=
   f.toMultilinearMap.map_coord_zero i h
 #align alternating_map.map_coord_zero AlternatingMap.map_coord_zero
+-/
 
+#print AlternatingMap.map_update_zero /-
 @[simp]
 theorem map_update_zero [DecidableEq ι] (m : ι → M) (i : ι) : f (update m i 0) = 0 :=
   f.toMultilinearMap.map_update_zero m i
 #align alternating_map.map_update_zero AlternatingMap.map_update_zero
+-/
 
+#print AlternatingMap.map_zero /-
 @[simp]
 theorem map_zero [Nonempty ι] : f 0 = 0 :=
   f.toMultilinearMap.map_zero
 #align alternating_map.map_zero AlternatingMap.map_zero
+-/
 
+#print AlternatingMap.map_eq_zero_of_not_injective /-
 theorem map_eq_zero_of_not_injective (v : ι → M) (hv : ¬Function.Injective v) : f v = 0 :=
   by
   rw [Function.Injective] at hv 
@@ -237,6 +272,7 @@ theorem map_eq_zero_of_not_injective (v : ι → M) (hv : ¬Function.Injective v
   rcases hv with ⟨i₁, i₂, heq, hne⟩
   exact f.map_eq_zero_of_eq v HEq hne
 #align alternating_map.map_eq_zero_of_not_injective AlternatingMap.map_eq_zero_of_not_injective
+-/
 
 /-!
 ### Algebraic structure inherited from `multilinear_map`
@@ -255,20 +291,26 @@ instance : SMul S (AlternatingMap R M N ι) :=
     { (c • f : MultilinearMap R (fun i : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }⟩
 
+#print AlternatingMap.smul_apply /-
 @[simp]
 theorem smul_apply (c : S) (m : ι → M) : (c • f) m = c • f m :=
   rfl
 #align alternating_map.smul_apply AlternatingMap.smul_apply
+-/
 
+#print AlternatingMap.coe_smul /-
 @[norm_cast]
 theorem coe_smul (c : S) :
     ((c • f : AlternatingMap R M N ι) : MultilinearMap R (fun i : ι => M) N) = c • f :=
   rfl
 #align alternating_map.coe_smul AlternatingMap.coe_smul
+-/
 
+#print AlternatingMap.coeFn_smul /-
 theorem coeFn_smul (c : S) (f : AlternatingMap R M N ι) : ⇑(c • f) = c • f :=
   rfl
 #align alternating_map.coe_fn_smul AlternatingMap.coeFn_smul
+-/
 
 instance [DistribMulAction Sᵐᵒᵖ N] [IsCentralScalar S N] :
     IsCentralScalar S (AlternatingMap R M N ι) :=
@@ -276,6 +318,7 @@ instance [DistribMulAction Sᵐᵒᵖ N] [IsCentralScalar S N] :
 
 end SMul
 
+#print AlternatingMap.prod /-
 /-- The cartesian product of two alternating maps, as a multilinear map. -/
 @[simps (config := { simpRhs := true })]
 def prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) : AlternatingMap R M (N × P) ι :=
@@ -283,12 +326,15 @@ def prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) : Alternati
     map_eq_zero_of_eq' := fun v i j h hne =>
       Prod.ext (f.map_eq_zero_of_eq _ h hne) (g.map_eq_zero_of_eq _ h hne) }
 #align alternating_map.prod AlternatingMap.prod
+-/
 
+#print AlternatingMap.coe_prod /-
 @[simp]
 theorem coe_prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) :
     (f.Prod g : MultilinearMap R (fun _ : ι => M) (N × P)) = MultilinearMap.prod f g :=
   rfl
 #align alternating_map.coe_prod AlternatingMap.coe_prod
+-/
 
 #print AlternatingMap.pi /-
 /-- Combine a family of alternating maps with the same domain and codomains `N i` into an
@@ -301,12 +347,14 @@ def pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)] [∀ i,
 #align alternating_map.pi AlternatingMap.pi
 -/
 
+#print AlternatingMap.coe_pi /-
 @[simp]
 theorem coe_pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
     (f : ∀ i, AlternatingMap R M (N i) ι) :
     (pi f : MultilinearMap R (fun _ : ι => M) (∀ i, N i)) = MultilinearMap.pi fun a => f a :=
   rfl
 #align alternating_map.coe_pi AlternatingMap.coe_pi
+-/
 
 #print AlternatingMap.smulRight /-
 /-- Given an alternating `R`-multilinear map `f` taking values in `R`, `f.smul_right z` is the map
@@ -319,12 +367,14 @@ def smulRight {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁] [A
 #align alternating_map.smul_right AlternatingMap.smulRight
 -/
 
+#print AlternatingMap.coe_smulRight /-
 @[simp]
 theorem coe_smulRight {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
     [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) :
     (f.smul_right z : MultilinearMap R (fun _ : ι => M₁) M₂) = MultilinearMap.smulRight f z :=
   rfl
 #align alternating_map.coe_smul_right AlternatingMap.coe_smulRight
+-/
 
 instance : Add (AlternatingMap R M N ι) :=
   ⟨fun a b =>
@@ -332,29 +382,37 @@ instance : Add (AlternatingMap R M N ι) :=
       map_eq_zero_of_eq' := fun v i j h hij => by
         simp [a.map_eq_zero_of_eq v h hij, b.map_eq_zero_of_eq v h hij] }⟩
 
+#print AlternatingMap.add_apply /-
 @[simp]
 theorem add_apply : (f + f') v = f v + f' v :=
   rfl
 #align alternating_map.add_apply AlternatingMap.add_apply
+-/
 
+#print AlternatingMap.coe_add /-
 @[norm_cast]
 theorem coe_add : (↑(f + f') : MultilinearMap R (fun i : ι => M) N) = f + f' :=
   rfl
 #align alternating_map.coe_add AlternatingMap.coe_add
+-/
 
 instance : Zero (AlternatingMap R M N ι) :=
   ⟨{ (0 : MultilinearMap R (fun i : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by simp }⟩
 
+#print AlternatingMap.zero_apply /-
 @[simp]
 theorem zero_apply : (0 : AlternatingMap R M N ι) v = 0 :=
   rfl
 #align alternating_map.zero_apply AlternatingMap.zero_apply
+-/
 
+#print AlternatingMap.coe_zero /-
 @[norm_cast]
 theorem coe_zero : ((0 : AlternatingMap R M N ι) : MultilinearMap R (fun i : ι => M) N) = 0 :=
   rfl
 #align alternating_map.coe_zero AlternatingMap.coe_zero
+-/
 
 instance : Inhabited (AlternatingMap R M N ι) :=
   ⟨0⟩
@@ -367,15 +425,19 @@ instance : Neg (AlternatingMap R M N' ι) :=
     { -(f : MultilinearMap R (fun i : ι => M) N') with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }⟩
 
+#print AlternatingMap.neg_apply /-
 @[simp]
 theorem neg_apply (m : ι → M) : (-g) m = -g m :=
   rfl
 #align alternating_map.neg_apply AlternatingMap.neg_apply
+-/
 
+#print AlternatingMap.coe_neg /-
 @[norm_cast]
 theorem coe_neg : ((-g : AlternatingMap R M N' ι) : MultilinearMap R (fun i : ι => M) N') = -g :=
   rfl
 #align alternating_map.coe_neg AlternatingMap.coe_neg
+-/
 
 instance : Sub (AlternatingMap R M N' ι) :=
   ⟨fun f g =>
@@ -383,15 +445,19 @@ instance : Sub (AlternatingMap R M N' ι) :=
       map_eq_zero_of_eq' := fun v i j h hij => by
         simp [f.map_eq_zero_of_eq v h hij, g.map_eq_zero_of_eq v h hij] }⟩
 
+#print AlternatingMap.sub_apply /-
 @[simp]
 theorem sub_apply (m : ι → M) : (g - g₂) m = g m - g₂ m :=
   rfl
 #align alternating_map.sub_apply AlternatingMap.sub_apply
+-/
 
+#print AlternatingMap.coe_sub /-
 @[norm_cast]
 theorem coe_sub : (↑(g - g₂) : MultilinearMap R (fun i : ι => M) N') = g - g₂ :=
   rfl
 #align alternating_map.coe_sub AlternatingMap.coe_sub
+-/
 
 instance : AddCommGroup (AlternatingMap R M N' ι) :=
   coe_injective.AddCommGroup _ rfl (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl)
@@ -495,30 +561,39 @@ def compAlternatingMap (g : N →ₗ[R] N₂) : AlternatingMap R M N ι →+ Alt
 #align linear_map.comp_alternating_map LinearMap.compAlternatingMap
 -/
 
+#print LinearMap.coe_compAlternatingMap /-
 @[simp]
 theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) :
     ⇑(g.compAlternatingMap f) = g ∘ f :=
   rfl
 #align linear_map.coe_comp_alternating_map LinearMap.coe_compAlternatingMap
+-/
 
+#print LinearMap.compAlternatingMap_apply /-
 @[simp]
 theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) (m : ι → M) :
     g.compAlternatingMap f m = g (f m) :=
   rfl
 #align linear_map.comp_alternating_map_apply LinearMap.compAlternatingMap_apply
+-/
 
+#print LinearMap.smulRight_eq_comp /-
 theorem smulRight_eq_comp {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁]
     [AddCommMonoid M₂] [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) :
     f.smul_right z = (LinearMap.id.smul_right z).compAlternatingMap f :=
   rfl
 #align linear_map.smul_right_eq_comp LinearMap.smulRight_eq_comp
+-/
 
+#print LinearMap.subtype_compAlternatingMap_codRestrict /-
 @[simp]
 theorem subtype_compAlternatingMap_codRestrict (f : AlternatingMap R M N ι) (p : Submodule R N)
     (h) : p.Subtype.compAlternatingMap (f.codRestrict p h) = f :=
   AlternatingMap.ext fun v => rfl
 #align linear_map.subtype_comp_alternating_map_cod_restrict LinearMap.subtype_compAlternatingMap_codRestrict
+-/
 
+#print LinearMap.compAlternatingMap_codRestrict /-
 @[simp]
 theorem compAlternatingMap_codRestrict (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι)
     (p : Submodule R N₂) (h) :
@@ -526,6 +601,7 @@ theorem compAlternatingMap_codRestrict (g : N →ₗ[R] N₂) (f : AlternatingMa
       (g.compAlternatingMap f).codRestrict p fun v => h (f v) :=
   AlternatingMap.ext fun v => rfl
 #align linear_map.comp_alternating_map_cod_restrict LinearMap.compAlternatingMap_codRestrict
+-/
 
 end LinearMap
 
@@ -544,58 +620,76 @@ def compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) : Alterna
 #align alternating_map.comp_linear_map AlternatingMap.compLinearMap
 -/
 
+#print AlternatingMap.coe_compLinearMap /-
 theorem coe_compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
     ⇑(f.compLinearMap g) = f ∘ (· ∘ ·) g :=
   rfl
 #align alternating_map.coe_comp_linear_map AlternatingMap.coe_compLinearMap
+-/
 
+#print AlternatingMap.compLinearMap_apply /-
 @[simp]
 theorem compLinearMap_apply (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) (v : ι → M₂) :
     f.compLinearMap g v = f fun i => g (v i) :=
   rfl
 #align alternating_map.comp_linear_map_apply AlternatingMap.compLinearMap_apply
+-/
 
+#print AlternatingMap.compLinearMap_assoc /-
 /-- Composing an alternating map twice with the same linear map in each argument is
 the same as composing with their composition. -/
 theorem compLinearMap_assoc (f : AlternatingMap R M N ι) (g₁ : M₂ →ₗ[R] M) (g₂ : M₃ →ₗ[R] M₂) :
     (f.compLinearMap g₁).compLinearMap g₂ = f.compLinearMap (g₁ ∘ₗ g₂) :=
   rfl
 #align alternating_map.comp_linear_map_assoc AlternatingMap.compLinearMap_assoc
+-/
 
+#print AlternatingMap.zero_compLinearMap /-
 @[simp]
 theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : AlternatingMap R M N ι).compLinearMap g = 0 := by
   ext; simp only [comp_linear_map_apply, zero_apply]
 #align alternating_map.zero_comp_linear_map AlternatingMap.zero_compLinearMap
+-/
 
+#print AlternatingMap.add_compLinearMap /-
 @[simp]
 theorem add_compLinearMap (f₁ f₂ : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
     (f₁ + f₂).compLinearMap g = f₁.compLinearMap g + f₂.compLinearMap g := by ext;
   simp only [comp_linear_map_apply, add_apply]
 #align alternating_map.add_comp_linear_map AlternatingMap.add_compLinearMap
+-/
 
+#print AlternatingMap.compLinearMap_zero /-
 @[simp]
 theorem compLinearMap_zero [Nonempty ι] (f : AlternatingMap R M N ι) :
     f.compLinearMap (0 : M₂ →ₗ[R] M) = 0 := by
   ext
   simp_rw [comp_linear_map_apply, LinearMap.zero_apply, ← Pi.zero_def, map_zero, zero_apply]
 #align alternating_map.comp_linear_map_zero AlternatingMap.compLinearMap_zero
+-/
 
+#print AlternatingMap.compLinearMap_id /-
 /-- Composing an alternating map with the identity linear map in each argument. -/
 @[simp]
 theorem compLinearMap_id (f : AlternatingMap R M N ι) : f.compLinearMap LinearMap.id = f :=
   ext fun _ => rfl
 #align alternating_map.comp_linear_map_id AlternatingMap.compLinearMap_id
+-/
 
+#print AlternatingMap.compLinearMap_injective /-
 /-- Composing with a surjective linear map is injective. -/
 theorem compLinearMap_injective (f : M₂ →ₗ[R] M) (hf : Function.Surjective f) :
     Function.Injective fun g : AlternatingMap R M N ι => g.compLinearMap f := fun g₁ g₂ h =>
   ext fun x => by simpa [Function.surjInv_eq hf] using ext_iff.mp h (Function.surjInv hf ∘ x)
 #align alternating_map.comp_linear_map_injective AlternatingMap.compLinearMap_injective
+-/
 
+#print AlternatingMap.compLinearMap_inj /-
 theorem compLinearMap_inj (f : M₂ →ₗ[R] M) (hf : Function.Surjective f)
     (g₁ g₂ : AlternatingMap R M N ι) : g₁.compLinearMap f = g₂.compLinearMap f ↔ g₁ = g₂ :=
   (compLinearMap_injective _ hf).eq_iff
 #align alternating_map.comp_linear_map_inj AlternatingMap.compLinearMap_inj
+-/
 
 section DomLcongr
 
@@ -615,23 +709,30 @@ def domLCongr (e : M ≃ₗ[R] M₂) : AlternatingMap R M N ι ≃ₗ[S] Alterna
 #align alternating_map.dom_lcongr AlternatingMap.domLCongr
 -/
 
+#print AlternatingMap.domLCongr_refl /-
 @[simp]
 theorem domLCongr_refl : domLCongr R N ι S (LinearEquiv.refl R M) = LinearEquiv.refl S _ :=
   LinearEquiv.ext fun _ => AlternatingMap.ext fun v => rfl
 #align alternating_map.dom_lcongr_refl AlternatingMap.domLCongr_refl
+-/
 
+#print AlternatingMap.domLCongr_symm /-
 @[simp]
 theorem domLCongr_symm (e : M ≃ₗ[R] M₂) : (domLCongr R N ι S e).symm = domLCongr R N ι S e.symm :=
   rfl
 #align alternating_map.dom_lcongr_symm AlternatingMap.domLCongr_symm
+-/
 
+#print AlternatingMap.domLCongr_trans /-
 theorem domLCongr_trans (e : M ≃ₗ[R] M₂) (f : M₂ ≃ₗ[R] M₃) :
     (domLCongr R N ι S e).trans (domLCongr R N ι S f) = domLCongr R N ι S (e.trans f) :=
   rfl
 #align alternating_map.dom_lcongr_trans AlternatingMap.domLCongr_trans
+-/
 
 end DomLcongr
 
+#print AlternatingMap.compLinearEquiv_eq_zero_iff /-
 /-- Composing an alternating map with the same linear equiv on each argument gives the zero map
 if and only if the alternating map is the zero map. -/
 @[simp]
@@ -639,6 +740,7 @@ theorem compLinearEquiv_eq_zero_iff (f : AlternatingMap R M N ι) (g : M₂ ≃
     f.compLinearMap (g : M₂ →ₗ[R] M) = 0 ↔ f = 0 :=
   (domLCongr R N ι ℕ g.symm).map_eq_zero_iff
 #align alternating_map.comp_linear_equiv_eq_zero_iff AlternatingMap.compLinearEquiv_eq_zero_iff
+-/
 
 variable (f f' : AlternatingMap R M N ι)
 
@@ -676,17 +778,22 @@ Various properties of reordered and repeated inputs which follow from
 -/
 
 
+#print AlternatingMap.map_update_self /-
 theorem map_update_self [DecidableEq ι] {i j : ι} (hij : i ≠ j) :
     f (Function.update v i (v j)) = 0 :=
   f.map_eq_zero_of_eq _ (by rw [Function.update_same, Function.update_noteq hij.symm]) hij
 #align alternating_map.map_update_self AlternatingMap.map_update_self
+-/
 
+#print AlternatingMap.map_update_update /-
 theorem map_update_update [DecidableEq ι] {i j : ι} (hij : i ≠ j) (m : M) :
     f (Function.update (Function.update v i m) j m) = 0 :=
   f.map_eq_zero_of_eq _
     (by rw [Function.update_same, Function.update_noteq hij, Function.update_same]) hij
 #align alternating_map.map_update_update AlternatingMap.map_update_update
+-/
 
+#print AlternatingMap.map_swap_add /-
 theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equiv.swap i j) + f v = 0 :=
   by
   rw [Equiv.comp_swap_eq_update]
@@ -694,10 +801,13 @@ theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equi
   simp [f.map_update_self _ hij, f.map_update_self _ hij.symm,
     Function.update_comm hij (v i + v j) (v _) v, Function.update_comm hij.symm (v i) (v i) v]
 #align alternating_map.map_swap_add AlternatingMap.map_swap_add
+-/
 
+#print AlternatingMap.map_add_swap /-
 theorem map_add_swap [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f v + f (v ∘ Equiv.swap i j) = 0 :=
   by rw [add_comm]; exact f.map_swap_add v hij
 #align alternating_map.map_add_swap AlternatingMap.map_add_swap
+-/
 
 #print AlternatingMap.map_swap /-
 theorem map_swap [DecidableEq ι] {i j : ι} (hij : i ≠ j) : g (v ∘ Equiv.swap i j) = -g v :=
@@ -716,9 +826,11 @@ theorem map_perm [DecidableEq ι] [Fintype ι] (v : ι → M) (σ : Equiv.Perm 
 #align alternating_map.map_perm AlternatingMap.map_perm
 -/
 
+#print AlternatingMap.map_congr_perm /-
 theorem map_congr_perm [DecidableEq ι] [Fintype ι] (σ : Equiv.Perm ι) : g v = σ.sign • g (v ∘ σ) :=
   by rw [g.map_perm, smul_smul]; simp
 #align alternating_map.map_congr_perm AlternatingMap.map_congr_perm
+-/
 
 section DomDomCongr
 
@@ -737,26 +849,34 @@ def domDomCongr (σ : ι ≃ ι') (f : AlternatingMap R M N ι) : AlternatingMap
 #align alternating_map.dom_dom_congr AlternatingMap.domDomCongr
 -/
 
+#print AlternatingMap.domDomCongr_refl /-
 @[simp]
 theorem domDomCongr_refl (f : AlternatingMap R M N ι) : f.domDomCongr (Equiv.refl ι) = f :=
   ext fun v => rfl
 #align alternating_map.dom_dom_congr_refl AlternatingMap.domDomCongr_refl
+-/
 
+#print AlternatingMap.domDomCongr_trans /-
 theorem domDomCongr_trans (σ₁ : ι ≃ ι') (σ₂ : ι' ≃ ι'') (f : AlternatingMap R M N ι) :
     f.domDomCongr (σ₁.trans σ₂) = (f.domDomCongr σ₁).domDomCongr σ₂ :=
   rfl
 #align alternating_map.dom_dom_congr_trans AlternatingMap.domDomCongr_trans
+-/
 
+#print AlternatingMap.domDomCongr_zero /-
 @[simp]
 theorem domDomCongr_zero (σ : ι ≃ ι') : (0 : AlternatingMap R M N ι).domDomCongr σ = 0 :=
   rfl
 #align alternating_map.dom_dom_congr_zero AlternatingMap.domDomCongr_zero
+-/
 
+#print AlternatingMap.domDomCongr_add /-
 @[simp]
 theorem domDomCongr_add (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
     (f + g).domDomCongr σ = f.domDomCongr σ + g.domDomCongr σ :=
   rfl
 #align alternating_map.dom_dom_congr_add AlternatingMap.domDomCongr_add
+-/
 
 #print AlternatingMap.domDomCongrEquiv /-
 /-- `alternating_map.dom_dom_congr` as an equivalence.
@@ -773,32 +893,41 @@ def domDomCongrEquiv (σ : ι ≃ ι') : AlternatingMap R M N ι ≃+ Alternatin
 #align alternating_map.dom_dom_congr_equiv AlternatingMap.domDomCongrEquiv
 -/
 
+#print AlternatingMap.domDomCongr_eq_iff /-
 /-- The results of applying `dom_dom_congr` to two maps are equal if and only if those maps are. -/
 @[simp]
 theorem domDomCongr_eq_iff (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
     f.domDomCongr σ = g.domDomCongr σ ↔ f = g :=
   (domDomCongrEquiv σ : _ ≃+ AlternatingMap R M N ι').apply_eq_iff_eq
 #align alternating_map.dom_dom_congr_eq_iff AlternatingMap.domDomCongr_eq_iff
+-/
 
+#print AlternatingMap.domDomCongr_eq_zero_iff /-
 @[simp]
 theorem domDomCongr_eq_zero_iff (σ : ι ≃ ι') (f : AlternatingMap R M N ι) :
     f.domDomCongr σ = 0 ↔ f = 0 :=
   (domDomCongrEquiv σ : AlternatingMap R M N ι ≃+ AlternatingMap R M N ι').map_eq_zero_iff
 #align alternating_map.dom_dom_congr_eq_zero_iff AlternatingMap.domDomCongr_eq_zero_iff
+-/
 
+#print AlternatingMap.domDomCongr_perm /-
 theorem domDomCongr_perm [Fintype ι] [DecidableEq ι] (σ : Equiv.Perm ι) :
     g.domDomCongr σ = σ.sign • g :=
   AlternatingMap.ext fun v => g.map_perm v σ
 #align alternating_map.dom_dom_congr_perm AlternatingMap.domDomCongr_perm
+-/
 
+#print AlternatingMap.coe_domDomCongr /-
 @[norm_cast]
 theorem coe_domDomCongr (σ : ι ≃ ι') :
     ↑(f.domDomCongr σ) = (f : MultilinearMap R (fun _ : ι => M) N).domDomCongr σ :=
   MultilinearMap.ext fun v => rfl
 #align alternating_map.coe_dom_dom_congr AlternatingMap.coe_domDomCongr
+-/
 
 end DomDomCongr
 
+#print AlternatingMap.map_linearDependent /-
 /-- If the arguments are linearly dependent then the result is `0`. -/
 theorem map_linearDependent {K : Type _} [Ring K] {M : Type _} [AddCommGroup M] [Module K M]
     {N : Type _} [AddCommGroup N] [Module K N] [NoZeroSMulDivisors K N] (f : AlternatingMap K M N ι)
@@ -818,22 +947,27 @@ theorem map_linearDependent {K : Type _} [Ring K] {M : Type _} [AddCommGroup M]
   obtain ⟨hij, _⟩ := finset.mem_erase.mp hj
   rw [f.map_smul, f.map_update_self _ hij.symm, smul_zero]
 #align alternating_map.map_linear_dependent AlternatingMap.map_linearDependent
+-/
 
 section Fin
 
 open Fin
 
+#print AlternatingMap.map_vecCons_add /-
 /-- A version of `multilinear_map.cons_add` for `alternating_map`. -/
 theorem map_vecCons_add {n : ℕ} (f : AlternatingMap R M N (Fin n.succ)) (m : Fin n → M) (x y : M) :
     f (Matrix.vecCons (x + y) m) = f (Matrix.vecCons x m) + f (Matrix.vecCons y m) :=
   f.toMultilinearMap.cons_add _ _ _
 #align alternating_map.map_vec_cons_add AlternatingMap.map_vecCons_add
+-/
 
+#print AlternatingMap.map_vecCons_smul /-
 /-- A version of `multilinear_map.cons_smul` for `alternating_map`. -/
 theorem map_vecCons_smul {n : ℕ} (f : AlternatingMap R M N (Fin n.succ)) (m : Fin n → M) (c : R)
     (x : M) : f (Matrix.vecCons (c • x) m) = c • f (Matrix.vecCons x m) :=
   f.toMultilinearMap.cons_smul _ _ _
 #align alternating_map.map_vec_cons_smul AlternatingMap.map_vecCons_smul
+-/
 
 end Fin
 
@@ -858,6 +992,7 @@ private theorem alternization_map_eq_zero_of_eq_aux (m : MultilinearMap R (fun i
       (fun σ _ _ => (not_congr swap_mul_eq_iff).mpr i_ne_j) (fun σ _ => Finset.mem_univ _)
       fun σ _ => swap_mul_involutive i j σ
 
+#print MultilinearMap.alternatization /-
 /-- Produce an `alternating_map` out of a `multilinear_map`, by summing over all argument
 permutations. -/
 def alternatization : MultilinearMap R (fun i : ι => M) N' →+ AlternatingMap R M N' ι
@@ -880,26 +1015,34 @@ def alternatization : MultilinearMap R (fun i : ι => M) N' →+ AlternatingMap
     simp only [Finset.sum_const_zero, smul_zero, zero_apply, dom_dom_congr_apply,
       AlternatingMap.zero_apply, AlternatingMap.coe_mk, smul_apply, sum_apply]
 #align multilinear_map.alternatization MultilinearMap.alternatization
+-/
 
+#print MultilinearMap.alternatization_def /-
 theorem alternatization_def (m : MultilinearMap R (fun i : ι => M) N') :
     ⇑(alternatization m) = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
   rfl
 #align multilinear_map.alternatization_def MultilinearMap.alternatization_def
+-/
 
+#print MultilinearMap.alternatization_coe /-
 theorem alternatization_coe (m : MultilinearMap R (fun i : ι => M) N') :
     ↑m.alternatization = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
   coe_injective rfl
 #align multilinear_map.alternatization_coe MultilinearMap.alternatization_coe
+-/
 
+#print MultilinearMap.alternatization_apply /-
 theorem alternatization_apply (m : MultilinearMap R (fun i : ι => M) N') (v : ι → M) :
     alternatization m v = ∑ σ : Perm ι, σ.sign • m.domDomCongr σ v := by
   simp only [alternatization_def, smul_apply, sum_apply]
 #align multilinear_map.alternatization_apply MultilinearMap.alternatization_apply
+-/
 
 end MultilinearMap
 
 namespace AlternatingMap
 
+#print AlternatingMap.coe_alternatization /-
 /-- Alternatizing a multilinear map that is already alternating results in a scale factor of `n!`,
 where `n` is the number of inputs. -/
 theorem coe_alternatization [DecidableEq ι] [Fintype ι] (a : AlternatingMap R M N' ι) :
@@ -910,6 +1053,7 @@ theorem coe_alternatization [DecidableEq ι] [Fintype ι] (a : AlternatingMap R
     smul_smul, Int.units_mul_self, one_smul, Finset.sum_const, Finset.card_univ, Fintype.card_perm,
     ← coe_multilinear_map, coe_smul]
 #align alternating_map.coe_alternatization AlternatingMap.coe_alternatization
+-/
 
 end AlternatingMap
 
@@ -917,12 +1061,14 @@ namespace LinearMap
 
 variable {N'₂ : Type _} [AddCommGroup N'₂] [Module R N'₂] [DecidableEq ι] [Fintype ι]
 
+#print LinearMap.compMultilinearMap_alternatization /-
 /-- Composition with a linear map before and after alternatization are equivalent. -/
 theorem compMultilinearMap_alternatization (g : N' →ₗ[R] N'₂)
     (f : MultilinearMap R (fun _ : ι => M) N') :
     (g.compMultilinearMap f).alternatization = g.compAlternatingMap f.alternatization := by ext;
   simp [MultilinearMap.alternatization_def]
 #align linear_map.comp_multilinear_map_alternatization LinearMap.compMultilinearMap_alternatization
+-/
 
 end LinearMap
 
@@ -946,12 +1092,14 @@ abbrev ModSumCongr (α β : Type _) :=
 #align equiv.perm.mod_sum_congr Equiv.Perm.ModSumCongr
 -/
 
+#print Equiv.Perm.ModSumCongr.swap_smul_involutive /-
 theorem ModSumCongr.swap_smul_involutive {α β : Type _} [DecidableEq (Sum α β)] (i j : Sum α β) :
     Function.Involutive (SMul.smul (Equiv.swap i j) : ModSumCongr α β → ModSumCongr α β) := fun σ =>
   by
   apply σ.induction_on' fun σ => _
   exact _root_.congr_arg Quotient.mk'' (Equiv.swap_mul_involutive i j σ)
 #align equiv.perm.mod_sum_congr.swap_smul_involutive Equiv.Perm.ModSumCongr.swap_smul_involutive
+-/
 
 end Equiv.Perm
 
@@ -961,6 +1109,7 @@ open Equiv
 
 variable [DecidableEq ιa] [DecidableEq ιb]
 
+#print AlternatingMap.domCoprod.summand /-
 /-- summand used in `alternating_map.dom_coprod` -/
 def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
     (σ : Perm.ModSumCongr ιa ιb) : MultilinearMap R' (fun _ : Sum ιa ιb => Mᵢ) (N₁ ⊗[R'] N₂) :=
@@ -982,7 +1131,9 @@ def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap
       Function.comp_apply, perm.coe_mul]
     rw [← a.map_congr_perm fun i => v (σ₁ _), ← b.map_congr_perm fun i => v (σ₁ _)]
 #align alternating_map.dom_coprod.summand AlternatingMap.domCoprod.summand
+-/
 
+#print AlternatingMap.domCoprod.summand_mk'' /-
 theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
     (σ : Equiv.Perm (Sum ιa ιb)) :
     domCoprod.summand a b (Quotient.mk'' σ) =
@@ -991,7 +1142,9 @@ theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : Altern
           σ :=
   rfl
 #align alternating_map.dom_coprod.summand_mk' AlternatingMap.domCoprod.summand_mk''
+-/
 
+#print AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero /-
 /-- Swapping elements in `σ` with equal values in `v` results in an addition that cancels -/
 theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁ ιa)
     (b : AlternatingMap R' Mᵢ N₂ ιb) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
@@ -1007,7 +1160,9 @@ theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁
     MultilinearMap.domCoprod_apply]
   convert add_right_neg _ <;> · ext k; rw [Equiv.apply_swap_eq_self hv]
 #align alternating_map.dom_coprod.summand_add_swap_smul_eq_zero AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero
+-/
 
+#print AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant /-
 /-- Swapping elements in `σ` with equal values in `v` result in zero if the swap has no effect
 on the quotient. -/
 theorem domCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ N₁ ιa)
@@ -1042,7 +1197,9 @@ theorem domCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ
     on_goal 2 => convert TensorProduct.zero_tmul _ _
     all_goals exact AlternatingMap.map_eq_zero_of_eq _ _ hv fun hij' => hij (hij' ▸ rfl)
 #align alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant
+-/
 
+#print AlternatingMap.domCoprod /-
 /-- Like `multilinear_map.dom_coprod`, but ensures the result is also alternating.
 
 Note that this is usually defined (for instance, as used in Proposition 22.24 in [Gallier2011Notes])
@@ -1081,12 +1238,15 @@ def domCoprod (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ
           (fun σ _ => Finset.mem_univ _) fun σ _ =>
           Equiv.Perm.ModSumCongr.swap_smul_involutive i j σ }
 #align alternating_map.dom_coprod AlternatingMap.domCoprod
+-/
 
+#print AlternatingMap.domCoprod_coe /-
 theorem domCoprod_coe (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
     (↑(a.domCoprod b) : MultilinearMap R' (fun _ => Mᵢ) _) =
       ∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ :=
   MultilinearMap.ext fun _ => rfl
 #align alternating_map.dom_coprod_coe AlternatingMap.domCoprod_coe
+-/
 
 #print AlternatingMap.domCoprod' /-
 /-- A more bundled version of `alternating_map.dom_coprod` that maps
@@ -1115,16 +1275,19 @@ def domCoprod' :
 #align alternating_map.dom_coprod' AlternatingMap.domCoprod'
 -/
 
+#print AlternatingMap.domCoprod'_apply /-
 @[simp]
 theorem domCoprod'_apply (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
     domCoprod' (a ⊗ₜ[R'] b) = domCoprod a b :=
   rfl
 #align alternating_map.dom_coprod'_apply AlternatingMap.domCoprod'_apply
+-/
 
 end AlternatingMap
 
 open Equiv
 
+#print MultilinearMap.domCoprod_alternization_coe /-
 /-- A helper lemma for `multilinear_map.dom_coprod_alternization`. -/
 theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableEq ιb]
     (a : MultilinearMap R' (fun _ : ιa => Mᵢ) N₁) (b : MultilinearMap R' (fun _ : ιb => Mᵢ) N₂) :
@@ -1136,9 +1299,11 @@ theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableE
   simp_rw [TensorProduct.sum_tmul, TensorProduct.tmul_sum, LinearMap.map_sum, ←
     TensorProduct.smul_tmul', TensorProduct.tmul_smul, LinearMap.map_smul_of_tower]
 #align multilinear_map.dom_coprod_alternization_coe MultilinearMap.domCoprod_alternization_coe
+-/
 
 open AlternatingMap
 
+#print MultilinearMap.domCoprod_alternization /-
 /-- Computing the `multilinear_map.alternatization` of the `multilinear_map.dom_coprod` is the same
 as computing the `alternating_map.dom_coprod` of the `multilinear_map.alternatization`s.
 -/
@@ -1177,7 +1342,9 @@ theorem MultilinearMap.domCoprod_alternization [DecidableEq ιa] [DecidableEq ι
   rw [MultilinearMap.domDomCongr_mul, perm.sign_mul, perm.sum_congr_hom_apply,
     MultilinearMap.domCoprod_domDomCongr_sumCongr, perm.sign_sum_congr, mul_smul, mul_smul]
 #align multilinear_map.dom_coprod_alternization MultilinearMap.domCoprod_alternization
+-/
 
+#print MultilinearMap.domCoprod_alternization_eq /-
 /-- Taking the `multilinear_map.alternatization` of the `multilinear_map.dom_coprod` of two
 `alternating_map`s gives a scaled version of the `alternating_map.coprod` of those maps.
 -/
@@ -1194,6 +1361,7 @@ theorem MultilinearMap.domCoprod_alternization_eq [DecidableEq ιa] [DecidableEq
   infer_instance;
   infer_instance
 #align multilinear_map.dom_coprod_alternization_eq MultilinearMap.domCoprod_alternization_eq
+-/
 
 end Coprod
 
@@ -1207,6 +1375,7 @@ variable {R' : Type _} {N₁ N₂ : Type _} [CommSemiring R'] [AddCommMonoid N
 
 variable [Module R' N₁] [Module R' N₂]
 
+#print Basis.ext_alternating /-
 /-- Two alternating maps indexed by a `fintype` are equal if they are equal when all arguments
 are distinct basis vectors. -/
 theorem Basis.ext_alternating {f g : AlternatingMap R' N₁ N₂ ι} (e : Basis ι₁ R' N₁)
@@ -1220,6 +1389,7 @@ theorem Basis.ext_alternating {f g : AlternatingMap R' N₁ N₂ ι} (e : Basis
     rw [coe_multilinear_map, coe_multilinear_map, f.map_eq_zero_of_not_injective _ this,
       g.map_eq_zero_of_not_injective _ this]
 #align basis.ext_alternating Basis.ext_alternating
+-/
 
 end Basis
 
@@ -1258,22 +1428,28 @@ def curryLeft {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ)) :
 #align alternating_map.curry_left AlternatingMap.curryLeft
 -/
 
+#print AlternatingMap.curryLeft_zero /-
 @[simp]
 theorem curryLeft_zero {n : ℕ} : curryLeft (0 : AlternatingMap R' M'' N'' (Fin n.succ)) = 0 :=
   rfl
 #align alternating_map.curry_left_zero AlternatingMap.curryLeft_zero
+-/
 
+#print AlternatingMap.curryLeft_add /-
 @[simp]
 theorem curryLeft_add {n : ℕ} (f g : AlternatingMap R' M'' N'' (Fin n.succ)) :
     curryLeft (f + g) = curryLeft f + curryLeft g :=
   rfl
 #align alternating_map.curry_left_add AlternatingMap.curryLeft_add
+-/
 
+#print AlternatingMap.curryLeft_smul /-
 @[simp]
 theorem curryLeft_smul {n : ℕ} (r : R') (f : AlternatingMap R' M'' N'' (Fin n.succ)) :
     curryLeft (r • f) = r • curryLeft f :=
   rfl
 #align alternating_map.curry_left_smul AlternatingMap.curryLeft_smul
+-/
 
 #print AlternatingMap.curryLeftLinearMap /-
 /-- `alternating_map.curry_left` as a `linear_map`. This is a separate definition as dot notation
@@ -1288,20 +1464,25 @@ def curryLeftLinearMap {n : ℕ} :
 #align alternating_map.curry_left_linear_map AlternatingMap.curryLeftLinearMap
 -/
 
+#print AlternatingMap.curryLeft_same /-
 /-- Currying with the same element twice gives the zero map. -/
 @[simp]
 theorem curryLeft_same {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ.succ)) (m : M'') :
     (f.curryLeft m).curryLeft m = 0 :=
   ext fun x => f.map_eq_zero_of_eq _ (by simp) Fin.zero_ne_one
 #align alternating_map.curry_left_same AlternatingMap.curryLeft_same
+-/
 
+#print AlternatingMap.curryLeft_compAlternatingMap /-
 @[simp]
 theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
     (f : AlternatingMap R' M'' N'' (Fin n.succ)) (m : M'') :
     (g.compAlternatingMap f).curryLeft m = g.compAlternatingMap (f.curryLeft m) :=
   rfl
 #align alternating_map.curry_left_comp_alternating_map AlternatingMap.curryLeft_compAlternatingMap
+-/
 
+#print AlternatingMap.curryLeft_compLinearMap /-
 @[simp]
 theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')
     (f : AlternatingMap R' M'' N'' (Fin n.succ)) (m : M₂'') :
@@ -1313,6 +1494,7 @@ theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')
         · rfl
         · simp
 #align alternating_map.curry_left_comp_linear_map AlternatingMap.curryLeft_compLinearMap
+-/
 
 #print AlternatingMap.constLinearEquivOfIsEmpty /-
 /-- The space of constant maps is equivalent to the space of maps that are alternating with respect

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

@@ -233,7 +233,7 @@ theorem map_zero [Nonempty ι] : f 0 = 0 :=
 theorem map_eq_zero_of_not_injective (v : ι → M) (hv : ¬Function.Injective v) : f v = 0 :=
   by
   rw [Function.Injective] at hv 
-  push_neg  at hv 
+  push_neg at hv 
   rcases hv with ⟨i₁, i₂, heq, hne⟩
   exact f.map_eq_zero_of_eq v HEq hne
 #align alternating_map.map_eq_zero_of_not_injective AlternatingMap.map_eq_zero_of_not_injective
@@ -1213,12 +1213,12 @@ theorem Basis.ext_alternating {f g : AlternatingMap R' N₁ N₂ ι} (e : Basis
     (h : ∀ v : ι → ι₁, Function.Injective v → (f fun i => e (v i)) = g fun i => e (v i)) : f = g :=
   by
   classical
-    refine' AlternatingMap.coe_multilinearMap_injective (Basis.ext_multilinear e fun v => _)
-    by_cases hi : Function.Injective v
-    · exact h v hi
-    · have : ¬Function.Injective fun i => e (v i) := hi.imp Function.Injective.of_comp
-      rw [coe_multilinear_map, coe_multilinear_map, f.map_eq_zero_of_not_injective _ this,
-        g.map_eq_zero_of_not_injective _ this]
+  refine' AlternatingMap.coe_multilinearMap_injective (Basis.ext_multilinear e fun v => _)
+  by_cases hi : Function.Injective v
+  · exact h v hi
+  · have : ¬Function.Injective fun i => e (v i) := hi.imp Function.Injective.of_comp
+    rw [coe_multilinear_map, coe_multilinear_map, f.map_eq_zero_of_not_injective _ this,
+      g.map_eq_zero_of_not_injective _ this]
 #align basis.ext_alternating Basis.ext_alternating
 
 end Basis

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

@@ -232,8 +232,8 @@ theorem map_zero [Nonempty ι] : f 0 = 0 :=
 
 theorem map_eq_zero_of_not_injective (v : ι → M) (hv : ¬Function.Injective v) : f v = 0 :=
   by
-  rw [Function.Injective] at hv
-  push_neg  at hv
+  rw [Function.Injective] at hv 
+  push_neg  at hv 
   rcases hv with ⟨i₁, i₂, heq, hne⟩
   exact f.map_eq_zero_of_eq v HEq hne
 #align alternating_map.map_eq_zero_of_not_injective AlternatingMap.map_eq_zero_of_not_injective
@@ -808,11 +808,11 @@ theorem map_linearDependent {K : Type _} [Ring K] {M : Type _} [AddCommGroup M]
   letI := Classical.decEq ι
   suffices f (update v i (g i • v i)) = 0
     by
-    rw [f.map_smul, Function.update_eq_self, smul_eq_zero] at this
+    rw [f.map_smul, Function.update_eq_self, smul_eq_zero] at this 
     exact Or.resolve_left this hz
   conv at h in g _ • v _ => rw [← if_t_t (i = x) (g _ • v _)]
   rw [Finset.sum_ite, Finset.filter_eq, Finset.filter_ne, if_pos hi, Finset.sum_singleton,
-    add_eq_zero_iff_eq_neg] at h
+    add_eq_zero_iff_eq_neg] at h 
   rw [h, f.map_neg, f.map_update_sum, neg_eq_zero, Finset.sum_eq_zero]
   intro j hj
   obtain ⟨hij, _⟩ := finset.mem_erase.mp hj
@@ -969,7 +969,7 @@ def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap
       σ.sign •
         (MultilinearMap.domCoprod ↑a ↑b : MultilinearMap R' (fun _ => Mᵢ) (N₁ ⊗ N₂)).domDomCongr σ)
     fun σ₁ σ₂ H => by
-    rw [QuotientGroup.leftRel_apply] at H
+    rw [QuotientGroup.leftRel_apply] at H 
     obtain ⟨⟨sl, sr⟩, h⟩ := H
     ext v
     simp only [MultilinearMap.domDomCongr_apply, MultilinearMap.domCoprod_apply,
@@ -1019,7 +1019,7 @@ theorem domCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ
   dsimp only [Quotient.liftOn'_mk'', Quotient.map'_mk'', MultilinearMap.smul_apply,
     MultilinearMap.domDomCongr_apply, MultilinearMap.domCoprod_apply, dom_coprod.summand]
   intro hσ
-  cases hi : σ⁻¹ i <;> cases hj : σ⁻¹ j <;> rw [perm.inv_eq_iff_eq] at hi hj <;> substs hi hj <;>
+  cases hi : σ⁻¹ i <;> cases hj : σ⁻¹ j <;> rw [perm.inv_eq_iff_eq] at hi hj  <;> substs hi hj <;>
     revert val val_1
   case inl.inr |
     inr.inl =>
@@ -1030,7 +1030,7 @@ theorem domCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ
     on_goal 1 => replace hσ := Equiv.congr_fun hσ (Sum.inl i')
     on_goal 2 => replace hσ := Equiv.congr_fun hσ (Sum.inr i')
     all_goals
-      rw [smul_eq_mul, ← mul_swap_eq_swap_mul, mul_inv_rev, swap_inv, inv_mul_cancel_right] at hσ
+      rw [smul_eq_mul, ← mul_swap_eq_swap_mul, mul_inv_rev, swap_inv, inv_mul_cancel_right] at hσ 
       simpa using hσ
   case inr.inr |
     inl.inl =>
@@ -1108,7 +1108,9 @@ def domCoprod' :
           MultilinearMap.domCoprod'_apply]
         simp only [TensorProduct.add_tmul, ← TensorProduct.smul_tmul', TensorProduct.tmul_add,
           TensorProduct.tmul_smul, LinearMap.map_add, LinearMap.map_smul]
-        first |rw [← smul_add]|rw [smul_comm]
+        first
+        | rw [← smul_add]
+        | rw [smul_comm]
         congr
 #align alternating_map.dom_coprod' AlternatingMap.domCoprod'
 -/

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Zhangir Azerbayev
 
 ! This file was ported from Lean 3 source module linear_algebra.alternating
-! leanprover-community/mathlib commit 78fdf68dcd2fdb3fe64c0dd6f88926a49418a6ea
+! leanprover-community/mathlib commit bd65478311e4dfd41f48bf38c7e3b02fb75d0163
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -165,12 +165,10 @@ theorem coe_multilinearMap_injective :
   fun x y h => ext <| MultilinearMap.congr_fun h
 #align alternating_map.coe_multilinear_map_injective AlternatingMap.coe_multilinearMap_injective
 
-/- warning: alternating_map.to_multilinear_map_eq_coe clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align alternating_map.to_multilinear_map_eq_coe [anonymous]ₓ'. -/
 @[simp]
-theorem [anonymous] : f.toMultilinearMap = f :=
+theorem toMultilinearMap_eq_coe : f.toMultilinearMap = f :=
   rfl
-#align alternating_map.to_multilinear_map_eq_coe [anonymous]
+#align alternating_map.to_multilinear_map_eq_coe AlternatingMap.toMultilinearMap_eq_coe
 
 @[simp]
 theorem coe_multilinearMap_mk (f : (ι → M) → N) (h₁ h₂ h₃) :
@@ -292,6 +290,7 @@ theorem coe_prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) :
   rfl
 #align alternating_map.coe_prod AlternatingMap.coe_prod
 
+#print AlternatingMap.pi /-
 /-- Combine a family of alternating maps with the same domain and codomains `N i` into an
 alternating map taking values in the space of functions `Π i, N i`. -/
 @[simps (config := { simpRhs := true })]
@@ -300,6 +299,7 @@ def pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)] [∀ i,
   { MultilinearMap.pi fun a => (f a).toMultilinearMap with
     map_eq_zero_of_eq' := fun v i j h hne => funext fun a => (f a).map_eq_zero_of_eq _ h hne }
 #align alternating_map.pi AlternatingMap.pi
+-/
 
 @[simp]
 theorem coe_pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
@@ -308,6 +308,7 @@ theorem coe_pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)]
   rfl
 #align alternating_map.coe_pi AlternatingMap.coe_pi
 
+#print AlternatingMap.smulRight /-
 /-- Given an alternating `R`-multilinear map `f` taking values in `R`, `f.smul_right z` is the map
 sending `m` to `f m • z`. -/
 @[simps (config := { simpRhs := true })]
@@ -316,6 +317,7 @@ def smulRight {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁] [A
   { f.toMultilinearMap.smul_right z with
     map_eq_zero_of_eq' := fun v i j h hne => by simp [f.map_eq_zero_of_eq v h hne] }
 #align alternating_map.smul_right AlternatingMap.smulRight
+-/
 
 @[simp]
 theorem coe_smulRight {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
@@ -441,6 +443,8 @@ def ofSubsingleton [Subsingleton ι] (i : ι) : AlternatingMap R M M ι :=
 #align alternating_map.of_subsingleton AlternatingMap.ofSubsingleton
 -/
 
+variable (ι)
+
 #print AlternatingMap.constOfIsEmpty /-
 /-- The constant map is alternating when `ι` is empty. -/
 @[simps (config := { fullyApplied := false })]
@@ -1314,7 +1318,7 @@ to an empty family. -/
 @[simps]
 def constLinearEquivOfIsEmpty [IsEmpty ι] : N'' ≃ₗ[R'] AlternatingMap R' M'' N'' ι
     where
-  toFun := AlternatingMap.constOfIsEmpty R' M''
+  toFun := AlternatingMap.constOfIsEmpty R' M'' ι
   map_add' x y := rfl
   map_smul' t x := rfl
   invFun f := f 0

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

@@ -653,7 +653,7 @@ open Function
 
 section
 
-open BigOperators
+open scoped BigOperators
 
 #print AlternatingMap.map_update_sum /-
 theorem map_update_sum {α : Type _} [DecidableEq ι] (t : Finset α) (i : ι) (g : α → M) (m : ι → M) :
@@ -835,7 +835,7 @@ end Fin
 
 end AlternatingMap
 
-open BigOperators
+open scoped BigOperators
 
 namespace MultilinearMap
 
@@ -924,9 +924,9 @@ end LinearMap
 
 section Coprod
 
-open BigOperators
+open scoped BigOperators
 
-open TensorProduct
+open scoped TensorProduct
 
 variable {ιa ιb : Type _} [Fintype ιa] [Fintype ιb]
 

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

@@ -116,12 +116,6 @@ instance : CoeFun (AlternatingMap R M N ι) fun _ => (ι → M) → N :=
 
 initialize_simps_projections AlternatingMap (toFun → apply)
 
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 @[simp]
 theorem toFun_eq_coe : f.toFun = f :=
   rfl
@@ -132,64 +126,28 @@ theorem coe_mk (f : (ι → M) → N) (h₁ h₂ h₃) : ⇑(⟨f, h₁, h₂, h
   rfl
 #align alternating_map.coe_mk AlternatingMap.coe_mkₓ
 
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 theorem congr_fun {f g : AlternatingMap R M N ι} (h : f = g) (x : ι → M) : f x = g x :=
   congr_arg (fun h : AlternatingMap R M N ι => h x) h
 #align alternating_map.congr_fun AlternatingMap.congr_fun
 
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 theorem congr_arg (f : AlternatingMap R M N ι) {x y : ι → M} (h : x = y) : f x = f y :=
   congr_arg (fun x : ι → M => f x) h
 #align alternating_map.congr_arg AlternatingMap.congr_arg
 
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 theorem coe_injective : Injective (coeFn : AlternatingMap R M N ι → (ι → M) → N) :=
   FunLike.coe_injective
 #align alternating_map.coe_injective AlternatingMap.coe_injective
 
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 @[simp, norm_cast]
 theorem coe_inj {f g : AlternatingMap R M N ι} : (f : (ι → M) → N) = g ↔ f = g :=
   coe_injective.eq_iff
 #align alternating_map.coe_inj AlternatingMap.coe_inj
 
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 @[ext]
 theorem ext {f f' : AlternatingMap R M N ι} (H : ∀ x, f x = f' x) : f = f' :=
   FunLike.ext _ _ H
 #align alternating_map.ext AlternatingMap.ext
 
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 theorem ext_iff {f g : AlternatingMap R M N ι} : f = g ↔ ∀ x, f x = g x :=
   ⟨fun h x => h ▸ rfl, fun h => ext h⟩
 #align alternating_map.ext_iff AlternatingMap.ext_iff
@@ -197,43 +155,23 @@ theorem ext_iff {f g : AlternatingMap R M N ι} : f = g ↔ ∀ x, f x = g x :=
 instance : Coe (AlternatingMap R M N ι) (MultilinearMap R (fun i : ι => M) N) :=
   ⟨fun x => x.toMultilinearMap⟩
 
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 @[simp, norm_cast]
 theorem coe_multilinearMap : ⇑(f : MultilinearMap R (fun i : ι => M) N) = f :=
   rfl
 #align alternating_map.coe_multilinear_map AlternatingMap.coe_multilinearMap
 
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 theorem coe_multilinearMap_injective :
     Function.Injective (coe : AlternatingMap R M N ι → MultilinearMap R (fun i : ι => M) N) :=
   fun x y h => ext <| MultilinearMap.congr_fun h
 #align alternating_map.coe_multilinear_map_injective AlternatingMap.coe_multilinearMap_injective
 
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 @[simp]
 theorem [anonymous] : f.toMultilinearMap = f :=
   rfl
 #align alternating_map.to_multilinear_map_eq_coe [anonymous]
 
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 @[simp]
 theorem coe_multilinearMap_mk (f : (ι → M) → N) (h₁ h₂ h₃) :
     ((⟨f, h₁, h₂, h₃⟩ : AlternatingMap R M N ι) : MultilinearMap R (fun i : ι => M) N) =
@@ -250,27 +188,18 @@ These are expressed in terms of `⇑f` instead of `f.to_fun`.
 -/
 
 
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 @[simp]
 theorem map_add [DecidableEq ι] (i : ι) (x y : M) :
     f (update v i (x + y)) = f (update v i x) + f (update v i y) :=
   f.toMultilinearMap.map_add' v i x y
 #align alternating_map.map_add AlternatingMap.map_add
 
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 @[simp]
 theorem map_sub [DecidableEq ι] (i : ι) (x y : M') :
     g' (update v' i (x - y)) = g' (update v' i x) - g' (update v' i y) :=
   g'.toMultilinearMap.map_sub v' i x y
 #align alternating_map.map_sub AlternatingMap.map_sub
 
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 @[simp]
 theorem map_neg [DecidableEq ι] (i : ι) (x : M') : g' (update v' i (-x)) = -g' (update v' i x) :=
   g'.toMultilinearMap.map_neg v' i x
@@ -284,52 +213,25 @@ theorem map_smul [DecidableEq ι] (i : ι) (r : R) (x : M) :
 #align alternating_map.map_smul AlternatingMap.map_smul
 -/
 
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 @[simp]
 theorem map_eq_zero_of_eq (v : ι → M) {i j : ι} (h : v i = v j) (hij : i ≠ j) : f v = 0 :=
   f.map_eq_zero_of_eq' v i j h hij
 #align alternating_map.map_eq_zero_of_eq AlternatingMap.map_eq_zero_of_eq
 
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 theorem map_coord_zero {m : ι → M} (i : ι) (h : m i = 0) : f m = 0 :=
   f.toMultilinearMap.map_coord_zero i h
 #align alternating_map.map_coord_zero AlternatingMap.map_coord_zero
 
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 @[simp]
 theorem map_update_zero [DecidableEq ι] (m : ι → M) (i : ι) : f (update m i 0) = 0 :=
   f.toMultilinearMap.map_update_zero m i
 #align alternating_map.map_update_zero AlternatingMap.map_update_zero
 
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 @[simp]
 theorem map_zero [Nonempty ι] : f 0 = 0 :=
   f.toMultilinearMap.map_zero
 #align alternating_map.map_zero AlternatingMap.map_zero
 
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 theorem map_eq_zero_of_not_injective (v : ι → M) (hv : ¬Function.Injective v) : f v = 0 :=
   by
   rw [Function.Injective] at hv
@@ -355,26 +257,17 @@ instance : SMul S (AlternatingMap R M N ι) :=
     { (c • f : MultilinearMap R (fun i : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }⟩
 
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 @[simp]
 theorem smul_apply (c : S) (m : ι → M) : (c • f) m = c • f m :=
   rfl
 #align alternating_map.smul_apply AlternatingMap.smul_apply
 
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 @[norm_cast]
 theorem coe_smul (c : S) :
     ((c • f : AlternatingMap R M N ι) : MultilinearMap R (fun i : ι => M) N) = c • f :=
   rfl
 #align alternating_map.coe_smul AlternatingMap.coe_smul
 
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 theorem coeFn_smul (c : S) (f : AlternatingMap R M N ι) : ⇑(c • f) = c • f :=
   rfl
 #align alternating_map.coe_fn_smul AlternatingMap.coeFn_smul
@@ -437,20 +330,11 @@ instance : Add (AlternatingMap R M N ι) :=
       map_eq_zero_of_eq' := fun v i j h hij => by
         simp [a.map_eq_zero_of_eq v h hij, b.map_eq_zero_of_eq v h hij] }⟩
 
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 @[simp]
 theorem add_apply : (f + f') v = f v + f' v :=
   rfl
 #align alternating_map.add_apply AlternatingMap.add_apply
 
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 @[norm_cast]
 theorem coe_add : (↑(f + f') : MultilinearMap R (fun i : ι => M) N) = f + f' :=
   rfl
@@ -460,23 +344,11 @@ instance : Zero (AlternatingMap R M N ι) :=
   ⟨{ (0 : MultilinearMap R (fun i : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by simp }⟩
 
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 @[simp]
 theorem zero_apply : (0 : AlternatingMap R M N ι) v = 0 :=
   rfl
 #align alternating_map.zero_apply AlternatingMap.zero_apply
 
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 @[norm_cast]
 theorem coe_zero : ((0 : AlternatingMap R M N ι) : MultilinearMap R (fun i : ι => M) N) = 0 :=
   rfl
@@ -493,23 +365,11 @@ instance : Neg (AlternatingMap R M N' ι) :=
     { -(f : MultilinearMap R (fun i : ι => M) N') with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }⟩
 
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 @[simp]
 theorem neg_apply (m : ι → M) : (-g) m = -g m :=
   rfl
 #align alternating_map.neg_apply AlternatingMap.neg_apply
 
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 @[norm_cast]
 theorem coe_neg : ((-g : AlternatingMap R M N' ι) : MultilinearMap R (fun i : ι => M) N') = -g :=
   rfl
@@ -521,17 +381,11 @@ instance : Sub (AlternatingMap R M N' ι) :=
       map_eq_zero_of_eq' := fun v i j h hij => by
         simp [f.map_eq_zero_of_eq v h hij, g.map_eq_zero_of_eq v h hij] }⟩
 
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 @[simp]
 theorem sub_apply (m : ι → M) : (g - g₂) m = g m - g₂ m :=
   rfl
 #align alternating_map.sub_apply AlternatingMap.sub_apply
 
-/- warning: alternating_map.coe_sub -> AlternatingMap.coe_sub is a dubious translation:
-<too large>
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 @[norm_cast]
 theorem coe_sub : (↑(g - g₂) : MultilinearMap R (fun i : ι => M) N') = g - g₂ :=
   rfl
@@ -637,18 +491,12 @@ def compAlternatingMap (g : N →ₗ[R] N₂) : AlternatingMap R M N ι →+ Alt
 #align linear_map.comp_alternating_map LinearMap.compAlternatingMap
 -/
 
-/- warning: linear_map.coe_comp_alternating_map -> LinearMap.coe_compAlternatingMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.coe_comp_alternating_map LinearMap.coe_compAlternatingMapₓ'. -/
 @[simp]
 theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) :
     ⇑(g.compAlternatingMap f) = g ∘ f :=
   rfl
 #align linear_map.coe_comp_alternating_map LinearMap.coe_compAlternatingMap
 
-/- warning: linear_map.comp_alternating_map_apply -> LinearMap.compAlternatingMap_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.comp_alternating_map_apply LinearMap.compAlternatingMap_applyₓ'. -/
 @[simp]
 theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) (m : ι → M) :
     g.compAlternatingMap f m = g (f m) :=
@@ -661,18 +509,12 @@ theorem smulRight_eq_comp {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMon
   rfl
 #align linear_map.smul_right_eq_comp LinearMap.smulRight_eq_comp
 
-/- warning: linear_map.subtype_comp_alternating_map_cod_restrict -> LinearMap.subtype_compAlternatingMap_codRestrict is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.subtype_comp_alternating_map_cod_restrict LinearMap.subtype_compAlternatingMap_codRestrictₓ'. -/
 @[simp]
 theorem subtype_compAlternatingMap_codRestrict (f : AlternatingMap R M N ι) (p : Submodule R N)
     (h) : p.Subtype.compAlternatingMap (f.codRestrict p h) = f :=
   AlternatingMap.ext fun v => rfl
 #align linear_map.subtype_comp_alternating_map_cod_restrict LinearMap.subtype_compAlternatingMap_codRestrict
 
-/- warning: linear_map.comp_alternating_map_cod_restrict -> LinearMap.compAlternatingMap_codRestrict is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.comp_alternating_map_cod_restrict LinearMap.compAlternatingMap_codRestrictₓ'. -/
 @[simp]
 theorem compAlternatingMap_codRestrict (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι)
     (p : Submodule R N₂) (h) :
@@ -698,26 +540,17 @@ def compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) : Alterna
 #align alternating_map.comp_linear_map AlternatingMap.compLinearMap
 -/
 
-/- warning: alternating_map.coe_comp_linear_map -> AlternatingMap.coe_compLinearMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.coe_comp_linear_map AlternatingMap.coe_compLinearMapₓ'. -/
 theorem coe_compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
     ⇑(f.compLinearMap g) = f ∘ (· ∘ ·) g :=
   rfl
 #align alternating_map.coe_comp_linear_map AlternatingMap.coe_compLinearMap
 
-/- warning: alternating_map.comp_linear_map_apply -> AlternatingMap.compLinearMap_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_apply AlternatingMap.compLinearMap_applyₓ'. -/
 @[simp]
 theorem compLinearMap_apply (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) (v : ι → M₂) :
     f.compLinearMap g v = f fun i => g (v i) :=
   rfl
 #align alternating_map.comp_linear_map_apply AlternatingMap.compLinearMap_apply
 
-/- warning: alternating_map.comp_linear_map_assoc -> AlternatingMap.compLinearMap_assoc is a dubious translation:
-<too large>
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 /-- Composing an alternating map twice with the same linear map in each argument is
 the same as composing with their composition. -/
 theorem compLinearMap_assoc (f : AlternatingMap R M N ι) (g₁ : M₂ →ₗ[R] M) (g₂ : M₃ →ₗ[R] M₂) :
@@ -725,29 +558,17 @@ theorem compLinearMap_assoc (f : AlternatingMap R M N ι) (g₁ : M₂ →ₗ[R]
   rfl
 #align alternating_map.comp_linear_map_assoc AlternatingMap.compLinearMap_assoc
 
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 @[simp]
 theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : AlternatingMap R M N ι).compLinearMap g = 0 := by
   ext; simp only [comp_linear_map_apply, zero_apply]
 #align alternating_map.zero_comp_linear_map AlternatingMap.zero_compLinearMap
 
-/- warning: alternating_map.add_comp_linear_map -> AlternatingMap.add_compLinearMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.add_comp_linear_map AlternatingMap.add_compLinearMapₓ'. -/
 @[simp]
 theorem add_compLinearMap (f₁ f₂ : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
     (f₁ + f₂).compLinearMap g = f₁.compLinearMap g + f₂.compLinearMap g := by ext;
   simp only [comp_linear_map_apply, add_apply]
 #align alternating_map.add_comp_linear_map AlternatingMap.add_compLinearMap
 
-/- warning: alternating_map.comp_linear_map_zero -> AlternatingMap.compLinearMap_zero is a dubious translation:
-<too large>
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 @[simp]
 theorem compLinearMap_zero [Nonempty ι] (f : AlternatingMap R M N ι) :
     f.compLinearMap (0 : M₂ →ₗ[R] M) = 0 := by
@@ -755,30 +576,18 @@ theorem compLinearMap_zero [Nonempty ι] (f : AlternatingMap R M N ι) :
   simp_rw [comp_linear_map_apply, LinearMap.zero_apply, ← Pi.zero_def, map_zero, zero_apply]
 #align alternating_map.comp_linear_map_zero AlternatingMap.compLinearMap_zero
 
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 /-- Composing an alternating map with the identity linear map in each argument. -/
 @[simp]
 theorem compLinearMap_id (f : AlternatingMap R M N ι) : f.compLinearMap LinearMap.id = f :=
   ext fun _ => rfl
 #align alternating_map.comp_linear_map_id AlternatingMap.compLinearMap_id
 
-/- warning: alternating_map.comp_linear_map_injective -> AlternatingMap.compLinearMap_injective is a dubious translation:
-<too large>
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 /-- Composing with a surjective linear map is injective. -/
 theorem compLinearMap_injective (f : M₂ →ₗ[R] M) (hf : Function.Surjective f) :
     Function.Injective fun g : AlternatingMap R M N ι => g.compLinearMap f := fun g₁ g₂ h =>
   ext fun x => by simpa [Function.surjInv_eq hf] using ext_iff.mp h (Function.surjInv hf ∘ x)
 #align alternating_map.comp_linear_map_injective AlternatingMap.compLinearMap_injective
 
-/- warning: alternating_map.comp_linear_map_inj -> AlternatingMap.compLinearMap_inj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_inj AlternatingMap.compLinearMap_injₓ'. -/
 theorem compLinearMap_inj (f : M₂ →ₗ[R] M) (hf : Function.Surjective f)
     (g₁ g₂ : AlternatingMap R M N ι) : g₁.compLinearMap f = g₂.compLinearMap f ↔ g₁ = g₂ :=
   (compLinearMap_injective _ hf).eq_iff
@@ -802,25 +611,16 @@ def domLCongr (e : M ≃ₗ[R] M₂) : AlternatingMap R M N ι ≃ₗ[S] Alterna
 #align alternating_map.dom_lcongr AlternatingMap.domLCongr
 -/
 
-/- warning: alternating_map.dom_lcongr_refl -> AlternatingMap.domLCongr_refl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.dom_lcongr_refl AlternatingMap.domLCongr_reflₓ'. -/
 @[simp]
 theorem domLCongr_refl : domLCongr R N ι S (LinearEquiv.refl R M) = LinearEquiv.refl S _ :=
   LinearEquiv.ext fun _ => AlternatingMap.ext fun v => rfl
 #align alternating_map.dom_lcongr_refl AlternatingMap.domLCongr_refl
 
-/- warning: alternating_map.dom_lcongr_symm -> AlternatingMap.domLCongr_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.dom_lcongr_symm AlternatingMap.domLCongr_symmₓ'. -/
 @[simp]
 theorem domLCongr_symm (e : M ≃ₗ[R] M₂) : (domLCongr R N ι S e).symm = domLCongr R N ι S e.symm :=
   rfl
 #align alternating_map.dom_lcongr_symm AlternatingMap.domLCongr_symm
 
-/- warning: alternating_map.dom_lcongr_trans -> AlternatingMap.domLCongr_trans is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.dom_lcongr_trans AlternatingMap.domLCongr_transₓ'. -/
 theorem domLCongr_trans (e : M ≃ₗ[R] M₂) (f : M₂ ≃ₗ[R] M₃) :
     (domLCongr R N ι S e).trans (domLCongr R N ι S f) = domLCongr R N ι S (e.trans f) :=
   rfl
@@ -828,9 +628,6 @@ theorem domLCongr_trans (e : M ≃ₗ[R] M₂) (f : M₂ ≃ₗ[R] M₃) :
 
 end DomLcongr
 
-/- warning: alternating_map.comp_linear_equiv_eq_zero_iff -> AlternatingMap.compLinearEquiv_eq_zero_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_equiv_eq_zero_iff AlternatingMap.compLinearEquiv_eq_zero_iffₓ'. -/
 /-- Composing an alternating map with the same linear equiv on each argument gives the zero map
 if and only if the alternating map is the zero map. -/
 @[simp]
@@ -875,26 +672,17 @@ Various properties of reordered and repeated inputs which follow from
 -/
 
 
-/- warning: alternating_map.map_update_self -> AlternatingMap.map_update_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.map_update_self AlternatingMap.map_update_selfₓ'. -/
 theorem map_update_self [DecidableEq ι] {i j : ι} (hij : i ≠ j) :
     f (Function.update v i (v j)) = 0 :=
   f.map_eq_zero_of_eq _ (by rw [Function.update_same, Function.update_noteq hij.symm]) hij
 #align alternating_map.map_update_self AlternatingMap.map_update_self
 
-/- warning: alternating_map.map_update_update -> AlternatingMap.map_update_update is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.map_update_update AlternatingMap.map_update_updateₓ'. -/
 theorem map_update_update [DecidableEq ι] {i j : ι} (hij : i ≠ j) (m : M) :
     f (Function.update (Function.update v i m) j m) = 0 :=
   f.map_eq_zero_of_eq _
     (by rw [Function.update_same, Function.update_noteq hij, Function.update_same]) hij
 #align alternating_map.map_update_update AlternatingMap.map_update_update
 
-/- warning: alternating_map.map_swap_add -> AlternatingMap.map_swap_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.map_swap_add AlternatingMap.map_swap_addₓ'. -/
 theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equiv.swap i j) + f v = 0 :=
   by
   rw [Equiv.comp_swap_eq_update]
@@ -903,9 +691,6 @@ theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equi
     Function.update_comm hij (v i + v j) (v _) v, Function.update_comm hij.symm (v i) (v i) v]
 #align alternating_map.map_swap_add AlternatingMap.map_swap_add
 
-/- warning: alternating_map.map_add_swap -> AlternatingMap.map_add_swap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.map_add_swap AlternatingMap.map_add_swapₓ'. -/
 theorem map_add_swap [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f v + f (v ∘ Equiv.swap i j) = 0 :=
   by rw [add_comm]; exact f.map_swap_add v hij
 #align alternating_map.map_add_swap AlternatingMap.map_add_swap
@@ -927,9 +712,6 @@ theorem map_perm [DecidableEq ι] [Fintype ι] (v : ι → M) (σ : Equiv.Perm 
 #align alternating_map.map_perm AlternatingMap.map_perm
 -/
 
-/- warning: alternating_map.map_congr_perm -> AlternatingMap.map_congr_perm is a dubious translation:
-<too large>
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 theorem map_congr_perm [DecidableEq ι] [Fintype ι] (σ : Equiv.Perm ι) : g v = σ.sign • g (v ∘ σ) :=
   by rw [g.map_perm, smul_smul]; simp
 #align alternating_map.map_congr_perm AlternatingMap.map_congr_perm
@@ -951,42 +733,21 @@ def domDomCongr (σ : ι ≃ ι') (f : AlternatingMap R M N ι) : AlternatingMap
 #align alternating_map.dom_dom_congr AlternatingMap.domDomCongr
 -/
 
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 @[simp]
 theorem domDomCongr_refl (f : AlternatingMap R M N ι) : f.domDomCongr (Equiv.refl ι) = f :=
   ext fun v => rfl
 #align alternating_map.dom_dom_congr_refl AlternatingMap.domDomCongr_refl
 
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 theorem domDomCongr_trans (σ₁ : ι ≃ ι') (σ₂ : ι' ≃ ι'') (f : AlternatingMap R M N ι) :
     f.domDomCongr (σ₁.trans σ₂) = (f.domDomCongr σ₁).domDomCongr σ₂ :=
   rfl
 #align alternating_map.dom_dom_congr_trans AlternatingMap.domDomCongr_trans
 
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 @[simp]
 theorem domDomCongr_zero (σ : ι ≃ ι') : (0 : AlternatingMap R M N ι).domDomCongr σ = 0 :=
   rfl
 #align alternating_map.dom_dom_congr_zero AlternatingMap.domDomCongr_zero
 
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 @[simp]
 theorem domDomCongr_add (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
     (f + g).domDomCongr σ = f.domDomCongr σ + g.domDomCongr σ :=
@@ -1008,12 +769,6 @@ def domDomCongrEquiv (σ : ι ≃ ι') : AlternatingMap R M N ι ≃+ Alternatin
 #align alternating_map.dom_dom_congr_equiv AlternatingMap.domDomCongrEquiv
 -/
 
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 /-- The results of applying `dom_dom_congr` to two maps are equal if and only if those maps are. -/
 @[simp]
 theorem domDomCongr_eq_iff (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
@@ -1021,32 +776,17 @@ theorem domDomCongr_eq_iff (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
   (domDomCongrEquiv σ : _ ≃+ AlternatingMap R M N ι').apply_eq_iff_eq
 #align alternating_map.dom_dom_congr_eq_iff AlternatingMap.domDomCongr_eq_iff
 
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 @[simp]
 theorem domDomCongr_eq_zero_iff (σ : ι ≃ ι') (f : AlternatingMap R M N ι) :
     f.domDomCongr σ = 0 ↔ f = 0 :=
   (domDomCongrEquiv σ : AlternatingMap R M N ι ≃+ AlternatingMap R M N ι').map_eq_zero_iff
 #align alternating_map.dom_dom_congr_eq_zero_iff AlternatingMap.domDomCongr_eq_zero_iff
 
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 theorem domDomCongr_perm [Fintype ι] [DecidableEq ι] (σ : Equiv.Perm ι) :
     g.domDomCongr σ = σ.sign • g :=
   AlternatingMap.ext fun v => g.map_perm v σ
 #align alternating_map.dom_dom_congr_perm AlternatingMap.domDomCongr_perm
 
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 @[norm_cast]
 theorem coe_domDomCongr (σ : ι ≃ ι') :
     ↑(f.domDomCongr σ) = (f : MultilinearMap R (fun _ : ι => M) N).domDomCongr σ :=
@@ -1055,9 +795,6 @@ theorem coe_domDomCongr (σ : ι ≃ ι') :
 
 end DomDomCongr
 
-/- warning: alternating_map.map_linear_dependent -> AlternatingMap.map_linearDependent is a dubious translation:
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 /-- If the arguments are linearly dependent then the result is `0`. -/
 theorem map_linearDependent {K : Type _} [Ring K] {M : Type _} [AddCommGroup M] [Module K M]
     {N : Type _} [AddCommGroup N] [Module K N] [NoZeroSMulDivisors K N] (f : AlternatingMap K M N ι)
@@ -1082,21 +819,12 @@ section Fin
 
 open Fin
 
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 /-- A version of `multilinear_map.cons_add` for `alternating_map`. -/
 theorem map_vecCons_add {n : ℕ} (f : AlternatingMap R M N (Fin n.succ)) (m : Fin n → M) (x y : M) :
     f (Matrix.vecCons (x + y) m) = f (Matrix.vecCons x m) + f (Matrix.vecCons y m) :=
   f.toMultilinearMap.cons_add _ _ _
 #align alternating_map.map_vec_cons_add AlternatingMap.map_vecCons_add
 
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 /-- A version of `multilinear_map.cons_smul` for `alternating_map`. -/
 theorem map_vecCons_smul {n : ℕ} (f : AlternatingMap R M N (Fin n.succ)) (m : Fin n → M) (c : R)
     (x : M) : f (Matrix.vecCons (c • x) m) = c • f (Matrix.vecCons x m) :=
@@ -1126,12 +854,6 @@ private theorem alternization_map_eq_zero_of_eq_aux (m : MultilinearMap R (fun i
       (fun σ _ _ => (not_congr swap_mul_eq_iff).mpr i_ne_j) (fun σ _ => Finset.mem_univ _)
       fun σ _ => swap_mul_involutive i j σ
 
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-Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization MultilinearMap.alternatizationₓ'. -/
 /-- Produce an `alternating_map` out of a `multilinear_map`, by summing over all argument
 permutations. -/
 def alternatization : MultilinearMap R (fun i : ι => M) N' →+ AlternatingMap R M N' ι
@@ -1155,25 +877,16 @@ def alternatization : MultilinearMap R (fun i : ι => M) N' →+ AlternatingMap
       AlternatingMap.zero_apply, AlternatingMap.coe_mk, smul_apply, sum_apply]
 #align multilinear_map.alternatization MultilinearMap.alternatization
 
-/- warning: multilinear_map.alternatization_def -> MultilinearMap.alternatization_def is a dubious translation:
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 theorem alternatization_def (m : MultilinearMap R (fun i : ι => M) N') :
     ⇑(alternatization m) = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
   rfl
 #align multilinear_map.alternatization_def MultilinearMap.alternatization_def
 
-/- warning: multilinear_map.alternatization_coe -> MultilinearMap.alternatization_coe is a dubious translation:
-<too large>
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 theorem alternatization_coe (m : MultilinearMap R (fun i : ι => M) N') :
     ↑m.alternatization = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
   coe_injective rfl
 #align multilinear_map.alternatization_coe MultilinearMap.alternatization_coe
 
-/- warning: multilinear_map.alternatization_apply -> MultilinearMap.alternatization_apply is a dubious translation:
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 theorem alternatization_apply (m : MultilinearMap R (fun i : ι => M) N') (v : ι → M) :
     alternatization m v = ∑ σ : Perm ι, σ.sign • m.domDomCongr σ v := by
   simp only [alternatization_def, smul_apply, sum_apply]
@@ -1183,9 +896,6 @@ end MultilinearMap
 
 namespace AlternatingMap
 
-/- warning: alternating_map.coe_alternatization -> AlternatingMap.coe_alternatization is a dubious translation:
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 /-- Alternatizing a multilinear map that is already alternating results in a scale factor of `n!`,
 where `n` is the number of inputs. -/
 theorem coe_alternatization [DecidableEq ι] [Fintype ι] (a : AlternatingMap R M N' ι) :
@@ -1203,9 +913,6 @@ namespace LinearMap
 
 variable {N'₂ : Type _} [AddCommGroup N'₂] [Module R N'₂] [DecidableEq ι] [Fintype ι]
 
-/- warning: linear_map.comp_multilinear_map_alternatization -> LinearMap.compMultilinearMap_alternatization is a dubious translation:
-<too large>
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 /-- Composition with a linear map before and after alternatization are equivalent. -/
 theorem compMultilinearMap_alternatization (g : N' →ₗ[R] N'₂)
     (f : MultilinearMap R (fun _ : ι => M) N') :
@@ -1235,12 +942,6 @@ abbrev ModSumCongr (α β : Type _) :=
 #align equiv.perm.mod_sum_congr Equiv.Perm.ModSumCongr
 -/
 
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 theorem ModSumCongr.swap_smul_involutive {α β : Type _} [DecidableEq (Sum α β)] (i j : Sum α β) :
     Function.Involutive (SMul.smul (Equiv.swap i j) : ModSumCongr α β → ModSumCongr α β) := fun σ =>
   by
@@ -1256,9 +957,6 @@ open Equiv
 
 variable [DecidableEq ιa] [DecidableEq ιb]
 
-/- warning: alternating_map.dom_coprod.summand -> AlternatingMap.domCoprod.summand is a dubious translation:
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 /-- summand used in `alternating_map.dom_coprod` -/
 def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
     (σ : Perm.ModSumCongr ιa ιb) : MultilinearMap R' (fun _ : Sum ιa ιb => Mᵢ) (N₁ ⊗[R'] N₂) :=
@@ -1281,9 +979,6 @@ def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap
     rw [← a.map_congr_perm fun i => v (σ₁ _), ← b.map_congr_perm fun i => v (σ₁ _)]
 #align alternating_map.dom_coprod.summand AlternatingMap.domCoprod.summand
 
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 theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
     (σ : Equiv.Perm (Sum ιa ιb)) :
     domCoprod.summand a b (Quotient.mk'' σ) =
@@ -1293,9 +988,6 @@ theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : Altern
   rfl
 #align alternating_map.dom_coprod.summand_mk' AlternatingMap.domCoprod.summand_mk''
 
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 /-- Swapping elements in `σ` with equal values in `v` results in an addition that cancels -/
 theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁ ιa)
     (b : AlternatingMap R' Mᵢ N₂ ιb) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
@@ -1312,9 +1004,6 @@ theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁
   convert add_right_neg _ <;> · ext k; rw [Equiv.apply_swap_eq_self hv]
 #align alternating_map.dom_coprod.summand_add_swap_smul_eq_zero AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero
 
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 /-- Swapping elements in `σ` with equal values in `v` result in zero if the swap has no effect
 on the quotient. -/
 theorem domCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ N₁ ιa)
@@ -1350,9 +1039,6 @@ theorem domCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ
     all_goals exact AlternatingMap.map_eq_zero_of_eq _ _ hv fun hij' => hij (hij' ▸ rfl)
 #align alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant
 
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 /-- Like `multilinear_map.dom_coprod`, but ensures the result is also alternating.
 
 Note that this is usually defined (for instance, as used in Proposition 22.24 in [Gallier2011Notes])
@@ -1392,9 +1078,6 @@ def domCoprod (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ
           Equiv.Perm.ModSumCongr.swap_smul_involutive i j σ }
 #align alternating_map.dom_coprod AlternatingMap.domCoprod
 
-/- warning: alternating_map.dom_coprod_coe -> AlternatingMap.domCoprod_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod_coe AlternatingMap.domCoprod_coeₓ'. -/
 theorem domCoprod_coe (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
     (↑(a.domCoprod b) : MultilinearMap R' (fun _ => Mᵢ) _) =
       ∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ :=
@@ -1426,9 +1109,6 @@ def domCoprod' :
 #align alternating_map.dom_coprod' AlternatingMap.domCoprod'
 -/
 
-/- warning: alternating_map.dom_coprod'_apply -> AlternatingMap.domCoprod'_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod'_apply AlternatingMap.domCoprod'_applyₓ'. -/
 @[simp]
 theorem domCoprod'_apply (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
     domCoprod' (a ⊗ₜ[R'] b) = domCoprod a b :=
@@ -1439,9 +1119,6 @@ end AlternatingMap
 
 open Equiv
 
-/- warning: multilinear_map.dom_coprod_alternization_coe -> MultilinearMap.domCoprod_alternization_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_alternization_coe MultilinearMap.domCoprod_alternization_coeₓ'. -/
 /-- A helper lemma for `multilinear_map.dom_coprod_alternization`. -/
 theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableEq ιb]
     (a : MultilinearMap R' (fun _ : ιa => Mᵢ) N₁) (b : MultilinearMap R' (fun _ : ιb => Mᵢ) N₂) :
@@ -1456,9 +1133,6 @@ theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableE
 
 open AlternatingMap
 
-/- warning: multilinear_map.dom_coprod_alternization -> MultilinearMap.domCoprod_alternization is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_alternization MultilinearMap.domCoprod_alternizationₓ'. -/
 /-- Computing the `multilinear_map.alternatization` of the `multilinear_map.dom_coprod` is the same
 as computing the `alternating_map.dom_coprod` of the `multilinear_map.alternatization`s.
 -/
@@ -1498,9 +1172,6 @@ theorem MultilinearMap.domCoprod_alternization [DecidableEq ιa] [DecidableEq ι
     MultilinearMap.domCoprod_domDomCongr_sumCongr, perm.sign_sum_congr, mul_smul, mul_smul]
 #align multilinear_map.dom_coprod_alternization MultilinearMap.domCoprod_alternization
 
-/- warning: multilinear_map.dom_coprod_alternization_eq -> MultilinearMap.domCoprod_alternization_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_alternization_eq MultilinearMap.domCoprod_alternization_eqₓ'. -/
 /-- Taking the `multilinear_map.alternatization` of the `multilinear_map.dom_coprod` of two
 `alternating_map`s gives a scaled version of the `alternating_map.coprod` of those maps.
 -/
@@ -1530,9 +1201,6 @@ variable {R' : Type _} {N₁ N₂ : Type _} [CommSemiring R'] [AddCommMonoid N
 
 variable [Module R' N₁] [Module R' N₂]
 
-/- warning: basis.ext_alternating -> Basis.ext_alternating is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.ext_alternating Basis.ext_alternatingₓ'. -/
 /-- Two alternating maps indexed by a `fintype` are equal if they are equal when all arguments
 are distinct basis vectors. -/
 theorem Basis.ext_alternating {f g : AlternatingMap R' N₁ N₂ ι} (e : Basis ι₁ R' N₁)
@@ -1584,26 +1252,17 @@ def curryLeft {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ)) :
 #align alternating_map.curry_left AlternatingMap.curryLeft
 -/
 
-/- warning: alternating_map.curry_left_zero -> AlternatingMap.curryLeft_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_zero AlternatingMap.curryLeft_zeroₓ'. -/
 @[simp]
 theorem curryLeft_zero {n : ℕ} : curryLeft (0 : AlternatingMap R' M'' N'' (Fin n.succ)) = 0 :=
   rfl
 #align alternating_map.curry_left_zero AlternatingMap.curryLeft_zero
 
-/- warning: alternating_map.curry_left_add -> AlternatingMap.curryLeft_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_add AlternatingMap.curryLeft_addₓ'. -/
 @[simp]
 theorem curryLeft_add {n : ℕ} (f g : AlternatingMap R' M'' N'' (Fin n.succ)) :
     curryLeft (f + g) = curryLeft f + curryLeft g :=
   rfl
 #align alternating_map.curry_left_add AlternatingMap.curryLeft_add
 
-/- warning: alternating_map.curry_left_smul -> AlternatingMap.curryLeft_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_smul AlternatingMap.curryLeft_smulₓ'. -/
 @[simp]
 theorem curryLeft_smul {n : ℕ} (r : R') (f : AlternatingMap R' M'' N'' (Fin n.succ)) :
     curryLeft (r • f) = r • curryLeft f :=
@@ -1623,9 +1282,6 @@ def curryLeftLinearMap {n : ℕ} :
 #align alternating_map.curry_left_linear_map AlternatingMap.curryLeftLinearMap
 -/
 
-/- warning: alternating_map.curry_left_same -> AlternatingMap.curryLeft_same is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_same AlternatingMap.curryLeft_sameₓ'. -/
 /-- Currying with the same element twice gives the zero map. -/
 @[simp]
 theorem curryLeft_same {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ.succ)) (m : M'') :
@@ -1633,9 +1289,6 @@ theorem curryLeft_same {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ.succ
   ext fun x => f.map_eq_zero_of_eq _ (by simp) Fin.zero_ne_one
 #align alternating_map.curry_left_same AlternatingMap.curryLeft_same
 
-/- warning: alternating_map.curry_left_comp_alternating_map -> AlternatingMap.curryLeft_compAlternatingMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_comp_alternating_map AlternatingMap.curryLeft_compAlternatingMapₓ'. -/
 @[simp]
 theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
     (f : AlternatingMap R' M'' N'' (Fin n.succ)) (m : M'') :
@@ -1643,9 +1296,6 @@ theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
   rfl
 #align alternating_map.curry_left_comp_alternating_map AlternatingMap.curryLeft_compAlternatingMap
 
-/- warning: alternating_map.curry_left_comp_linear_map -> AlternatingMap.curryLeft_compLinearMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_comp_linear_map AlternatingMap.curryLeft_compLinearMapₓ'. -/
 @[simp]
 theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')
     (f : AlternatingMap R' M'' N'' (Fin n.succ)) (m : M₂'') :

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

@@ -106,10 +106,7 @@ section Coercions
 instance funLike : FunLike (AlternatingMap R M N ι) (ι → M) fun _ => N
     where
   coe := AlternatingMap.toFun
-  coe_injective' f g h := by
-    cases f
-    cases g
-    congr
+  coe_injective' f g h := by cases f; cases g; congr
 #align alternating_map.fun_like AlternatingMap.funLike
 -/
 
@@ -635,12 +632,8 @@ def compAlternatingMap (g : N →ₗ[R] N₂) : AlternatingMap R M N ι →+ Alt
   toFun f :=
     { g.compMultilinearMap (f : MultilinearMap R (fun _ : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }
-  map_zero' := by
-    ext
-    simp
-  map_add' a b := by
-    ext
-    simp
+  map_zero' := by ext; simp
+  map_add' a b := by ext; simp
 #align linear_map.comp_alternating_map LinearMap.compAlternatingMap
 -/
 
@@ -739,10 +732,8 @@ but is expected to have type
   forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u3}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u5, u3} R M _inst_1 _inst_2] {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u5, u2} R N _inst_1 _inst_4] {ι : Type.{u1}} {M₂ : Type.{u4}} [_inst_12 : AddCommMonoid.{u4} M₂] [_inst_13 : Module.{u5, u4} R M₂ _inst_1 _inst_12] (g : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_12 _inst_2 _inst_13 _inst_3), Eq.{max (max (succ u2) (succ u1)) (succ u4)} (AlternatingMap.{u5, u4, u2, u1} R _inst_1 M₂ _inst_12 _inst_13 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_12 _inst_13 (OfNat.ofNat.{max (max u3 u2) u1} (AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.zero.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) g) (OfNat.ofNat.{max (max u2 u1) u4} (AlternatingMap.{u5, u4, u2, u1} R _inst_1 M₂ _inst_12 _inst_13 N _inst_4 _inst_5 ι) 0 (Zero.toOfNat0.{max (max u2 u1) u4} (AlternatingMap.{u5, u4, u2, u1} R _inst_1 M₂ _inst_12 _inst_13 N _inst_4 _inst_5 ι) (AlternatingMap.zero.{u5, u4, u2, u1} R _inst_1 M₂ _inst_12 _inst_13 N _inst_4 _inst_5 ι)))
 Case conversion may be inaccurate. Consider using '#align alternating_map.zero_comp_linear_map AlternatingMap.zero_compLinearMapₓ'. -/
 @[simp]
-theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : AlternatingMap R M N ι).compLinearMap g = 0 :=
-  by
-  ext
-  simp only [comp_linear_map_apply, zero_apply]
+theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : AlternatingMap R M N ι).compLinearMap g = 0 := by
+  ext; simp only [comp_linear_map_apply, zero_apply]
 #align alternating_map.zero_comp_linear_map AlternatingMap.zero_compLinearMap
 
 /- warning: alternating_map.add_comp_linear_map -> AlternatingMap.add_compLinearMap is a dubious translation:
@@ -750,9 +741,7 @@ theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : AlternatingMap R M N ι
 Case conversion may be inaccurate. Consider using '#align alternating_map.add_comp_linear_map AlternatingMap.add_compLinearMapₓ'. -/
 @[simp]
 theorem add_compLinearMap (f₁ f₂ : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
-    (f₁ + f₂).compLinearMap g = f₁.compLinearMap g + f₂.compLinearMap g :=
-  by
-  ext
+    (f₁ + f₂).compLinearMap g = f₁.compLinearMap g + f₂.compLinearMap g := by ext;
   simp only [comp_linear_map_apply, add_apply]
 #align alternating_map.add_comp_linear_map AlternatingMap.add_compLinearMap
 
@@ -918,9 +907,7 @@ theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equi
 <too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.map_add_swap AlternatingMap.map_add_swapₓ'. -/
 theorem map_add_swap [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f v + f (v ∘ Equiv.swap i j) = 0 :=
-  by
-  rw [add_comm]
-  exact f.map_swap_add v hij
+  by rw [add_comm]; exact f.map_swap_add v hij
 #align alternating_map.map_add_swap AlternatingMap.map_add_swap
 
 #print AlternatingMap.map_swap /-
@@ -944,9 +931,7 @@ theorem map_perm [DecidableEq ι] [Fintype ι] (v : ι → M) (σ : Equiv.Perm 
 <too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.map_congr_perm AlternatingMap.map_congr_permₓ'. -/
 theorem map_congr_perm [DecidableEq ι] [Fintype ι] (σ : Equiv.Perm ι) : g v = σ.sign • g (v ∘ σ) :=
-  by
-  rw [g.map_perm, smul_smul]
-  simp
+  by rw [g.map_perm, smul_smul]; simp
 #align alternating_map.map_congr_perm AlternatingMap.map_congr_perm
 
 section DomDomCongr
@@ -1017,12 +1002,8 @@ def domDomCongrEquiv (σ : ι ≃ ι') : AlternatingMap R M N ι ≃+ Alternatin
     where
   toFun := domDomCongr σ
   invFun := domDomCongr σ.symm
-  left_inv f := by
-    ext
-    simp [Function.comp]
-  right_inv m := by
-    ext
-    simp [Function.comp]
+  left_inv f := by ext; simp [Function.comp]
+  right_inv m := by ext; simp [Function.comp]
   map_add' := domDomCongr_add σ
 #align alternating_map.dom_dom_congr_equiv AlternatingMap.domDomCongrEquiv
 -/
@@ -1228,9 +1209,7 @@ Case conversion may be inaccurate. Consider using '#align linear_map.comp_multil
 /-- Composition with a linear map before and after alternatization are equivalent. -/
 theorem compMultilinearMap_alternatization (g : N' →ₗ[R] N'₂)
     (f : MultilinearMap R (fun _ : ι => M) N') :
-    (g.compMultilinearMap f).alternatization = g.compAlternatingMap f.alternatization :=
-  by
-  ext
+    (g.compMultilinearMap f).alternatization = g.compAlternatingMap f.alternatization := by ext;
   simp [MultilinearMap.alternatization_def]
 #align linear_map.comp_multilinear_map_alternatization LinearMap.compMultilinearMap_alternatization
 
@@ -1330,9 +1309,7 @@ theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁
   simp only [one_mul, neg_mul, Function.comp_apply, Units.neg_smul, perm.coe_mul, Units.val_neg,
     MultilinearMap.smul_apply, MultilinearMap.neg_apply, MultilinearMap.domDomCongr_apply,
     MultilinearMap.domCoprod_apply]
-  convert add_right_neg _ <;>
-    · ext k
-      rw [Equiv.apply_swap_eq_self hv]
+  convert add_right_neg _ <;> · ext k; rw [Equiv.apply_swap_eq_self hv]
 #align alternating_map.dom_coprod.summand_add_swap_smul_eq_zero AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero
 
 /- warning: alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant -> AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant is a dubious translation:

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Zhangir Azerbayev
 
 ! This file was ported from Lean 3 source module linear_algebra.alternating
-! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
+! leanprover-community/mathlib commit 78fdf68dcd2fdb3fe64c0dd6f88926a49418a6ea
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -59,6 +59,8 @@ variable {M : Type _} [AddCommMonoid M] [Module R M]
 
 variable {N : Type _} [AddCommMonoid N] [Module R N]
 
+variable {P : Type _} [AddCommMonoid P] [Module R P]
+
 -- semiring / add_comm_group
 variable {M' : Type _} [AddCommGroup M'] [Module R M']
 
@@ -223,7 +225,7 @@ theorem coe_multilinearMap_injective :
 /- warning: alternating_map.to_multilinear_map_eq_coe clashes with [anonymous] -> [anonymous]
 warning: alternating_map.to_multilinear_map_eq_coe -> [anonymous] is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u_1}} [_inst_1 : Semiring.{u_1} R] {M : Type.{u_2}} [_inst_2 : AddCommMonoid.{u_2} M] [_inst_3 : Module.{u_1, u_2} R M _inst_1 _inst_2] {N : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} N] [_inst_5 : Module.{u_1, u_3} R N _inst_1 _inst_4] {ι : Type.{u_6}} (f : AlternatingMap.{u_1, u_2, u_3, u_6} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Eq.{max (succ u_6) (succ u_2) (succ u_3)} (MultilinearMap.{u_1, u_2, u_3, u_6} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (AlternatingMap.toMultilinearMap.{u_1, u_2, u_3, u_6} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι f) ((fun (a : Sort.{max (succ u_2) (succ u_3) (succ u_6)}) (b : Sort.{max (succ u_6) (succ u_2) (succ u_3)}) [self : HasLiftT.{max (succ u_2) (succ u_3) (succ u_6), max (succ u_6) (succ u_2) (succ u_3)} a b] => self.0) (AlternatingMap.{u_1, u_2, u_3, u_6} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (MultilinearMap.{u_1, u_2, u_3, u_6} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (HasLiftT.mk.{max (succ u_2) (succ u_3) (succ u_6), max (succ u_6) (succ u_2) (succ u_3)} (AlternatingMap.{u_1, u_2, u_3, u_6} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (MultilinearMap.{u_1, u_2, u_3, u_6} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (CoeTCₓ.coe.{max (succ u_2) (succ u_3) (succ u_6), max (succ u_6) (succ u_2) (succ u_3)} (AlternatingMap.{u_1, u_2, u_3, u_6} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (MultilinearMap.{u_1, u_2, u_3, u_6} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (coeBase.{max (succ u_2) (succ u_3) (succ u_6), max (succ u_6) (succ u_2) (succ u_3)} (AlternatingMap.{u_1, u_2, u_3, u_6} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (MultilinearMap.{u_1, u_2, u_3, u_6} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (AlternatingMap.coe.{u_1, u_2, u_3, u_6} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι)))) f)
+  forall {R : Type.{u_1}} [_inst_1 : Semiring.{u_1} R] {M : Type.{u_2}} [_inst_2 : AddCommMonoid.{u_2} M] [_inst_3 : Module.{u_1, u_2} R M _inst_1 _inst_2] {N : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} N] [_inst_5 : Module.{u_1, u_3} R N _inst_1 _inst_4] {ι : Type.{u_7}} (f : AlternatingMap.{u_1, u_2, u_3, u_7} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Eq.{max (succ u_7) (succ u_2) (succ u_3)} (MultilinearMap.{u_1, u_2, u_3, u_7} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (AlternatingMap.toMultilinearMap.{u_1, u_2, u_3, u_7} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι f) ((fun (a : Sort.{max (succ u_2) (succ u_3) (succ u_7)}) (b : Sort.{max (succ u_7) (succ u_2) (succ u_3)}) [self : HasLiftT.{max (succ u_2) (succ u_3) (succ u_7), max (succ u_7) (succ u_2) (succ u_3)} a b] => self.0) (AlternatingMap.{u_1, u_2, u_3, u_7} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (MultilinearMap.{u_1, u_2, u_3, u_7} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (HasLiftT.mk.{max (succ u_2) (succ u_3) (succ u_7), max (succ u_7) (succ u_2) (succ u_3)} (AlternatingMap.{u_1, u_2, u_3, u_7} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (MultilinearMap.{u_1, u_2, u_3, u_7} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (CoeTCₓ.coe.{max (succ u_2) (succ u_3) (succ u_7), max (succ u_7) (succ u_2) (succ u_3)} (AlternatingMap.{u_1, u_2, u_3, u_7} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (MultilinearMap.{u_1, u_2, u_3, u_7} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (coeBase.{max (succ u_2) (succ u_3) (succ u_7), max (succ u_7) (succ u_2) (succ u_3)} (AlternatingMap.{u_1, u_2, u_3, u_7} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (MultilinearMap.{u_1, u_2, u_3, u_7} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (AlternatingMap.coe.{u_1, u_2, u_3, u_7} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι)))) f)
 but is expected to have type
   forall {R : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> R -> _inst_1) -> Nat -> (List.{u} R) -> (List.{v} _inst_1)
 Case conversion may be inaccurate. Consider using '#align alternating_map.to_multilinear_map_eq_coe [anonymous]ₓ'. -/
@@ -233,10 +235,7 @@ theorem [anonymous] : f.toMultilinearMap = f :=
 #align alternating_map.to_multilinear_map_eq_coe [anonymous]
 
 /- warning: alternating_map.coe_multilinear_map_mk -> AlternatingMap.coe_multilinearMap_mk is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alternating_map.coe_multilinear_map_mk AlternatingMap.coe_multilinearMap_mkₓ'. -/
 @[simp]
 theorem coe_multilinearMap_mk (f : (ι → M) → N) (h₁ h₂ h₃) :
@@ -255,10 +254,7 @@ These are expressed in terms of `⇑f` instead of `f.to_fun`.
 
 
 /- warning: alternating_map.map_add -> AlternatingMap.map_add is a dubious translation:
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 @[simp]
 theorem map_add [DecidableEq ι] (i : ι) (x y : M) :
@@ -267,10 +263,7 @@ theorem map_add [DecidableEq ι] (i : ι) (x y : M) :
 #align alternating_map.map_add AlternatingMap.map_add
 
 /- warning: alternating_map.map_sub -> AlternatingMap.map_sub is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alternating_map.map_sub AlternatingMap.map_subₓ'. -/
 @[simp]
 theorem map_sub [DecidableEq ι] (i : ι) (x y : M') :
@@ -279,10 +272,7 @@ theorem map_sub [DecidableEq ι] (i : ι) (x y : M') :
 #align alternating_map.map_sub AlternatingMap.map_sub
 
 /- warning: alternating_map.map_neg -> AlternatingMap.map_neg is a dubious translation:
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 @[simp]
 theorem map_neg [DecidableEq ι] (i : ι) (x : M') : g' (update v' i (-x)) = -g' (update v' i x) :=
@@ -298,10 +288,7 @@ theorem map_smul [DecidableEq ι] (i : ι) (r : R) (x : M) :
 -/
 
 /- warning: alternating_map.map_eq_zero_of_eq -> AlternatingMap.map_eq_zero_of_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alternating_map.map_eq_zero_of_eq AlternatingMap.map_eq_zero_of_eqₓ'. -/
 @[simp]
 theorem map_eq_zero_of_eq (v : ι → M) {i j : ι} (h : v i = v j) (hij : i ≠ j) : f v = 0 :=
@@ -320,9 +307,9 @@ theorem map_coord_zero {m : ι → M} (i : ι) (h : m i = 0) : f m = 0 :=
 
 /- warning: alternating_map.map_update_zero -> AlternatingMap.map_update_zero is a dubious translation:
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-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) [_inst_10 : DecidableEq.{succ u4} ι] (m : ι -> M) (i : ι), Eq.{succ u3} N (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (Function.update.{succ u4, succ u2} ι (fun (ᾰ : ι) => M) (fun (a : ι) (b : ι) => _inst_10 a b) m i (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))) (OfNat.ofNat.{u3} N 0 (Zero.toOfNat0.{u3} N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) [_inst_12 : DecidableEq.{succ u4} ι] (m : ι -> M) (i : ι), Eq.{succ u3} N (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (Function.update.{succ u4, succ u2} ι (fun (ᾰ : ι) => M) (fun (a : ι) (b : ι) => _inst_12 a b) m i (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))) (OfNat.ofNat.{u3} N 0 (Zero.toOfNat0.{u3} N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4))))
 Case conversion may be inaccurate. Consider using '#align alternating_map.map_update_zero AlternatingMap.map_update_zeroₓ'. -/
 @[simp]
 theorem map_update_zero [DecidableEq ι] (m : ι → M) (i : ι) : f (update m i 0) = 0 :=
@@ -331,9 +318,9 @@ theorem map_update_zero [DecidableEq ι] (m : ι → M) (i : ι) : f (update m i
 
 /- warning: alternating_map.map_zero -> AlternatingMap.map_zero is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) [_inst_12 : Nonempty.{succ u4} ι], Eq.{succ u3} N (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (OfNat.ofNat.{max u4 u2} (ι -> M) 0 (OfNat.mk.{max u4 u2} (ι -> M) 0 (Zero.zero.{max u4 u2} (ι -> M) (Pi.instZero.{u4, u2} ι (fun (ᾰ : ι) => M) (fun (i : ι) => AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))))) (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_4))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) [_inst_10 : Nonempty.{succ u4} ι], Eq.{succ u3} N (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (OfNat.ofNat.{max u2 u4} (ι -> M) 0 (Zero.toOfNat0.{max u2 u4} (ι -> M) (Pi.instZero.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Alternating._hyg.836 : ι) => M) (fun (i : ι) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))) (OfNat.ofNat.{u3} N 0 (Zero.toOfNat0.{u3} N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) [_inst_12 : Nonempty.{succ u4} ι], Eq.{succ u3} N (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (OfNat.ofNat.{max u2 u4} (ι -> M) 0 (Zero.toOfNat0.{max u2 u4} (ι -> M) (Pi.instZero.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Alternating._hyg.836 : ι) => M) (fun (i : ι) => AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))) (OfNat.ofNat.{u3} N 0 (Zero.toOfNat0.{u3} N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4))))
 Case conversion may be inaccurate. Consider using '#align alternating_map.map_zero AlternatingMap.map_zeroₓ'. -/
 @[simp]
 theorem map_zero [Nonempty ι] : f 0 = 0 :=
@@ -372,10 +359,7 @@ instance : SMul S (AlternatingMap R M N ι) :=
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }⟩
 
 /- warning: alternating_map.smul_apply -> AlternatingMap.smul_apply is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.smul_apply AlternatingMap.smul_applyₓ'. -/
 @[simp]
 theorem smul_apply (c : S) (m : ι → M) : (c • f) m = c • f m :=
@@ -383,10 +367,7 @@ theorem smul_apply (c : S) (m : ι → M) : (c • f) m = c • f m :=
 #align alternating_map.smul_apply AlternatingMap.smul_apply
 
 /- warning: alternating_map.coe_smul -> AlternatingMap.coe_smul is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alternating_map.coe_smul AlternatingMap.coe_smulₓ'. -/
 @[norm_cast]
 theorem coe_smul (c : S) :
@@ -395,10 +376,7 @@ theorem coe_smul (c : S) :
 #align alternating_map.coe_smul AlternatingMap.coe_smul
 
 /- warning: alternating_map.coe_fn_smul -> AlternatingMap.coeFn_smul is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alternating_map.coe_fn_smul AlternatingMap.coeFn_smulₓ'. -/
 theorem coeFn_smul (c : S) (f : AlternatingMap R M N ι) : ⇑(c • f) = c • f :=
   rfl
@@ -410,6 +388,52 @@ instance [DistribMulAction Sᵐᵒᵖ N] [IsCentralScalar S N] :
 
 end SMul
 
+/-- The cartesian product of two alternating maps, as a multilinear map. -/
+@[simps (config := { simpRhs := true })]
+def prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) : AlternatingMap R M (N × P) ι :=
+  { f.toMultilinearMap.Prod g.toMultilinearMap with
+    map_eq_zero_of_eq' := fun v i j h hne =>
+      Prod.ext (f.map_eq_zero_of_eq _ h hne) (g.map_eq_zero_of_eq _ h hne) }
+#align alternating_map.prod AlternatingMap.prod
+
+@[simp]
+theorem coe_prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) :
+    (f.Prod g : MultilinearMap R (fun _ : ι => M) (N × P)) = MultilinearMap.prod f g :=
+  rfl
+#align alternating_map.coe_prod AlternatingMap.coe_prod
+
+/-- Combine a family of alternating maps with the same domain and codomains `N i` into an
+alternating map taking values in the space of functions `Π i, N i`. -/
+@[simps (config := { simpRhs := true })]
+def pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
+    (f : ∀ i, AlternatingMap R M (N i) ι) : AlternatingMap R M (∀ i, N i) ι :=
+  { MultilinearMap.pi fun a => (f a).toMultilinearMap with
+    map_eq_zero_of_eq' := fun v i j h hne => funext fun a => (f a).map_eq_zero_of_eq _ h hne }
+#align alternating_map.pi AlternatingMap.pi
+
+@[simp]
+theorem coe_pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
+    (f : ∀ i, AlternatingMap R M (N i) ι) :
+    (pi f : MultilinearMap R (fun _ : ι => M) (∀ i, N i)) = MultilinearMap.pi fun a => f a :=
+  rfl
+#align alternating_map.coe_pi AlternatingMap.coe_pi
+
+/-- Given an alternating `R`-multilinear map `f` taking values in `R`, `f.smul_right z` is the map
+sending `m` to `f m • z`. -/
+@[simps (config := { simpRhs := true })]
+def smulRight {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
+    [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) : AlternatingMap R M₁ M₂ ι :=
+  { f.toMultilinearMap.smul_right z with
+    map_eq_zero_of_eq' := fun v i j h hne => by simp [f.map_eq_zero_of_eq v h hne] }
+#align alternating_map.smul_right AlternatingMap.smulRight
+
+@[simp]
+theorem coe_smulRight {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
+    [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) :
+    (f.smul_right z : MultilinearMap R (fun _ : ι => M₁) M₂) = MultilinearMap.smulRight f z :=
+  rfl
+#align alternating_map.coe_smul_right AlternatingMap.coe_smulRight
+
 instance : Add (AlternatingMap R M N ι) :=
   ⟨fun a b =>
     { (a + b : MultilinearMap R (fun i : ι => M) N) with
@@ -417,10 +441,7 @@ instance : Add (AlternatingMap R M N ι) :=
         simp [a.map_eq_zero_of_eq v h hij, b.map_eq_zero_of_eq v h hij] }⟩
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.add_apply AlternatingMap.add_applyₓ'. -/
 @[simp]
 theorem add_apply : (f + f') v = f v + f' v :=
@@ -477,9 +498,9 @@ instance : Neg (AlternatingMap R M N' ι) :=
 
 /- warning: alternating_map.neg_apply -> AlternatingMap.neg_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alternating_map.neg_apply AlternatingMap.neg_applyₓ'. -/
 @[simp]
 theorem neg_apply (m : ι → M) : (-g) m = -g m :=
@@ -488,9 +509,9 @@ theorem neg_apply (m : ι → M) : (-g) m = -g m :=
 
 /- warning: alternating_map.coe_neg -> AlternatingMap.coe_neg is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_10 : AddCommGroup.{u3} N'] [_inst_11 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10)] {ι : Type.{u4}} (g : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι), Eq.{max (succ u4) (succ u2) (succ u3)} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) ((fun (a : Sort.{max (succ u2) (succ u3) (succ u4)}) (b : Sort.{max (succ u4) (succ u2) (succ u3)}) [self : HasLiftT.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} a b] => self.0) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (HasLiftT.mk.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (CoeTCₓ.coe.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (coeBase.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (AlternatingMap.coe.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι)))) (Neg.neg.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (AlternatingMap.neg.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_10 _inst_11 ι) g)) (Neg.neg.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (MultilinearMap.hasNeg.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_10 (fun (i : ι) => _inst_3) _inst_11) ((fun (a : Sort.{max (succ u2) (succ u3) (succ u4)}) (b : Sort.{max (succ u4) (succ u2) (succ u3)}) [self : HasLiftT.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} a b] => self.0) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (HasLiftT.mk.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (CoeTCₓ.coe.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (coeBase.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (AlternatingMap.coe.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι)))) g))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u1, u4} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u2}} (g : AlternatingMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MultilinearMap.{u1, u4, u3, u2} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.toMultilinearMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι (Neg.neg.{max (max u4 u3) u2} (AlternatingMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.neg.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι) g)) (Neg.neg.{max (max u4 u3) u2} (MultilinearMap.{u1, u4, u3, u2} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.instNegMultilinearMapToAddCommMonoid.{u1, u4, u3, u2} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.toMultilinearMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι g))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u1, u4} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_10 : AddCommGroup.{u3} N'] [_inst_11 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10)] {ι : Type.{u2}} (g : AlternatingMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MultilinearMap.{u1, u4, u3, u2} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (AlternatingMap.toMultilinearMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι (Neg.neg.{max (max u4 u3) u2} (AlternatingMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (AlternatingMap.neg.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N' _inst_10 _inst_11 ι) g)) (Neg.neg.{max (max u4 u3) u2} (MultilinearMap.{u1, u4, u3, u2} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (MultilinearMap.instNegMultilinearMapToAddCommMonoid.{u1, u4, u3, u2} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_10 (fun (i : ι) => _inst_3) _inst_11) (AlternatingMap.toMultilinearMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι g))
 Case conversion may be inaccurate. Consider using '#align alternating_map.coe_neg AlternatingMap.coe_negₓ'. -/
 @[norm_cast]
 theorem coe_neg : ((-g : AlternatingMap R M N' ι) : MultilinearMap R (fun i : ι => M) N') = -g :=
@@ -504,10 +525,7 @@ instance : Sub (AlternatingMap R M N' ι) :=
         simp [f.map_eq_zero_of_eq v h hij, g.map_eq_zero_of_eq v h hij] }⟩
 
 /- warning: alternating_map.sub_apply -> AlternatingMap.sub_apply is a dubious translation:
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 @[simp]
 theorem sub_apply (m : ι → M) : (g - g₂) m = g m - g₂ m :=
@@ -515,10 +533,7 @@ theorem sub_apply (m : ι → M) : (g - g₂) m = g m - g₂ m :=
 #align alternating_map.sub_apply AlternatingMap.sub_apply
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.coe_sub AlternatingMap.coe_subₓ'. -/
 @[norm_cast]
 theorem coe_sub : (↑(g - g₂) : MultilinearMap R (fun i : ι => M) N') = g - g₂ :=
@@ -630,10 +645,7 @@ def compAlternatingMap (g : N →ₗ[R] N₂) : AlternatingMap R M N ι →+ Alt
 -/
 
 /- warning: linear_map.coe_comp_alternating_map -> LinearMap.coe_compAlternatingMap is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_map.coe_comp_alternating_map LinearMap.coe_compAlternatingMapₓ'. -/
 @[simp]
 theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) :
@@ -642,10 +654,7 @@ theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : AlternatingMap R M N
 #align linear_map.coe_comp_alternating_map LinearMap.coe_compAlternatingMap
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.comp_alternating_map_apply LinearMap.compAlternatingMap_applyₓ'. -/
 @[simp]
 theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) (m : ι → M) :
@@ -653,11 +662,14 @@ theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : AlternatingMap R M
   rfl
 #align linear_map.comp_alternating_map_apply LinearMap.compAlternatingMap_apply
 
+theorem smulRight_eq_comp {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁]
+    [AddCommMonoid M₂] [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) :
+    f.smul_right z = (LinearMap.id.smul_right z).compAlternatingMap f :=
+  rfl
+#align linear_map.smul_right_eq_comp LinearMap.smulRight_eq_comp
+
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.subtype_comp_alternating_map_cod_restrict LinearMap.subtype_compAlternatingMap_codRestrictₓ'. -/
 @[simp]
 theorem subtype_compAlternatingMap_codRestrict (f : AlternatingMap R M N ι) (p : Submodule R N)
@@ -666,10 +678,7 @@ theorem subtype_compAlternatingMap_codRestrict (f : AlternatingMap R M N ι) (p
 #align linear_map.subtype_comp_alternating_map_cod_restrict LinearMap.subtype_compAlternatingMap_codRestrict
 
 /- warning: linear_map.comp_alternating_map_cod_restrict -> LinearMap.compAlternatingMap_codRestrict is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_map.comp_alternating_map_cod_restrict LinearMap.compAlternatingMap_codRestrictₓ'. -/
 @[simp]
 theorem compAlternatingMap_codRestrict (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι)
@@ -697,10 +706,7 @@ def compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) : Alterna
 -/
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.coe_comp_linear_map AlternatingMap.coe_compLinearMapₓ'. -/
 theorem coe_compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
     ⇑(f.compLinearMap g) = f ∘ (· ∘ ·) g :=
@@ -708,10 +714,7 @@ theorem coe_compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
 #align alternating_map.coe_comp_linear_map AlternatingMap.coe_compLinearMap
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_apply AlternatingMap.compLinearMap_applyₓ'. -/
 @[simp]
 theorem compLinearMap_apply (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) (v : ι → M₂) :
@@ -720,10 +723,7 @@ theorem compLinearMap_apply (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M)
 #align alternating_map.comp_linear_map_apply AlternatingMap.compLinearMap_apply
 
 /- warning: alternating_map.comp_linear_map_assoc -> AlternatingMap.compLinearMap_assoc is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_assoc AlternatingMap.compLinearMap_assocₓ'. -/
 /-- Composing an alternating map twice with the same linear map in each argument is
 the same as composing with their composition. -/
@@ -734,9 +734,9 @@ theorem compLinearMap_assoc (f : AlternatingMap R M N ι) (g₁ : M₂ →ₗ[R]
 
 /- warning: alternating_map.zero_comp_linear_map -> AlternatingMap.zero_compLinearMap is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alternating_map.zero_comp_linear_map AlternatingMap.zero_compLinearMapₓ'. -/
 @[simp]
 theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : AlternatingMap R M N ι).compLinearMap g = 0 :=
@@ -746,10 +746,7 @@ theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : AlternatingMap R M N ι
 #align alternating_map.zero_comp_linear_map AlternatingMap.zero_compLinearMap
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.add_comp_linear_map AlternatingMap.add_compLinearMapₓ'. -/
 @[simp]
 theorem add_compLinearMap (f₁ f₂ : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
@@ -760,10 +757,7 @@ theorem add_compLinearMap (f₁ f₂ : AlternatingMap R M N ι) (g : M₂ →ₗ
 #align alternating_map.add_comp_linear_map AlternatingMap.add_compLinearMap
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_zero AlternatingMap.compLinearMap_zeroₓ'. -/
 @[simp]
 theorem compLinearMap_zero [Nonempty ι] (f : AlternatingMap R M N ι) :
@@ -785,10 +779,7 @@ theorem compLinearMap_id (f : AlternatingMap R M N ι) : f.compLinearMap LinearM
 #align alternating_map.comp_linear_map_id AlternatingMap.compLinearMap_id
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_injective AlternatingMap.compLinearMap_injectiveₓ'. -/
 /-- Composing with a surjective linear map is injective. -/
 theorem compLinearMap_injective (f : M₂ →ₗ[R] M) (hf : Function.Surjective f) :
@@ -797,10 +788,7 @@ theorem compLinearMap_injective (f : M₂ →ₗ[R] M) (hf : Function.Surjective
 #align alternating_map.comp_linear_map_injective AlternatingMap.compLinearMap_injective
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_inj AlternatingMap.compLinearMap_injₓ'. -/
 theorem compLinearMap_inj (f : M₂ →ₗ[R] M) (hf : Function.Surjective f)
     (g₁ g₂ : AlternatingMap R M N ι) : g₁.compLinearMap f = g₂.compLinearMap f ↔ g₁ = g₂ :=
@@ -826,10 +814,7 @@ def domLCongr (e : M ≃ₗ[R] M₂) : AlternatingMap R M N ι ≃ₗ[S] Alterna
 -/
 
 /- warning: alternating_map.dom_lcongr_refl -> AlternatingMap.domLCongr_refl is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_lcongr_refl AlternatingMap.domLCongr_reflₓ'. -/
 @[simp]
 theorem domLCongr_refl : domLCongr R N ι S (LinearEquiv.refl R M) = LinearEquiv.refl S _ :=
@@ -837,10 +822,7 @@ theorem domLCongr_refl : domLCongr R N ι S (LinearEquiv.refl R M) = LinearEquiv
 #align alternating_map.dom_lcongr_refl AlternatingMap.domLCongr_refl
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_lcongr_symm AlternatingMap.domLCongr_symmₓ'. -/
 @[simp]
 theorem domLCongr_symm (e : M ≃ₗ[R] M₂) : (domLCongr R N ι S e).symm = domLCongr R N ι S e.symm :=
@@ -848,10 +830,7 @@ theorem domLCongr_symm (e : M ≃ₗ[R] M₂) : (domLCongr R N ι S e).symm = do
 #align alternating_map.dom_lcongr_symm AlternatingMap.domLCongr_symm
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_lcongr_trans AlternatingMap.domLCongr_transₓ'. -/
 theorem domLCongr_trans (e : M ≃ₗ[R] M₂) (f : M₂ ≃ₗ[R] M₃) :
     (domLCongr R N ι S e).trans (domLCongr R N ι S f) = domLCongr R N ι S (e.trans f) :=
@@ -861,10 +840,7 @@ theorem domLCongr_trans (e : M ≃ₗ[R] M₂) (f : M₂ ≃ₗ[R] M₃) :
 end DomLcongr
 
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 /-- Composing an alternating map with the same linear equiv on each argument gives the zero map
 if and only if the alternating map is the zero map. -/
@@ -911,10 +887,7 @@ Various properties of reordered and repeated inputs which follow from
 
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.map_update_self AlternatingMap.map_update_selfₓ'. -/
 theorem map_update_self [DecidableEq ι] {i j : ι} (hij : i ≠ j) :
     f (Function.update v i (v j)) = 0 :=
@@ -922,10 +895,7 @@ theorem map_update_self [DecidableEq ι] {i j : ι} (hij : i ≠ j) :
 #align alternating_map.map_update_self AlternatingMap.map_update_self
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.map_update_update AlternatingMap.map_update_updateₓ'. -/
 theorem map_update_update [DecidableEq ι] {i j : ι} (hij : i ≠ j) (m : M) :
     f (Function.update (Function.update v i m) j m) = 0 :=
@@ -934,10 +904,7 @@ theorem map_update_update [DecidableEq ι] {i j : ι} (hij : i ≠ j) (m : M) :
 #align alternating_map.map_update_update AlternatingMap.map_update_update
 
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 theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equiv.swap i j) + f v = 0 :=
   by
@@ -948,10 +915,7 @@ theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equi
 #align alternating_map.map_swap_add AlternatingMap.map_swap_add
 
 /- warning: alternating_map.map_add_swap -> AlternatingMap.map_add_swap is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alternating_map.map_add_swap AlternatingMap.map_add_swapₓ'. -/
 theorem map_add_swap [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f v + f (v ∘ Equiv.swap i j) = 0 :=
   by
@@ -977,10 +941,7 @@ theorem map_perm [DecidableEq ι] [Fintype ι] (v : ι → M) (σ : Equiv.Perm 
 -/
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.map_congr_perm AlternatingMap.map_congr_permₓ'. -/
 theorem map_congr_perm [DecidableEq ι] [Fintype ι] (σ : Equiv.Perm ι) : g v = σ.sign • g (v ∘ σ) :=
   by
@@ -1039,10 +1000,7 @@ theorem domDomCongr_zero (σ : ι ≃ ι') : (0 : AlternatingMap R M N ι).domDo
 #align alternating_map.dom_dom_congr_zero AlternatingMap.domDomCongr_zero
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_dom_congr_add AlternatingMap.domDomCongr_addₓ'. -/
 @[simp]
 theorem domDomCongr_add (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
@@ -1095,10 +1053,7 @@ theorem domDomCongr_eq_zero_iff (σ : ι ≃ ι') (f : AlternatingMap R M N ι)
 #align alternating_map.dom_dom_congr_eq_zero_iff AlternatingMap.domDomCongr_eq_zero_iff
 
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 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_dom_congr_perm AlternatingMap.domDomCongr_permₓ'. -/
 theorem domDomCongr_perm [Fintype ι] [DecidableEq ι] (σ : Equiv.Perm ι) :
     g.domDomCongr σ = σ.sign • g :=
@@ -1120,10 +1075,7 @@ theorem coe_domDomCongr (σ : ι ≃ ι') :
 end DomDomCongr
 
 /- warning: alternating_map.map_linear_dependent -> AlternatingMap.map_linearDependent is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alternating_map.map_linear_dependent AlternatingMap.map_linearDependentₓ'. -/
 /-- If the arguments are linearly dependent then the result is `0`. -/
 theorem map_linearDependent {K : Type _} [Ring K] {M : Type _} [AddCommGroup M] [Module K M]
@@ -1150,10 +1102,7 @@ section Fin
 open Fin
 
 /- warning: alternating_map.map_vec_cons_add -> AlternatingMap.map_vecCons_add is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alternating_map.map_vec_cons_add AlternatingMap.map_vecCons_addₓ'. -/
 /-- A version of `multilinear_map.cons_add` for `alternating_map`. -/
 theorem map_vecCons_add {n : ℕ} (f : AlternatingMap R M N (Fin n.succ)) (m : Fin n → M) (x y : M) :
@@ -1195,13 +1144,12 @@ private theorem alternization_map_eq_zero_of_eq_aux (m : MultilinearMap R (fun i
       (fun σ _ => by simp [perm.sign_swap i_ne_j, apply_swap_eq_self hv])
       (fun σ _ _ => (not_congr swap_mul_eq_iff).mpr i_ne_j) (fun σ _ => Finset.mem_univ _)
       fun σ _ => swap_mul_involutive i j σ
-#align multilinear_map.alternization_map_eq_zero_of_eq_aux multilinear_map.alternization_map_eq_zero_of_eq_aux
 
 /- warning: multilinear_map.alternatization -> MultilinearMap.alternatization is a dubious translation:
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 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} [_inst_10 : Fintype.{u4} ι] [_inst_11 : DecidableEq.{succ u4} ι], AddMonoidHom.{max (max u4 u3) u2, max (max u4 u3) u2} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max (max u2 u3) u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max (max u2 u3) u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max (max u2 u3) u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max (max u2 u3) u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u2 u3) u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u2 u3) u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_10 : AddCommGroup.{u3} N'] [_inst_11 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10)] {ι : Type.{u4}} [_inst_12 : Fintype.{u4} ι] [_inst_13 : DecidableEq.{succ u4} ι], AddMonoidHom.{max (max u4 u3) u2, max (max u4 u3) u2} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (SubNegMonoid.toAddMonoid.{max (max u2 u3) u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (AddGroup.toSubNegMonoid.{max (max u2 u3) u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (AddCommGroup.toAddGroup.{max (max u2 u3) u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) (fun (i : ι) => _inst_3) _inst_11) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_10 (fun (i : ι) => _inst_3) _inst_11))))) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (SubNegMonoid.toAddMonoid.{max (max u2 u3) u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (AddGroup.toSubNegMonoid.{max (max u2 u3) u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (AddCommGroup.toAddGroup.{max (max u2 u3) u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_10) _inst_11 ι) (AlternatingMap.addCommGroup.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_10 _inst_11 ι)))))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization MultilinearMap.alternatizationₓ'. -/
 /-- Produce an `alternating_map` out of a `multilinear_map`, by summing over all argument
 permutations. -/
@@ -1227,10 +1175,7 @@ def alternatization : MultilinearMap R (fun i : ι => M) N' →+ AlternatingMap
 #align multilinear_map.alternatization MultilinearMap.alternatization
 
 /- warning: multilinear_map.alternatization_def -> MultilinearMap.alternatization_def is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_def MultilinearMap.alternatization_defₓ'. -/
 theorem alternatization_def (m : MultilinearMap R (fun i : ι => M) N') :
     ⇑(alternatization m) = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
@@ -1238,10 +1183,7 @@ theorem alternatization_def (m : MultilinearMap R (fun i : ι => M) N') :
 #align multilinear_map.alternatization_def MultilinearMap.alternatization_def
 
 /- warning: multilinear_map.alternatization_coe -> MultilinearMap.alternatization_coe is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_coe MultilinearMap.alternatization_coeₓ'. -/
 theorem alternatization_coe (m : MultilinearMap R (fun i : ι => M) N') :
     ↑m.alternatization = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
@@ -1249,10 +1191,7 @@ theorem alternatization_coe (m : MultilinearMap R (fun i : ι => M) N') :
 #align multilinear_map.alternatization_coe MultilinearMap.alternatization_coe
 
 /- warning: multilinear_map.alternatization_apply -> MultilinearMap.alternatization_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_apply MultilinearMap.alternatization_applyₓ'. -/
 theorem alternatization_apply (m : MultilinearMap R (fun i : ι => M) N') (v : ι → M) :
     alternatization m v = ∑ σ : Perm ι, σ.sign • m.domDomCongr σ v := by
@@ -1264,10 +1203,7 @@ end MultilinearMap
 namespace AlternatingMap
 
 /- warning: alternating_map.coe_alternatization -> AlternatingMap.coe_alternatization is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.coe_alternatization AlternatingMap.coe_alternatizationₓ'. -/
 /-- Alternatizing a multilinear map that is already alternating results in a scale factor of `n!`,
 where `n` is the number of inputs. -/
@@ -1287,10 +1223,7 @@ namespace LinearMap
 variable {N'₂ : Type _} [AddCommGroup N'₂] [Module R N'₂] [DecidableEq ι] [Fintype ι]
 
 /- warning: linear_map.comp_multilinear_map_alternatization -> LinearMap.compMultilinearMap_alternatization is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.comp_multilinear_map_alternatization LinearMap.compMultilinearMap_alternatizationₓ'. -/
 /-- Composition with a linear map before and after alternatization are equivalent. -/
 theorem compMultilinearMap_alternatization (g : N' →ₗ[R] N'₂)
@@ -1325,9 +1258,9 @@ abbrev ModSumCongr (α β : Type _) :=
 
 /- warning: equiv.perm.mod_sum_congr.swap_smul_involutive -> Equiv.Perm.ModSumCongr.swap_smul_involutive is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_19 : DecidableEq.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)] (i : Sum.{u1, u2} α β) (j : Sum.{u1, u2} α β), Function.Involutive.{succ (max u1 u2)} (Equiv.Perm.ModSumCongr.{u1, u2} α β) (SMul.smul.{max u1 u2, max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.ModSumCongr.{u1, u2} α β) (MulAction.toHasSmul.{max u1 u2, max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.ModSumCongr.{u1, u2} α β) (DivInvMonoid.toMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Group.toDivInvMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β)))) (MulAction.quotient.{max u1 u2, max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β)) (DivInvMonoid.toMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Group.toDivInvMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β)))) (Monoid.toMulAction.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (DivInvMonoid.toMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Group.toDivInvMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β))))) (MonoidHom.range.{max u1 u2, max u1 u2} (Prod.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β)) (Prod.group.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u1} α) (Equiv.Perm.permGroup.{u2} β)) (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β)) (Equiv.Perm.sumCongrHom.{u1, u2} α β)) (MulAction.left_quotientAction.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β)) (MonoidHom.range.{max u1 u2, max u1 u2} (Prod.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β)) (Prod.group.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u1} α) (Equiv.Perm.permGroup.{u2} β)) (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β)) (Equiv.Perm.sumCongrHom.{u1, u2} α β))))) (Equiv.swap.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β) (fun (a : Sum.{u1, u2} α β) (b : Sum.{u1, u2} α β) => _inst_19 a b) i j))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_21 : DecidableEq.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)] (i : Sum.{u1, u2} α β) (j : Sum.{u1, u2} α β), Function.Involutive.{succ (max u1 u2)} (Equiv.Perm.ModSumCongr.{u1, u2} α β) (SMul.smul.{max u1 u2, max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.ModSumCongr.{u1, u2} α β) (MulAction.toHasSmul.{max u1 u2, max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.ModSumCongr.{u1, u2} α β) (DivInvMonoid.toMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Group.toDivInvMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β)))) (MulAction.quotient.{max u1 u2, max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β)) (DivInvMonoid.toMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Group.toDivInvMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β)))) (Monoid.toMulAction.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (DivInvMonoid.toMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Group.toDivInvMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β))))) (MonoidHom.range.{max u1 u2, max u1 u2} (Prod.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β)) (Prod.group.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u1} α) (Equiv.Perm.permGroup.{u2} β)) (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β)) (Equiv.Perm.sumCongrHom.{u1, u2} α β)) (MulAction.left_quotientAction.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β)) (MonoidHom.range.{max u1 u2, max u1 u2} (Prod.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β)) (Prod.group.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u1} α) (Equiv.Perm.permGroup.{u2} β)) (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} α β)) (Equiv.Perm.sumCongrHom.{u1, u2} α β))))) (Equiv.swap.{max (succ u1) (succ u2)} (Sum.{u1, u2} α β) (fun (a : Sum.{u1, u2} α β) (b : Sum.{u1, u2} α β) => _inst_21 a b) i j))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_19 : DecidableEq.{max (succ u1) (succ u2)} (Sum.{u2, u1} α β)] (i : Sum.{u2, u1} α β) (j : Sum.{u2, u1} α β), Function.Involutive.{max (succ u2) (succ u1)} (Equiv.Perm.ModSumCongr.{u2, u1} α β) (SMul.smul.{max u2 u1, max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Equiv.Perm.ModSumCongr.{u2, u1} α β) (MulAction.toSMul.{max u2 u1, max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Equiv.Perm.ModSumCongr.{u2, u1} α β) (DivInvMonoid.toMonoid.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Group.toDivInvMonoid.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β)))) (MulAction.quotient.{max u2 u1, max u2 u1} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u2, u1} α β)) (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β)) (DivInvMonoid.toMonoid.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Group.toDivInvMonoid.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β)))) (Monoid.toMulAction.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (DivInvMonoid.toMonoid.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Group.toDivInvMonoid.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β))))) (MonoidHom.range.{max u2 u1, max u2 u1} (Prod.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β)) (Prod.instGroupProd.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u2} α) (Equiv.Perm.permGroup.{u1} β)) (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β)) (Equiv.Perm.sumCongrHom.{u2, u1} α β)) (MulAction.left_quotientAction.{max u2 u1} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β)) (MonoidHom.range.{max u2 u1, max u2 u1} (Prod.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β)) (Prod.instGroupProd.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u2} α) (Equiv.Perm.permGroup.{u1} β)) (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β)) (Equiv.Perm.sumCongrHom.{u2, u1} α β))))) (Equiv.swap.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β) (fun (a : Sum.{u2, u1} α β) (b : Sum.{u2, u1} α β) => _inst_19 a b) i j))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_21 : DecidableEq.{max (succ u1) (succ u2)} (Sum.{u2, u1} α β)] (i : Sum.{u2, u1} α β) (j : Sum.{u2, u1} α β), Function.Involutive.{max (succ u2) (succ u1)} (Equiv.Perm.ModSumCongr.{u2, u1} α β) (SMul.smul.{max u2 u1, max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Equiv.Perm.ModSumCongr.{u2, u1} α β) (MulAction.toSMul.{max u2 u1, max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Equiv.Perm.ModSumCongr.{u2, u1} α β) (DivInvMonoid.toMonoid.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Group.toDivInvMonoid.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β)))) (MulAction.quotient.{max u2 u1, max u2 u1} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u2, u1} α β)) (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β)) (DivInvMonoid.toMonoid.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Group.toDivInvMonoid.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β)))) (Monoid.toMulAction.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (DivInvMonoid.toMonoid.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Group.toDivInvMonoid.{max u2 u1} (Equiv.Perm.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β))))) (MonoidHom.range.{max u2 u1, max u2 u1} (Prod.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β)) (Prod.instGroupProd.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u2} α) (Equiv.Perm.permGroup.{u1} β)) (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β)) (Equiv.Perm.sumCongrHom.{u2, u1} α β)) (MulAction.left_quotientAction.{max u2 u1} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β)) (MonoidHom.range.{max u2 u1, max u2 u1} (Prod.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β)) (Prod.instGroupProd.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u2} α) (Equiv.Perm.permGroup.{u1} β)) (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u2, u1} α β)) (Equiv.Perm.permGroup.{max u2 u1} (Sum.{u2, u1} α β)) (Equiv.Perm.sumCongrHom.{u2, u1} α β))))) (Equiv.swap.{max (succ u2) (succ u1)} (Sum.{u2, u1} α β) (fun (a : Sum.{u2, u1} α β) (b : Sum.{u2, u1} α β) => _inst_21 a b) i j))
 Case conversion may be inaccurate. Consider using '#align equiv.perm.mod_sum_congr.swap_smul_involutive Equiv.Perm.ModSumCongr.swap_smul_involutiveₓ'. -/
 theorem ModSumCongr.swap_smul_involutive {α β : Type _} [DecidableEq (Sum α β)] (i j : Sum α β) :
     Function.Involutive (SMul.smul (Equiv.swap i j) : ModSumCongr α β → ModSumCongr α β) := fun σ =>
@@ -1345,10 +1278,7 @@ open Equiv
 variable [DecidableEq ιa] [DecidableEq ιb]
 
 /- warning: alternating_map.dom_coprod.summand -> AlternatingMap.domCoprod.summand is a dubious translation:
-lean 3 declaration is
-  forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb], (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) -> (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) -> (Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) -> (MultilinearMap.{u3, u4, max u5 u6, max u1 u2} R' (Sum.{u1, u2} ιa ιb) (fun (_x : Sum.{u1, u2} ιa ιb) => Mᵢ) (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_17) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_18) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16))
-but is expected to have type
-  forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb], (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) -> (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) -> (Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) -> (MultilinearMap.{u3, u4, max u6 u5, max u1 u2} R' (Sum.{u1, u2} ιa ιb) (fun (_x : Sum.{u1, u2} ιa ιb) => Mᵢ) (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_17) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_18) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16))
+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand AlternatingMap.domCoprod.summandₓ'. -/
 /-- summand used in `alternating_map.dom_coprod` -/
 def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
@@ -1373,10 +1303,7 @@ def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap
 #align alternating_map.dom_coprod.summand AlternatingMap.domCoprod.summand
 
 /- warning: alternating_map.dom_coprod.summand_mk' -> AlternatingMap.domCoprod.summand_mk'' is a dubious translation:
-lean 3 declaration is
-  forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_mk' AlternatingMap.domCoprod.summand_mk''ₓ'. -/
 theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
     (σ : Equiv.Perm (Sum ιa ιb)) :
@@ -1388,10 +1315,7 @@ theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : Altern
 #align alternating_map.dom_coprod.summand_mk' AlternatingMap.domCoprod.summand_mk''
 
 /- warning: alternating_map.dom_coprod.summand_add_swap_smul_eq_zero -> AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_add_swap_smul_eq_zero AlternatingMap.domCoprod.summand_add_swap_smul_eq_zeroₓ'. -/
 /-- Swapping elements in `σ` with equal values in `v` results in an addition that cancels -/
 theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁ ιa)
@@ -1412,10 +1336,7 @@ theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁
 #align alternating_map.dom_coprod.summand_add_swap_smul_eq_zero AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero
 
 /- warning: alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant -> AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariantₓ'. -/
 /-- Swapping elements in `σ` with equal values in `v` result in zero if the swap has no effect
 on the quotient. -/
@@ -1453,10 +1374,7 @@ theorem domCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ
 #align alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant
 
 /- warning: alternating_map.dom_coprod -> AlternatingMap.domCoprod is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod AlternatingMap.domCoprodₓ'. -/
 /-- Like `multilinear_map.dom_coprod`, but ensures the result is also alternating.
 
@@ -1498,10 +1416,7 @@ def domCoprod (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ
 #align alternating_map.dom_coprod AlternatingMap.domCoprod
 
 /- warning: alternating_map.dom_coprod_coe -> AlternatingMap.domCoprod_coe is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod_coe AlternatingMap.domCoprod_coeₓ'. -/
 theorem domCoprod_coe (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
     (↑(a.domCoprod b) : MultilinearMap R' (fun _ => Mᵢ) _) =
@@ -1535,10 +1450,7 @@ def domCoprod' :
 -/
 
 /- warning: alternating_map.dom_coprod'_apply -> AlternatingMap.domCoprod'_apply is a dubious translation:
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_inst_14 _inst_16) (Sum.{u1, u2} ιa ιb) R' (CommSemiring.toSemiring.{u3} R' _inst_12) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (AlternatingMap.domCoprod'._proof_3.{u3, u5, u6} R' N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16))) => (TensorProduct.{u3, max u4 u5 u1, max u4 u6 u2} R' _inst_12 (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u3, u4, u6, u2} R' 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u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (fun (_x : TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) => AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, max (max (max (max u2 u4) u5) u1) u3, max (max (max (max u2 u4) u5) u1) u3} R' R' (TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) (CommSemiring.toSemiring.{u6} R' _inst_12) (CommSemiring.toSemiring.{u6} R' _inst_12) (TensorProduct.addCommMonoid.{u6, max (max u3 u5) u4, max (max u1 u5) u2} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.addCommMonoid.{u6, u5, max u4 u2, max u3 u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ 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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod'_apply AlternatingMap.domCoprod'_applyₓ'. -/
 @[simp]
 theorem domCoprod'_apply (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
@@ -1551,10 +1463,7 @@ end AlternatingMap
 open Equiv
 
 /- warning: multilinear_map.dom_coprod_alternization_coe -> MultilinearMap.domCoprod_alternization_coe is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_alternization_coe MultilinearMap.domCoprod_alternization_coeₓ'. -/
 /-- A helper lemma for `multilinear_map.dom_coprod_alternization`. -/
 theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableEq ιb]
@@ -1571,10 +1480,7 @@ theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableE
 open AlternatingMap
 
 /- warning: multilinear_map.dom_coprod_alternization -> MultilinearMap.domCoprod_alternization is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_alternization MultilinearMap.domCoprod_alternizationₓ'. -/
 /-- Computing the `multilinear_map.alternatization` of the `multilinear_map.dom_coprod` is the same
 as computing the `alternating_map.dom_coprod` of the `multilinear_map.alternatization`s.
@@ -1616,10 +1522,7 @@ theorem MultilinearMap.domCoprod_alternization [DecidableEq ιa] [DecidableEq ι
 #align multilinear_map.dom_coprod_alternization MultilinearMap.domCoprod_alternization
 
 /- warning: multilinear_map.dom_coprod_alternization_eq -> MultilinearMap.domCoprod_alternization_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_alternization_eq MultilinearMap.domCoprod_alternization_eqₓ'. -/
 /-- Taking the `multilinear_map.alternatization` of the `multilinear_map.dom_coprod` of two
 `alternating_map`s gives a scaled version of the `alternating_map.coprod` of those maps.
@@ -1651,10 +1554,7 @@ variable {R' : Type _} {N₁ N₂ : Type _} [CommSemiring R'] [AddCommMonoid N
 variable [Module R' N₁] [Module R' N₂]
 
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 Case conversion may be inaccurate. Consider using '#align basis.ext_alternating Basis.ext_alternatingₓ'. -/
 /-- Two alternating maps indexed by a `fintype` are equal if they are equal when all arguments
 are distinct basis vectors. -/
@@ -1708,10 +1608,7 @@ def curryLeft {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ)) :
 -/
 
 /- warning: alternating_map.curry_left_zero -> AlternatingMap.curryLeft_zero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_zero AlternatingMap.curryLeft_zeroₓ'. -/
 @[simp]
 theorem curryLeft_zero {n : ℕ} : curryLeft (0 : AlternatingMap R' M'' N'' (Fin n.succ)) = 0 :=
@@ -1719,10 +1616,7 @@ theorem curryLeft_zero {n : ℕ} : curryLeft (0 : AlternatingMap R' M'' N'' (Fin
 #align alternating_map.curry_left_zero AlternatingMap.curryLeft_zero
 
 /- warning: alternating_map.curry_left_add -> AlternatingMap.curryLeft_add is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_add AlternatingMap.curryLeft_addₓ'. -/
 @[simp]
 theorem curryLeft_add {n : ℕ} (f g : AlternatingMap R' M'' N'' (Fin n.succ)) :
@@ -1731,10 +1625,7 @@ theorem curryLeft_add {n : ℕ} (f g : AlternatingMap R' M'' N'' (Fin n.succ)) :
 #align alternating_map.curry_left_add AlternatingMap.curryLeft_add
 
 /- warning: alternating_map.curry_left_smul -> AlternatingMap.curryLeft_smul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_smul AlternatingMap.curryLeft_smulₓ'. -/
 @[simp]
 theorem curryLeft_smul {n : ℕ} (r : R') (f : AlternatingMap R' M'' N'' (Fin n.succ)) :
@@ -1756,10 +1647,7 @@ def curryLeftLinearMap {n : ℕ} :
 -/
 
 /- warning: alternating_map.curry_left_same -> AlternatingMap.curryLeft_same is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_same AlternatingMap.curryLeft_sameₓ'. -/
 /-- Currying with the same element twice gives the zero map. -/
 @[simp]
@@ -1769,10 +1657,7 @@ theorem curryLeft_same {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ.succ
 #align alternating_map.curry_left_same AlternatingMap.curryLeft_same
 
 /- warning: alternating_map.curry_left_comp_alternating_map -> AlternatingMap.curryLeft_compAlternatingMap is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_comp_alternating_map AlternatingMap.curryLeft_compAlternatingMapₓ'. -/
 @[simp]
 theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
@@ -1782,10 +1667,7 @@ theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
 #align alternating_map.curry_left_comp_alternating_map AlternatingMap.curryLeft_compAlternatingMap
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_comp_linear_map AlternatingMap.curryLeft_compLinearMapₓ'. -/
 @[simp]
 theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')

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

@@ -633,7 +633,7 @@ def compAlternatingMap (g : N →ₗ[R] N₂) : AlternatingMap R M N ι →+ Alt
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {N₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} N₂] [_inst_11 : Module.{u1, u5} R N₂ _inst_1 _inst_10] (g : LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Eq.{max (max (succ u4) (succ u2)) (succ u5)} ((ι -> M) -> N₂) (coeFn.{max (succ u2) (succ u5) (succ u4), max (max (succ u4) (succ u2)) (succ u5)} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (fun (_x : AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) => (ι -> M) -> N₂) (AlternatingMap.coeFun.{u1, u2, u5, u4} R 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u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (fun (_x : AddMonoidHom.{max u2 u3 u4, max u2 u5 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) => (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) -> (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)) (AddMonoidHom.hasCoeToFun.{max u2 u3 u4, max u2 u5 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (LinearMap.compAlternatingMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι N₂ _inst_10 _inst_11 g) f)) (Function.comp.{max (succ u4) (succ u2), succ u3, succ u5} (ι -> M) N N₂ (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (fun (_x : LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) => N -> N₂) (LinearMap.hasCoeToFun.{u1, u1, u3, u5} R R N N₂ _inst_1 _inst_1 _inst_4 _inst_10 _inst_5 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) g) (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 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 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u5, u2} R M _inst_1 _inst_2] {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u5, u4} R N _inst_1 _inst_4] {ι : Type.{u1}} {N₂ : Type.{u3}} [_inst_10 : AddCommMonoid.{u3} N₂] [_inst_11 : Module.{u5, u3} R N₂ _inst_1 _inst_10] (g : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (f : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Eq.{max (max (succ u2) (succ u1)) (succ u3)} ((ι -> M) -> N₂) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (ι -> M) (fun (_x : ι -> M) => N₂) (AlternatingMap.funLike.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (FunLike.coe.{max (max 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_inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))))) (LinearMap.compAlternatingMap.{u5, u2, u4, u1, u3} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι N₂ _inst_10 _inst_11 g) f)) (Function.comp.{max (succ u2) (succ u1), succ u4, succ u3} (ι -> M) N N₂ (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => N₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R N N₂ _inst_1 _inst_1 _inst_4 _inst_10 _inst_5 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u1), max (succ u2) (succ u1), succ u4} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f))
 Case conversion may be inaccurate. Consider using '#align linear_map.coe_comp_alternating_map LinearMap.coe_compAlternatingMapₓ'. -/
 @[simp]
 theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) :
@@ -645,7 +645,7 @@ theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : AlternatingMap R M N
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {N₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} N₂] [_inst_11 : Module.{u1, u5} R N₂ _inst_1 _inst_10] (g : LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (m : ι -> M), Eq.{succ u5} N₂ (coeFn.{max (succ u2) (succ u5) (succ u4), max (max (succ u4) (succ u2)) (succ u5)} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (fun (_x : AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) => (ι -> M) -> N₂) (AlternatingMap.coeFun.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (coeFn.{max (succ (max u2 u5 u4)) (succ (max u2 u3 u4)), max (succ (max u2 u3 u4)) (succ (max u2 u5 u4))} (AddMonoidHom.{max u2 u3 u4, max u2 u5 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (fun (_x : AddMonoidHom.{max u2 u3 u4, max u2 u5 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) => (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) -> (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)) (AddMonoidHom.hasCoeToFun.{max u2 u3 u4, max u2 u5 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (LinearMap.compAlternatingMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι N₂ _inst_10 _inst_11 g) f) m) (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (fun (_x : LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) => N -> N₂) (LinearMap.hasCoeToFun.{u1, u1, u3, u5} R R N N₂ _inst_1 _inst_1 _inst_4 _inst_10 _inst_5 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) g (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f m))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u5, u2} R M _inst_1 _inst_2] {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u5, u4} R N _inst_1 _inst_4] {ι : Type.{u1}} {N₂ : Type.{u3}} [_inst_10 : AddCommMonoid.{u3} N₂] [_inst_11 : Module.{u5, u3} R N₂ _inst_1 _inst_10] (g : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (f : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (m : ι -> M), Eq.{succ u3} N₂ (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (ι -> M) (fun (_x : ι -> M) => N₂) (AlternatingMap.funLike.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ 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_inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) _x) (AddHomClass.toFunLike.{max (max (max u4 u3) u1) u2, max (max u4 u1) u2, max (max u3 u1) u2} (AddMonoidHom.{max (max u1 u4) u2, max (max u1 u3) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddZeroClass.toAdd.{max (max u4 u1) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι)))) (AddZeroClass.toAdd.{max (max u3 u1) u2} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AddMonoidHomClass.toAddHomClass.{max (max (max u4 u3) u1) u2, max (max u4 u1) u2, max (max u3 u1) u2} (AddMonoidHom.{max (max u1 u4) u2, max (max u1 u3) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι))) (AddMonoidHom.addMonoidHomClass.{max (max u4 u1) u2, max (max u3 u1) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))))) (LinearMap.compAlternatingMap.{u5, u2, u4, u1, u3} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι N₂ _inst_10 _inst_11 g) f) m) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => N₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R N N₂ _inst_1 _inst_1 _inst_4 _inst_10 _inst_5 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u1), max (succ u2) (succ u1), succ u4} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f m))
+  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u5, u2} R M _inst_1 _inst_2] {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u5, u4} R N _inst_1 _inst_4] {ι : Type.{u1}} {N₂ : Type.{u3}} [_inst_10 : AddCommMonoid.{u3} N₂] [_inst_11 : Module.{u5, u3} R N₂ _inst_1 _inst_10] (g : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (f : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (m : ι -> M), Eq.{succ u3} N₂ (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (ι -> M) (fun (_x : ι -> M) => N₂) (AlternatingMap.funLike.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ 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_inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) _x) (AddHomClass.toFunLike.{max (max (max u4 u3) u1) u2, max (max u4 u1) u2, max (max u3 u1) u2} (AddMonoidHom.{max (max u1 u4) u2, max (max u1 u3) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddZeroClass.toAdd.{max (max u4 u1) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι)))) (AddZeroClass.toAdd.{max (max u3 u1) u2} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AddMonoidHomClass.toAddHomClass.{max (max (max u4 u3) u1) u2, max (max u4 u1) u2, max (max u3 u1) u2} (AddMonoidHom.{max (max u1 u4) u2, max (max u1 u3) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι))) (AddMonoidHom.addMonoidHomClass.{max (max u4 u1) u2, max (max u3 u1) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))))) (LinearMap.compAlternatingMap.{u5, u2, u4, u1, u3} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι N₂ _inst_10 _inst_11 g) f) m) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => N₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R N N₂ _inst_1 _inst_1 _inst_4 _inst_10 _inst_5 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u1), max (succ u2) (succ u1), succ u4} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f m))
 Case conversion may be inaccurate. Consider using '#align linear_map.comp_alternating_map_apply LinearMap.compAlternatingMap_applyₓ'. -/
 @[simp]
 theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) (m : ι → M) :
@@ -669,7 +669,7 @@ theorem subtype_compAlternatingMap_codRestrict (f : AlternatingMap R M N ι) (p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {N₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} N₂] [_inst_11 : Module.{u1, u5} R N₂ _inst_1 _inst_10] (g : LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (p : Submodule.{u1, u5} R N₂ _inst_1 _inst_10 _inst_11) (h : forall (c : N), Membership.Mem.{u5, u5} N₂ (Submodule.{u1, u5} R N₂ _inst_1 _inst_10 _inst_11) (SetLike.hasMem.{u5, u5} (Submodule.{u1, u5} R N₂ _inst_1 _inst_10 _inst_11) N₂ (Submodule.setLike.{u1, u5} R N₂ _inst_1 _inst_10 _inst_11)) (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u1, u3, u5} R R 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 but is expected to have type
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(AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))))) (LinearMap.compAlternatingMap.{u5, u2, u4, u1, u3} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι N₂ _inst_10 _inst_11 g) f) p (fun (v : ι -> M) => h (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u1), max (succ u2) (succ u1), succ u4} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f v)))
 Case conversion may be inaccurate. Consider using '#align linear_map.comp_alternating_map_cod_restrict LinearMap.compAlternatingMap_codRestrictₓ'. -/
 @[simp]
 theorem compAlternatingMap_codRestrict (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι)
@@ -700,7 +700,7 @@ def compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) : Alterna
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {M₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u1, u5} R M₂ _inst_1 _inst_10] (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), Eq.{max (max (succ u4) (succ u5)) (succ u3)} ((ι -> M₂) -> N) (coeFn.{max (succ u5) (succ u3) (succ u4), max (max (succ u4) (succ u5)) (succ u3)} (AlternatingMap.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) => (ι -> M₂) -> N) (AlternatingMap.coeFun.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 f g)) (Function.comp.{max (succ u4) (succ u5), max (succ u4) (succ u2), succ u3} (ι -> M₂) (ι -> M) N (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f) (Function.comp.{succ u4, succ u5, succ u2} ι M₂ M (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) => M₂ -> M) (LinearMap.hasCoeToFun.{u1, u1, u5, u2} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) g)))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u5, u4} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u5, u3} R N _inst_1 _inst_4] {ι : Type.{u2}} {M₂ : Type.{u1}} [_inst_10 : AddCommMonoid.{u1} M₂] [_inst_11 : Module.{u5, u1} R M₂ _inst_1 _inst_10] (f : AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g : LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((ι -> M₂) -> N) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlternatingMap.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (ι -> M₂) (fun (_x : ι -> M₂) => N) (AlternatingMap.funLike.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 f g)) (Function.comp.{max (succ u1) (succ u2), max (succ u4) (succ u2), succ u3} (ι -> M₂) (ι -> M) N (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), succ u3} (AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f) ((fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.7564 : M₂ -> M) (x._@.Mathlib.LinearAlgebra.Alternating._hyg.7566 : ι -> M₂) => Function.comp.{succ u2, succ u1, succ u4} ι M₂ M x._@.Mathlib.LinearAlgebra.Alternating._hyg.7564 x._@.Mathlib.LinearAlgebra.Alternating._hyg.7566) (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u1, u4} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g)))
+  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u5, u4} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u5, u3} R N _inst_1 _inst_4] {ι : Type.{u2}} {M₂ : Type.{u1}} [_inst_10 : AddCommMonoid.{u1} M₂] [_inst_11 : Module.{u5, u1} R M₂ _inst_1 _inst_10] (f : AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g : LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((ι -> M₂) -> N) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlternatingMap.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (ι -> M₂) (fun (_x : ι -> M₂) => N) (AlternatingMap.funLike.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 f g)) (Function.comp.{max (succ u1) (succ u2), max (succ u4) (succ u2), succ u3} (ι -> M₂) (ι -> M) N (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), succ u3} (AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f) ((fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.7564 : M₂ -> M) (x._@.Mathlib.LinearAlgebra.Alternating._hyg.7566 : ι -> M₂) => Function.comp.{succ u2, succ u1, succ u4} ι M₂ M x._@.Mathlib.LinearAlgebra.Alternating._hyg.7564 x._@.Mathlib.LinearAlgebra.Alternating._hyg.7566) (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u1, u4} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g)))
 Case conversion may be inaccurate. Consider using '#align alternating_map.coe_comp_linear_map AlternatingMap.coe_compLinearMapₓ'. -/
 theorem coe_compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
     ⇑(f.compLinearMap g) = f ∘ (· ∘ ·) g :=
@@ -711,7 +711,7 @@ theorem coe_compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {M₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u1, u5} R M₂ _inst_1 _inst_10] (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (v : ι -> M₂), Eq.{succ u3} N (coeFn.{max (succ u5) (succ u3) (succ u4), max (max (succ u4) (succ u5)) (succ u3)} (AlternatingMap.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) => (ι -> M₂) -> N) (AlternatingMap.coeFun.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 f g) v) (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (fun (i : ι) => coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) => M₂ -> M) (LinearMap.hasCoeToFun.{u1, u1, u5, u2} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) g (v i)))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u5, u4} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u5, u3} R N _inst_1 _inst_4] {ι : Type.{u2}} {M₂ : Type.{u1}} [_inst_10 : AddCommMonoid.{u1} M₂] [_inst_11 : Module.{u5, u1} R M₂ _inst_1 _inst_10] (f : AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g : LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (v : ι -> M₂), Eq.{succ u3} N (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlternatingMap.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (ι -> M₂) (fun (_x : ι -> M₂) => N) (AlternatingMap.funLike.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 f g) v) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), succ u3} (AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (fun (i : ι) => FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u1, u4} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g (v i)))
+  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u5, u4} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u5, u3} R N _inst_1 _inst_4] {ι : Type.{u2}} {M₂ : Type.{u1}} [_inst_10 : AddCommMonoid.{u1} M₂] [_inst_11 : Module.{u5, u1} R M₂ _inst_1 _inst_10] (f : AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g : LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (v : ι -> M₂), Eq.{succ u3} N (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlternatingMap.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (ι -> M₂) (fun (_x : ι -> M₂) => N) (AlternatingMap.funLike.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 f g) v) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), succ u3} (AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (fun (i : ι) => FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u1, u4} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g (v i)))
 Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_apply AlternatingMap.compLinearMap_applyₓ'. -/
 @[simp]
 theorem compLinearMap_apply (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) (v : ι → M₂) :
@@ -788,7 +788,7 @@ theorem compLinearMap_id (f : AlternatingMap R M N ι) : f.compLinearMap LinearM
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {M₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u1, u5} R M₂ _inst_1 _inst_10] (f : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), (Function.Surjective.{succ u5, succ u2} M₂ M (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) => M₂ -> M) (LinearMap.hasCoeToFun.{u1, u1, u5, u2} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (Function.Injective.{max (succ u2) (succ u3) (succ u4), max (succ u5) (succ u3) (succ u4)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (fun (g : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => AlternatingMap.compLinearMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g f))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u3}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u5, u3} R M _inst_1 _inst_2] {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u5, u2} R N _inst_1 _inst_4] {ι : Type.{u1}} {M₂ : Type.{u4}} [_inst_10 : AddCommMonoid.{u4} M₂] [_inst_11 : Module.{u5, u4} R M₂ _inst_1 _inst_10] (f : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), (Function.Surjective.{succ u4, succ u3} M₂ M (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f)) -> (Function.Injective.{max (max (succ u3) (succ u2)) (succ u1), max (max (succ u2) (succ u1)) (succ u4)} (AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u4, u2, u1} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (fun (g : AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g f))
+  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u3}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u5, u3} R M _inst_1 _inst_2] {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u5, u2} R N _inst_1 _inst_4] {ι : Type.{u1}} {M₂ : Type.{u4}} [_inst_10 : AddCommMonoid.{u4} M₂] [_inst_11 : Module.{u5, u4} R M₂ _inst_1 _inst_10] (f : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), (Function.Surjective.{succ u4, succ u3} M₂ M (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f)) -> (Function.Injective.{max (max (succ u3) (succ u2)) (succ u1), max (max (succ u2) (succ u1)) (succ u4)} (AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u4, u2, u1} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (fun (g : AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g f))
 Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_injective AlternatingMap.compLinearMap_injectiveₓ'. -/
 /-- Composing with a surjective linear map is injective. -/
 theorem compLinearMap_injective (f : M₂ →ₗ[R] M) (hf : Function.Surjective f) :
@@ -800,7 +800,7 @@ theorem compLinearMap_injective (f : M₂ →ₗ[R] M) (hf : Function.Surjective
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {M₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u1, u5} R M₂ _inst_1 _inst_10] (f : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), (Function.Surjective.{succ u5, succ u2} M₂ M (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) => M₂ -> M) (LinearMap.hasCoeToFun.{u1, u1, u5, u2} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (forall (g₁ : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g₂ : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Iff (Eq.{max (succ u5) (succ u3) (succ u4)} (AlternatingMap.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g₁ f) (AlternatingMap.compLinearMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g₂ f)) (Eq.{max (succ u2) (succ u3) (succ u4)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) g₁ g₂))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u3}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u5, u3} R M _inst_1 _inst_2] {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u5, u2} R N _inst_1 _inst_4] {ι : Type.{u1}} {M₂ : Type.{u4}} [_inst_10 : AddCommMonoid.{u4} M₂] [_inst_11 : Module.{u5, u4} R M₂ _inst_1 _inst_10] (f : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), (Function.Surjective.{succ u4, succ u3} M₂ M (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f)) -> (forall (g₁ : AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g₂ : AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u4)} (AlternatingMap.{u5, u4, u2, u1} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g₁ f) (AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g₂ f)) (Eq.{max (max (succ u3) (succ u2)) (succ u1)} (AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) g₁ g₂))
+  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u3}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u5, u3} R M _inst_1 _inst_2] {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u5, u2} R N _inst_1 _inst_4] {ι : Type.{u1}} {M₂ : Type.{u4}} [_inst_10 : AddCommMonoid.{u4} M₂] [_inst_11 : Module.{u5, u4} R M₂ _inst_1 _inst_10] (f : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), (Function.Surjective.{succ u4, succ u3} M₂ M (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f)) -> (forall (g₁ : AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g₂ : AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u4)} (AlternatingMap.{u5, u4, u2, u1} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g₁ f) (AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g₂ f)) (Eq.{max (max (succ u3) (succ u2)) (succ u1)} (AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) g₁ g₂))
 Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_inj AlternatingMap.compLinearMap_injₓ'. -/
 theorem compLinearMap_inj (f : M₂ →ₗ[R] M) (hf : Function.Surjective f)
     (g₁ g₂ : AlternatingMap R M N ι) : g₁.compLinearMap f = g₂.compLinearMap f ↔ g₁ = g₂ :=
@@ -1538,7 +1538,7 @@ def domCoprod' :
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb), Eq.{max (succ u4) (succ (max u5 u6)) (succ (max u1 u2))} (AlternatingMap.{u3, u4, max u5 u6, max u1 u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u1, u2} ιa ιb)) (coeFn.{max (succ (max (max u4 u5 u1) u4 u6 u2)) (succ (max u4 (max u5 u6) u1 u2)), max (succ (max (max u4 u5 u1) u4 u6 u2)) (succ (max u4 (max u5 u6) u1 u2))} (LinearMap.{u3, u3, max (max u4 u5 u1) u4 u6 u2, max u4 (max u5 u6) u1 u2} R' R' (CommSemiring.toSemiring.{u3} R' _inst_12) (CommSemiring.toSemiring.{u3} R' _inst_12) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12))) (TensorProduct.{u3, max u4 u5 u1, max u4 u6 u2} R' _inst_12 (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u3, u4, u5, u1, u3} R' 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_inst_14 _inst_16) (Sum.{u1, u2} ιa ιb) R' (CommSemiring.toSemiring.{u3} R' _inst_12) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (AlternatingMap.domCoprod'._proof_3.{u3, u5, u6} R' N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16))) => (TensorProduct.{u3, max u4 u5 u1, max u4 u6 u2} R' _inst_12 (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u3, u4, u5, u1, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_14 (AlternatingMap.domCoprod'._proof_1.{u3, u5} R' N₁ _inst_12 _inst_13 _inst_14)) (AlternatingMap.module.{u3, u4, u6, u2, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_16 (AlternatingMap.domCoprod'._proof_2.{u3, u6} R' N₂ _inst_12 _inst_15 _inst_16))) -> (AlternatingMap.{u3, u4, max u5 u6, max u1 u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ 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(AlternatingMap.addCommMonoid.{u3, u4, max u5 u6, max u1 u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u1, u2} ιa ιb)) (TensorProduct.module.{u3, max u4 u5 u1, max u4 u6 u2} R' _inst_12 (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u3, u4, u5, u1, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_14 (AlternatingMap.domCoprod'._proof_1.{u3, u5} R' N₁ _inst_12 _inst_13 _inst_14)) (AlternatingMap.module.{u3, u4, u6, u2, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_16 (AlternatingMap.domCoprod'._proof_2.{u3, u6} 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_inst_16)) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12)))) (AlternatingMap.domCoprod'.{u1, u2, u3, u4, u5, u6} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b)) (TensorProduct.tmul.{u3, max u4 u5 u1, max u4 u6 u2} R' _inst_12 (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u3, u4, u5, u1, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_14 (AlternatingMap.domCoprod'._proof_1.{u3, u5} R' N₁ _inst_12 _inst_13 _inst_14)) (AlternatingMap.module.{u3, u4, u6, u2, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_16 (AlternatingMap.domCoprod'._proof_2.{u3, u6} R' N₂ _inst_12 _inst_15 _inst_16)) a b)) (AlternatingMap.domCoprod.{u1, u2, u3, u4, u5, u6} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b) a b)
 but is expected to have type
-  forall {ιa : Type.{u3}} {ιb : Type.{u1}} [_inst_10 : Fintype.{u3} ιa] [_inst_11 : Fintype.{u1} ιb] {R' : Type.{u6}} {Mᵢ : Type.{u5}} {N₁ : Type.{u4}} {N₂ : Type.{u2}} [_inst_12 : CommSemiring.{u6} R'] [_inst_13 : AddCommGroup.{u4} N₁] [_inst_14 : Module.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u2} N₂] [_inst_16 : Module.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u5} Mᵢ] [_inst_18 : Module.{u6, u5} R' Mᵢ (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u3} ιa] [_inst_20 : DecidableEq.{succ u1} ιb] (a : AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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_inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (fun (_x : TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) => AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, max (max (max (max u2 u4) u5) u1) u3, max (max (max (max u2 u4) u5) u1) u3} R' R' (TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) (CommSemiring.toSemiring.{u6} R' _inst_12) (CommSemiring.toSemiring.{u6} R' _inst_12) (TensorProduct.addCommMonoid.{u6, max (max u3 u5) u4, max (max u1 u5) u2} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.addCommMonoid.{u6, u5, max u4 u2, max u3 u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ 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(AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} 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_inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16))))) (RingHom.id.{u6} R' (Semiring.toNonAssocSemiring.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)))) (AlternatingMap.domCoprod'.{u3, u1, u6, u5, u4, u2} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b)) (TensorProduct.tmul.{u6, max (max u4 u5) u3, max (max u2 u5) u1} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) 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N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16)))) a b)) (AlternatingMap.domCoprod.{u3, u1, u6, u5, u4, u2} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b) a b)
+  forall {ιa : Type.{u3}} {ιb : Type.{u1}} [_inst_10 : Fintype.{u3} ιa] [_inst_11 : Fintype.{u1} ιb] {R' : Type.{u6}} {Mᵢ : Type.{u5}} {N₁ : Type.{u4}} {N₂ : Type.{u2}} [_inst_12 : CommSemiring.{u6} R'] [_inst_13 : AddCommGroup.{u4} N₁] [_inst_14 : Module.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u2} N₂] [_inst_16 : Module.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u5} Mᵢ] [_inst_18 : Module.{u6, u5} R' Mᵢ (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u3} ιa] [_inst_20 : DecidableEq.{succ u1} ιb] (a : AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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_inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (fun (_x : TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) => AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, max (max (max (max u2 u4) u5) u1) u3, max (max (max (max u2 u4) u5) u1) u3} R' R' (TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) (CommSemiring.toSemiring.{u6} R' _inst_12) (CommSemiring.toSemiring.{u6} R' _inst_12) (TensorProduct.addCommMonoid.{u6, max (max u3 u5) u4, max (max u1 u5) u2} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.addCommMonoid.{u6, u5, max u4 u2, max u3 u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, max (max u3 u5) u4, max (max u1 u5) u2} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.module.{u6, u5, max u4 u2, max u3 u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb) R' (CommSemiring.toSemiring.{u6} R' _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (smulCommClass_self.{u6, max u4 u2} R' (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, max u4 u2} R' (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (SubNegZeroMonoid.toNegZeroClass.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (SubtractionMonoid.toSubNegZeroMonoid.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (SubtractionCommMonoid.toSubtractionMonoid.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (AddCommGroup.toDivisionAddCommMonoid.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommGroup.{u6, u4, u2} R' _inst_12 N₁ N₂ _inst_13 _inst_15 _inst_14 _inst_16)))))) (Module.toMulActionWithZero.{u6, max u4 u2} R' (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u6} R' _inst_12) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16))))) (RingHom.id.{u6} R' (Semiring.toNonAssocSemiring.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)))) (AlternatingMap.domCoprod'.{u3, u1, u6, u5, u4, u2} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b)) (TensorProduct.tmul.{u6, max (max u4 u5) u3, max (max u2 u5) u1} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16)))) a b)) (AlternatingMap.domCoprod.{u3, u1, u6, u5, u4, u2} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b) a b)
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod'_apply AlternatingMap.domCoprod'_applyₓ'. -/
 @[simp]
 theorem domCoprod'_apply (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
@@ -1759,7 +1759,7 @@ def curryLeftLinearMap {n : ℕ} :
 lean 3 declaration is
   forall {R' : Type.{u1}} {M'' : Type.{u2}} {N'' : Type.{u3}} [_inst_10 : CommSemiring.{u1} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_13 : AddCommMonoid.{u3} N''] [_inst_15 : Module.{u1, u2} R' M'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11] [_inst_17 : Module.{u1, u3} R' N'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_13] {n : Nat} (f : AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ (Nat.succ n)))) (m : M''), Eq.{max (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (coeFn.{max (succ u2) (succ (max u2 u3)), max (succ u2) (succ (max u2 u3))} (LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) => M'' -> (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u3} R' R' M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) (AlternatingMap.curryLeft.{u1, u2, u3} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n (coeFn.{max (succ u2) (succ (max u2 u3)), max (succ u2) (succ (max u2 u3))} (LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) => M'' -> (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u3} R' R' M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) (AlternatingMap.curryLeft.{u1, u2, u3} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 (Nat.succ n) f) m)) m) (OfNat.ofNat.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) 0 (OfNat.mk.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) 0 (Zero.zero.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.zero.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)))))
 but is expected to have type
-  forall {R' : Type.{u3}} {M'' : Type.{u2}} {N'' : Type.{u1}} [_inst_10 : CommSemiring.{u3} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_13 : AddCommMonoid.{u1} N''] [_inst_15 : Module.{u3, u2} R' M'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11] [_inst_17 : Module.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13] {n : Nat} (f : AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ (Nat.succ n)))) (m : M''), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) m) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10))) M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u2 u1} R' R' M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)))) (AlternatingMap.curryLeft.{u3, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10))) M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u2 u1} R' R' M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)))) (AlternatingMap.curryLeft.{u3, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) f) m)) m) (OfNat.ofNat.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) m) 0 (Zero.toOfNat0.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) m) (AlternatingMap.zero.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n))))
+  forall {R' : Type.{u3}} {M'' : Type.{u2}} {N'' : Type.{u1}} [_inst_10 : CommSemiring.{u3} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_13 : AddCommMonoid.{u1} N''] [_inst_15 : Module.{u3, u2} R' M'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11] [_inst_17 : Module.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13] {n : Nat} (f : AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ (Nat.succ n)))) (m : M''), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) m) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10))) M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u2 u1} R' R' M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)))) (AlternatingMap.curryLeft.{u3, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10))) M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u2 u1} R' R' M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)))) (AlternatingMap.curryLeft.{u3, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) f) m)) m) (OfNat.ofNat.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) m) 0 (Zero.toOfNat0.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) m) (AlternatingMap.zero.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n))))
 Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_same AlternatingMap.curryLeft_sameₓ'. -/
 /-- Currying with the same element twice gives the zero map. -/
 @[simp]
@@ -1772,7 +1772,7 @@ theorem curryLeft_same {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ.succ
 lean 3 declaration is
   forall {R' : Type.{u1}} {M'' : Type.{u2}} {N'' : Type.{u3}} {N₂'' : Type.{u4}} [_inst_10 : CommSemiring.{u1} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_13 : AddCommMonoid.{u3} N''] [_inst_14 : AddCommMonoid.{u4} N₂''] [_inst_15 : Module.{u1, u2} R' M'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11] [_inst_17 : Module.{u1, u3} R' N'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_13] [_inst_18 : Module.{u1, u4} R' N₂'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_14] {n : Nat} (g : LinearMap.{u1, u1, u3, u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) N'' N₂'' _inst_13 _inst_14 _inst_17 _inst_18) (f : AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (m : M''), Eq.{max (succ u2) (succ u4)} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (coeFn.{max (succ u2) (succ (max u2 u4)), max (succ u2) (succ (max u2 u4))} (LinearMap.{u1, u1, u2, max u2 u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_18 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N₂'' _inst_10 _inst_14 _inst_18))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_18 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N₂'' _inst_10 _inst_14 _inst_18))) => M'' -> (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u4} R' R' M'' (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_18 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N₂'' _inst_10 _inst_14 _inst_18)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) (AlternatingMap.curryLeft.{u1, u2, u4} R' M'' N₂'' _inst_10 _inst_11 _inst_14 _inst_15 _inst_18 n (coeFn.{max (succ (max u2 u4)) (succ (max u2 u3)), max (succ (max u2 u3)) (succ (max u2 u4))} (AddMonoidHom.{max u2 u3, max u2 u4} 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(AddCommMonoid.toAddMonoid.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n))) (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n)))))) (fun (_x : AddMonoidHom.{max u2 u3, max u2 u4} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n))) (AddMonoid.toAddZeroClass.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (AddCommMonoid.toAddMonoid.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))))) (AddMonoid.toAddZeroClass.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n))) (AddCommMonoid.toAddMonoid.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n))) (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n)))))) => (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) -> (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin 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_inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n))) (AddCommMonoid.toAddMonoid.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n))) (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n)))))) (LinearMap.compAlternatingMap.{u1, u2, u3, 0, u4} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) N₂'' _inst_14 _inst_18 g) f)) m) (coeFn.{max (succ (max u2 u4)) (succ (max u2 u3)), max (succ (max u2 u3)) (succ (max u2 u4))} (AddMonoidHom.{max u2 u3, max u2 u4} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddMonoid.toAddZeroClass.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)))) (AddMonoid.toAddZeroClass.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n))))) (fun (_x : AddMonoidHom.{max u2 u3, max u2 u4} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddMonoid.toAddZeroClass.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)))) (AddMonoid.toAddZeroClass.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n))))) => (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) -> (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n))) (AddMonoidHom.hasCoeToFun.{max u2 u3, max u2 u4} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddMonoid.toAddZeroClass.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)))) (AddMonoid.toAddZeroClass.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n))))) (LinearMap.compAlternatingMap.{u1, u2, u3, 0, u4} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) N₂'' _inst_14 _inst_18 g) (coeFn.{max (succ u2) (succ (max u2 u3)), max (succ u2) (succ (max u2 u3))} (LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) => M'' -> (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u3} R' R' M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) (AlternatingMap.curryLeft.{u1, u2, u3} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f) m))
 but is expected to have type
-  forall {R' : Type.{u4}} {M'' : Type.{u1}} {N'' : Type.{u3}} {N₂'' : Type.{u2}} [_inst_10 : CommSemiring.{u4} R'] [_inst_11 : AddCommMonoid.{u1} M''] [_inst_13 : AddCommMonoid.{u3} N''] [_inst_14 : AddCommMonoid.{u2} N₂''] [_inst_15 : Module.{u4, u1} R' M'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11] [_inst_17 : Module.{u4, u3} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13] [_inst_18 : Module.{u4, u2} R' N₂'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_14] {n : Nat} (g : LinearMap.{u4, u4, u3, u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) N'' N₂'' _inst_13 _inst_14 _inst_17 _inst_18) (f : AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (m : M''), Eq.{max (succ u1) (succ u2)} ((fun 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n)))) (AddMonoidHom.addMonoidHomClass.{max u3 u1, max u2 u1} (AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.{u4, u1, u2, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddMonoid.toAddZeroClass.{max u1 u3} (AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AddCommMonoid.toAddMonoid.{max u1 u3} (AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.addCommMonoid.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)))) (AddMonoid.toAddZeroClass.{max u1 u2} (AlternatingMap.{u4, u1, u2, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddCommMonoid.toAddMonoid.{max u1 u2} (AlternatingMap.{u4, u1, u2, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AlternatingMap.addCommMonoid.{u4, u1, u2, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n))))))) (LinearMap.compAlternatingMap.{u4, u1, u3, 0, u2} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) N₂'' _inst_14 _inst_18 g) (FunLike.coe.{max (succ u1) (succ u3), succ u1, max (succ u1) (succ u3)} (LinearMap.{u4, u4, u1, max u3 u1} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M'' (AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u1, u3, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u3} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u3} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u3} N'' (AddCommMonoid.toAddMonoid.{u3} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u3} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M'') => AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u1 u3} R' R' M'' (AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u1, u3, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u3} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u3} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u3} N'' (AddCommMonoid.toAddMonoid.{u3} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u3} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) (AlternatingMap.curryLeft.{u4, u1, u3} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f) m))
 Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_comp_alternating_map AlternatingMap.curryLeft_compAlternatingMapₓ'. -/
 @[simp]
 theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
@@ -1785,7 +1785,7 @@ theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
 lean 3 declaration is
   forall {R' : Type.{u1}} {M'' : Type.{u2}} {M₂'' : Type.{u3}} {N'' : Type.{u4}} [_inst_10 : CommSemiring.{u1} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_12 : AddCommMonoid.{u3} M₂''] [_inst_13 : AddCommMonoid.{u4} N''] [_inst_15 : Module.{u1, u2} R' M'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11] [_inst_16 : Module.{u1, u3} R' M₂'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_12] [_inst_17 : Module.{u1, u4} R' N'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_13] {n : Nat} (g : LinearMap.{u1, u1, u3, u2} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) (f : AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (m : M₂''), Eq.{max (succ u3) (succ u4)} (AlternatingMap.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) (coeFn.{max (succ u3) (succ (max u3 u4)), max (succ u3) (succ (max u3 u4))} (LinearMap.{u1, u1, u3, max u3 u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M₂'' (AlternatingMap.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_12 (AlternatingMap.addCommMonoid.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_16 (AlternatingMap.module.{u1, u3, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N'' _inst_10 _inst_13 _inst_17))) (fun (_x : LinearMap.{u1, u1, u3, max u3 u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M₂'' (AlternatingMap.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_12 (AlternatingMap.addCommMonoid.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_16 (AlternatingMap.module.{u1, u3, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N'' _inst_10 _inst_13 _inst_17))) => M₂'' -> (AlternatingMap.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n))) (LinearMap.hasCoeToFun.{u1, u1, u3, max u3 u4} R' R' M₂'' (AlternatingMap.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_12 (AlternatingMap.addCommMonoid.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_16 (AlternatingMap.module.{u1, u3, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N'' _inst_10 _inst_13 _inst_17)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) (AlternatingMap.curryLeft.{u1, u3, u4} R' M₂'' N'' _inst_10 _inst_12 _inst_13 _inst_16 _inst_17 n (AlternatingMap.compLinearMap.{u1, u2, u4, 0, u3} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) M₂'' _inst_12 _inst_16 f g)) m) (AlternatingMap.compLinearMap.{u1, u2, u4, 0, u3} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) M₂'' _inst_12 _inst_16 (coeFn.{max (succ u2) (succ (max u2 u4)), max (succ u2) (succ (max u2 u4))} (LinearMap.{u1, u1, u2, max u2 u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N'' _inst_10 _inst_13 _inst_17))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N'' _inst_10 _inst_13 _inst_17))) => M'' -> (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u4} R' R' M'' (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N'' _inst_10 _inst_13 _inst_17)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) (AlternatingMap.curryLeft.{u1, u2, u4} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f) (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, u3, u2} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) (fun (_x : LinearMap.{u1, u1, u3, u2} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) => M₂'' -> M'') (LinearMap.hasCoeToFun.{u1, u1, u3, u2} R' R' M₂'' M'' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_12 _inst_11 _inst_16 _inst_15 (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) g m)) g)
 but is expected to have type
-  forall {R' : Type.{u4}} {M'' : Type.{u2}} {M₂'' : Type.{u3}} {N'' : Type.{u1}} [_inst_10 : CommSemiring.{u4} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_12 : AddCommMonoid.{u3} M₂''] [_inst_13 : AddCommMonoid.{u1} N''] [_inst_15 : Module.{u4, u2} R' M'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11] [_inst_16 : Module.{u4, u3} R' M₂'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12] [_inst_17 : Module.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13] {n : Nat} (g : LinearMap.{u4, u4, u3, u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) (f : AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (m : M₂''), Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂'') => AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) m) (FunLike.coe.{max (succ u3) (succ u1), succ u3, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u3, max u1 u3} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' (AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_12 (AlternatingMap.addCommMonoid.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_16 (AlternatingMap.module.{u4, u3, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17))))) M₂'' (fun (_x : M₂'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂'') => AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u3 u1} R' R' M₂'' (AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12 (AlternatingMap.addCommMonoid.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' 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(Fin (Nat.succ n)) M₂'' _inst_12 _inst_16 f g)) m) (AlternatingMap.compLinearMap.{u4, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) M₂'' _inst_12 _inst_16 (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u4, u4, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M'' (AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u2, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u2, max u2 u1} R' R' M'' (AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u2, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) (AlternatingMap.curryLeft.{u4, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) M₂'' (fun (_x : M₂'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂'') => M'') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R' R' M₂'' M'' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12 _inst_11 _inst_16 _inst_15 (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) g m)) g)
+  forall {R' : Type.{u4}} {M'' : Type.{u2}} {M₂'' : Type.{u3}} {N'' : Type.{u1}} [_inst_10 : CommSemiring.{u4} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_12 : AddCommMonoid.{u3} M₂''] [_inst_13 : AddCommMonoid.{u1} N''] [_inst_15 : Module.{u4, u2} R' M'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11] [_inst_16 : Module.{u4, u3} R' M₂'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12] [_inst_17 : Module.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13] {n : Nat} (g : LinearMap.{u4, u4, u3, u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) (f : AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (m : M₂''), Eq.{max (succ u3) (succ u1)} ((fun 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(smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17))))) M₂'' (fun (_x : M₂'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₂'') => AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u3 u1} R' R' M₂'' (AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12 (AlternatingMap.addCommMonoid.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' 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(Fin (Nat.succ n)) M₂'' _inst_12 _inst_16 f g)) m) (AlternatingMap.compLinearMap.{u4, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) M₂'' _inst_12 _inst_16 (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u4, u4, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M'' (AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u2, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M'') => AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u2, max u2 u1} R' R' M'' (AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u2, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) (AlternatingMap.curryLeft.{u4, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) M₂'' (fun (_x : M₂'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₂'') => M'') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R' R' M₂'' M'' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12 _inst_11 _inst_16 _inst_15 (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) g m)) g)
 Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_comp_linear_map AlternatingMap.curryLeft_compLinearMapₓ'. -/
 @[simp]
 theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -937,7 +937,7 @@ theorem map_update_update [DecidableEq ι] {i j : ι} (hij : i ≠ j) (m : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (v : ι -> M) [_inst_14 : DecidableEq.{succ u4} ι] {i : ι} {j : ι}, (Ne.{succ u4} ι i j) -> (Eq.{succ u3} N (HAdd.hAdd.{u3, u3, u3} N N N (instHAdd.{u3} N (AddZeroClass.toHasAdd.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))) (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (Function.comp.{succ u4, succ u4, succ u2} ι ι M v (coeFn.{succ u4, succ u4} (Equiv.Perm.{succ u4} ι) (fun (_x : Equiv.{succ u4, succ u4} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u4, succ u4} ι ι) (Equiv.swap.{succ u4} ι (fun (a : ι) (b : ι) => _inst_14 a b) i j)))) (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f v)) (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_4)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (v : ι -> M) [_inst_14 : DecidableEq.{succ u4} ι] {i : ι} {j : ι}, (Ne.{succ u4} ι i j) -> (Eq.{succ u3} N (HAdd.hAdd.{u3, u3, u3} N N N (instHAdd.{u3} N (AddZeroClass.toAdd.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (Function.comp.{succ u4, succ u4, succ u2} ι ι M v (FunLike.coe.{succ u4, succ u4, succ u4} (Equiv.Perm.{succ u4} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u4} ι ι) (Equiv.swap.{succ u4} ι (fun (a : ι) (b : ι) => _inst_14 a b) i j)))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f v)) (OfNat.ofNat.{u3} N 0 (Zero.toOfNat0.{u3} N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (v : ι -> M) [_inst_14 : DecidableEq.{succ u4} ι] {i : ι} {j : ι}, (Ne.{succ u4} ι i j) -> (Eq.{succ u3} N (HAdd.hAdd.{u3, u3, u3} N N N (instHAdd.{u3} N (AddZeroClass.toAdd.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (Function.comp.{succ u4, succ u4, succ u2} ι ι M v (FunLike.coe.{succ u4, succ u4, succ u4} (Equiv.Perm.{succ u4} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u4} ι ι) (Equiv.swap.{succ u4} ι (fun (a : ι) (b : ι) => _inst_14 a b) i j)))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f v)) (OfNat.ofNat.{u3} N 0 (Zero.toOfNat0.{u3} N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))))
 Case conversion may be inaccurate. Consider using '#align alternating_map.map_swap_add AlternatingMap.map_swap_addₓ'. -/
 theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equiv.swap i j) + f v = 0 :=
   by
@@ -951,7 +951,7 @@ theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equi
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (v : ι -> M) [_inst_14 : DecidableEq.{succ u4} ι] {i : ι} {j : ι}, (Ne.{succ u4} ι i j) -> (Eq.{succ u3} N (HAdd.hAdd.{u3, u3, u3} N N N (instHAdd.{u3} N (AddZeroClass.toHasAdd.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))) (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f v) (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (Function.comp.{succ u4, succ u4, succ u2} ι ι M v (coeFn.{succ u4, succ u4} (Equiv.Perm.{succ u4} ι) (fun (_x : Equiv.{succ u4, succ u4} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u4, succ u4} ι ι) (Equiv.swap.{succ u4} ι (fun (a : ι) (b : ι) => _inst_14 a b) i j))))) (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_4)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (v : ι -> M) [_inst_14 : DecidableEq.{succ u4} ι] {i : ι} {j : ι}, (Ne.{succ u4} ι i j) -> (Eq.{succ u3} N (HAdd.hAdd.{u3, u3, u3} N N N (instHAdd.{u3} N (AddZeroClass.toAdd.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f v) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (Function.comp.{succ u4, succ u4, succ u2} ι ι M v (FunLike.coe.{succ u4, succ u4, succ u4} (Equiv.Perm.{succ u4} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u4} ι ι) (Equiv.swap.{succ u4} ι (fun (a : ι) (b : ι) => _inst_14 a b) i j))))) (OfNat.ofNat.{u3} N 0 (Zero.toOfNat0.{u3} N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (v : ι -> M) [_inst_14 : DecidableEq.{succ u4} ι] {i : ι} {j : ι}, (Ne.{succ u4} ι i j) -> (Eq.{succ u3} N (HAdd.hAdd.{u3, u3, u3} N N N (instHAdd.{u3} N (AddZeroClass.toAdd.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f v) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (Function.comp.{succ u4, succ u4, succ u2} ι ι M v (FunLike.coe.{succ u4, succ u4, succ u4} (Equiv.Perm.{succ u4} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u4} ι ι) (Equiv.swap.{succ u4} ι (fun (a : ι) (b : ι) => _inst_14 a b) i j))))) (OfNat.ofNat.{u3} N 0 (Zero.toOfNat0.{u3} N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))))
 Case conversion may be inaccurate. Consider using '#align alternating_map.map_add_swap AlternatingMap.map_add_swapₓ'. -/
 theorem map_add_swap [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f v + f (v ∘ Equiv.swap i j) = 0 :=
   by
@@ -980,7 +980,7 @@ theorem map_perm [DecidableEq ι] [Fintype ι] (v : ι → M) (σ : Equiv.Perm 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} (g : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (v : ι -> M) [_inst_14 : DecidableEq.{succ u4} ι] [_inst_15 : Fintype.{u4} ι] (σ : Equiv.Perm.{succ u4} ι), Eq.{succ u3} N' (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) => (ι -> M) -> N') (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) g v) (SMul.smul.{0, u3} (Units.{0} Int Int.monoid) N' (Units.hasSmul.{0, u3} Int N' Int.monoid (SubNegMonoid.SMulInt.{u3} N' (AddGroup.toSubNegMonoid.{u3} N' (AddCommGroup.toAddGroup.{u3} N' _inst_8)))) (coeFn.{succ u4, succ u4} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u4} ι) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u4} ι (fun (a : ι) (b : ι) => _inst_14 a b) _inst_15) σ) (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) => (ι -> M) -> N') (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) g (Function.comp.{succ u4, succ u4, succ u2} ι ι M v (coeFn.{succ u4, succ u4} (Equiv.Perm.{succ u4} ι) (fun (_x : Equiv.{succ u4, succ u4} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u4, succ u4} ι ι) σ))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} (g : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (v : ι -> M) [_inst_14 : DecidableEq.{succ u4} ι] [_inst_15 : Fintype.{u4} ι] (σ : Equiv.Perm.{succ u4} ι), Eq.{succ u3} N' (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (ι -> M) (fun (_x : ι -> M) => N') (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) g v) (HSMul.hSMul.{0, u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u4} ι) => Units.{0} Int Int.instMonoidInt) σ) N' N' (instHSMul.{0, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u4} ι) => Units.{0} Int Int.instMonoidInt) σ) N' (Units.instSMulUnits.{0, u3} Int N' Int.instMonoidInt (SubNegMonoid.SMulInt.{u3} N' (AddGroup.toSubNegMonoid.{u3} N' (AddCommGroup.toAddGroup.{u3} N' _inst_8))))) (FunLike.coe.{succ u4, succ u4, 1} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u4} ι) (fun (_x : Equiv.Perm.{succ u4} ι) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u4} ι) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u4, u4, 0} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u4} (Equiv.Perm.{succ u4} ι) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u4, u4, 0} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u4} ι (fun (a : ι) (b : ι) => _inst_14 a b) _inst_15) σ) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (ι -> M) (fun (_x : ι -> M) => N') (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) g (Function.comp.{succ u4, succ u4, succ u2} ι ι M v (FunLike.coe.{succ u4, succ u4, succ u4} (Equiv.Perm.{succ u4} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u4} ι ι) σ))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} (g : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (v : ι -> M) [_inst_14 : DecidableEq.{succ u4} ι] [_inst_15 : Fintype.{u4} ι] (σ : Equiv.Perm.{succ u4} ι), Eq.{succ u3} N' (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (ι -> M) (fun (_x : ι -> M) => N') (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) g v) (HSMul.hSMul.{0, u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u4} ι) => Units.{0} Int Int.instMonoidInt) σ) N' N' (instHSMul.{0, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u4} ι) => Units.{0} Int Int.instMonoidInt) σ) N' (Units.instSMulUnits.{0, u3} Int N' Int.instMonoidInt (SubNegMonoid.SMulInt.{u3} N' (AddGroup.toSubNegMonoid.{u3} N' (AddCommGroup.toAddGroup.{u3} N' _inst_8))))) (FunLike.coe.{succ u4, succ u4, 1} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u4} ι) (fun (_x : Equiv.Perm.{succ u4} ι) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u4} ι) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u4, u4, 0} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u4} (Equiv.Perm.{succ u4} ι) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u4, u4, 0} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u4} ι (fun (a : ι) (b : ι) => _inst_14 a b) _inst_15) σ) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (ι -> M) (fun (_x : ι -> M) => N') (AlternatingMap.funLike.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) g (Function.comp.{succ u4, succ u4, succ u2} ι ι M v (FunLike.coe.{succ u4, succ u4, succ u4} (Equiv.Perm.{succ u4} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u4} ι ι) σ))))
 Case conversion may be inaccurate. Consider using '#align alternating_map.map_congr_perm AlternatingMap.map_congr_permₓ'. -/
 theorem map_congr_perm [DecidableEq ι] [Fintype ι] (σ : Equiv.Perm ι) : g v = σ.sign • g (v ∘ σ) :=
   by
@@ -1098,7 +1098,7 @@ theorem domDomCongr_eq_zero_iff (σ : ι ≃ ι') (f : AlternatingMap R M N ι)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} (g : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) [_inst_14 : Fintype.{u4} ι] [_inst_15 : DecidableEq.{succ u4} ι] (σ : Equiv.Perm.{succ u4} ι), Eq.{max (succ u2) (succ u3) (succ u4)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.domDomCongr.{u1, u2, u3, u4, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι ι σ g) (SMul.smul.{0, max u2 u3 u4} (Units.{0} Int Int.monoid) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.smul.{u1, u2, u3, u4, 0} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι (Units.{0} Int Int.monoid) (DivInvMonoid.toMonoid.{0} (Units.{0} Int Int.monoid) (Group.toDivInvMonoid.{0} (Units.{0} Int Int.monoid) (Units.group.{0} Int Int.monoid))) (Units.distribMulAction.{0, u3} Int N' Int.monoid (AddCommMonoid.toAddMonoid.{u3} N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)) (Module.toDistribMulAction.{0, u3} Int N' Int.semiring (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (AddCommGroup.intModule.{u3} N' _inst_8))) (Units.smulCommClass_right.{u1, 0, u3} R Int N' Int.monoid (SMulZeroClass.toHasSmul.{u1, u3} R N' (AddZeroClass.toHasZero.{u3} N' (AddMonoid.toAddZeroClass.{u3} N' (AddCommMonoid.toAddMonoid.{u3} N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)))) (SMulWithZero.toSmulZeroClass.{u1, u3} R N' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N' (AddMonoid.toAddZeroClass.{u3} N' (AddCommMonoid.toAddMonoid.{u3} N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)))) (MulActionWithZero.toSMulWithZero.{u1, u3} R N' (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} N' (AddMonoid.toAddZeroClass.{u3} N' (AddCommMonoid.toAddMonoid.{u3} N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)))) (Module.toMulActionWithZero.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9)))) (SubNegMonoid.SMulInt.{u3} N' (AddGroup.toSubNegMonoid.{u3} N' (AddCommGroup.toAddGroup.{u3} N' _inst_8))) (AddGroup.int_smulCommClass'.{u1, u3} R N' (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommGroup.toAddGroup.{u3} N' _inst_8) (Module.toDistribMulAction.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9)))) (coeFn.{succ u4, succ u4} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u4} ι) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u4} ι (fun (a : ι) (b : ι) => _inst_15 a b) _inst_14) σ) g)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u3}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] {N' : Type.{u2}} [_inst_8 : AddCommGroup.{u2} N'] [_inst_9 : Module.{u1, u2} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8)] {ι : Type.{u4}} (g : AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) [_inst_14 : Fintype.{u4} ι] [_inst_15 : DecidableEq.{succ u4} ι] (σ : Equiv.Perm.{succ u4} ι), Eq.{max (max (succ u3) (succ u2)) (succ u4)} (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AlternatingMap.domDomCongr.{u1, u3, u2, u4, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι ι σ g) (HSMul.hSMul.{0, max (max u3 u2) u4, max (max u3 u2) u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u4} ι) => Units.{0} Int Int.instMonoidInt) σ) (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (instHSMul.{0, max (max u3 u2) u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u4} ι) => Units.{0} Int Int.instMonoidInt) σ) (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (Units.instSMulUnits.{0, max (max u3 u2) u4} Int (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) Int.instMonoidInt (SubNegMonoid.SMulInt.{max (max u3 u2) u4} (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u3 u2) u4} (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u3 u2) u4} (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (FunLike.coe.{succ u4, succ u4, 1} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u4} ι) (fun (_x : Equiv.Perm.{succ u4} ι) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u4} ι) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u4, u4, 0} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u4} (Equiv.Perm.{succ u4} ι) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u4, u4, 0} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u4} ι (fun (a : ι) (b : ι) => _inst_15 a b) _inst_14) σ) g)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u3}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] {N' : Type.{u2}} [_inst_8 : AddCommGroup.{u2} N'] [_inst_9 : Module.{u1, u2} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8)] {ι : Type.{u4}} (g : AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) [_inst_14 : Fintype.{u4} ι] [_inst_15 : DecidableEq.{succ u4} ι] (σ : Equiv.Perm.{succ u4} ι), Eq.{max (max (succ u3) (succ u2)) (succ u4)} (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AlternatingMap.domDomCongr.{u1, u3, u2, u4, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι ι σ g) (HSMul.hSMul.{0, max (max u3 u2) u4, max (max u3 u2) u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u4} ι) => Units.{0} Int Int.instMonoidInt) σ) (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (instHSMul.{0, max (max u3 u2) u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u4} ι) => Units.{0} Int Int.instMonoidInt) σ) (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (Units.instSMulUnits.{0, max (max u3 u2) u4} Int (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) Int.instMonoidInt (SubNegMonoid.SMulInt.{max (max u3 u2) u4} (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u3 u2) u4} (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u3 u2) u4} (AlternatingMap.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u1, u3, u2, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (FunLike.coe.{succ u4, succ u4, 1} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u4} ι) (fun (_x : Equiv.Perm.{succ u4} ι) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u4} ι) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u4, u4, 0} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u4} (Equiv.Perm.{succ u4} ι) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u4, u4, 0} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u4} ι (fun (a : ι) (b : ι) => _inst_15 a b) _inst_14) σ) g)
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_dom_congr_perm AlternatingMap.domDomCongr_permₓ'. -/
 theorem domDomCongr_perm [Fintype ι] [DecidableEq ι] (σ : Equiv.Perm ι) :
     g.domDomCongr σ = σ.sign • g :=
@@ -1230,7 +1230,7 @@ def alternatization : MultilinearMap R (fun i : ι => M) N' →+ AlternatingMap
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} [_inst_10 : Fintype.{u4} ι] [_inst_11 : DecidableEq.{succ u4} ι] (m : MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9), Eq.{max (max (succ u4) (succ u2)) (succ u3)} ((ι -> M) -> N') (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) => (ι -> M) -> N') (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (coeFn.{max (succ (max u2 u3 u4)) (succ (max u4 u2 u3)), max (succ (max u4 u2 u3)) (succ (max u2 u3 u4))} (AddMonoidHom.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max 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 but is expected to have type
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_inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9)))))) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.Perm.{succ u1} ι) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} ι) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} ι (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10) σ) (MultilinearMap.domDomCongr.{u4, u3, u2, u1, u1} R M N' _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_3 _inst_9 ι ι σ m))))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_def MultilinearMap.alternatization_defₓ'. -/
 theorem alternatization_def (m : MultilinearMap R (fun i : ι => M) N') :
     ⇑(alternatization m) = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
@@ -1241,7 +1241,7 @@ theorem alternatization_def (m : MultilinearMap R (fun i : ι => M) N') :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} [_inst_10 : Fintype.{u4} ι] [_inst_11 : DecidableEq.{succ u4} ι] (m : MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9), Eq.{max (succ u4) (succ u2) (succ u3)} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) ((fun (a : Sort.{max (succ u2) (succ u3) (succ u4)}) (b : Sort.{max (succ u4) (succ u2) (succ u3)}) [self : HasLiftT.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} a b] => self.0) (AlternatingMap.{u1, u2, u3, u4} R 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N' (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommGroup.toAddGroup.{u3} N' _inst_8) (Module.toDistribMulAction.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9)))) (coeFn.{succ u4, succ u4} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u4} ι) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int 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 but is expected to have type
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(x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max (max u3 u2) u1} (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max (max u3 u2) u1} (AlternatingMap.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u3 u2) u1} (AlternatingMap.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u3 u2) u1} (AlternatingMap.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))))) (MultilinearMap.alternatization.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι _inst_10 (fun (a : ι) (b : ι) => _inst_11 a b)) m)) (Finset.sum.{max (max u3 u2) u1, u1} (MultilinearMap.{u4, u3, u2, u1} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (Equiv.Perm.{succ u1} ι) (MultilinearMap.addCommMonoid.{u4, u3, u2, u1} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (Finset.univ.{u1} (Equiv.Perm.{succ u1} ι) (equivFintype.{u1, u1} ι ι (fun (a : ι) (b : ι) => _inst_11 a b) (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10 _inst_10)) (fun (σ : Equiv.Perm.{succ u1} ι) => HSMul.hSMul.{0, max (max u1 u2) u3, max (max u3 u2) u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) σ) (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.{u4, u3, u2, u1} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (instHSMul.{0, max (max u3 u2) u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) σ) (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (Units.instSMulUnits.{0, max (max u3 u2) u1} Int (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) Int.instMonoidInt (SubNegMonoid.SMulInt.{max (max u3 u2) u1} (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max (max u3 u2) u1} (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max (max u3 u2) u1} (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9)))))) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.Perm.{succ u1} ι) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} ι) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} ι (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10) σ) (MultilinearMap.domDomCongr.{u4, u3, u2, u1, u1} R M N' _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_3 _inst_9 ι ι σ m)))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_coe MultilinearMap.alternatization_coeₓ'. -/
 theorem alternatization_coe (m : MultilinearMap R (fun i : ι => M) N') :
     ↑m.alternatization = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
@@ -1252,7 +1252,7 @@ theorem alternatization_coe (m : MultilinearMap R (fun i : ι => M) N') :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} [_inst_10 : Fintype.{u4} ι] [_inst_11 : DecidableEq.{succ u4} ι] (m : MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (v : ι -> M), Eq.{succ u3} N' (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) => (ι -> M) -> N') (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (coeFn.{max (succ (max u2 u3 u4)) (succ (max u4 u2 u3)), max (succ (max u4 u2 u3)) (succ (max u2 u3 u4))} (AddMonoidHom.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max u4 u2 u3} 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(AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (fun (_x : AddMonoidHom.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : 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 but is expected to have type
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_inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u3 u2) u1} (AlternatingMap.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u3 u2) u1} (AlternatingMap.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))))) (MultilinearMap.alternatization.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι _inst_10 (fun (a : ι) (b : ι) => _inst_11 a b)) m) v) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) (Equiv.Perm.{succ u1} ι) (AddCommGroup.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) _inst_8) (Finset.univ.{u1} (Equiv.Perm.{succ u1} ι) (equivFintype.{u1, u1} ι ι (fun (a : ι) (b : ι) => _inst_11 a b) (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10 _inst_10)) (fun (σ : Equiv.Perm.{succ u1} ι) => HSMul.hSMul.{0, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) σ) ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) (instHSMul.{0, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) σ) ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) (Units.instSMulUnits.{0, u2} Int ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) Int.instMonoidInt (SubNegMonoid.SMulInt.{u2} ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) (AddGroup.toSubNegMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) (AddCommGroup.toAddGroup.{u2} ((fun 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u1} ι) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} ι) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} ι (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10) σ) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (ι -> M) (fun (f : ι -> M) => (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') f) (MultilinearMap.instFunLikeMultilinearMapForAll.{u4, u3, u2, u1} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.domDomCongr.{u4, u3, u2, u1, u1} R M N' _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_3 _inst_9 ι ι σ m) v)))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_apply MultilinearMap.alternatization_applyₓ'. -/
 theorem alternatization_apply (m : MultilinearMap R (fun i : ι => M) N') (v : ι → M) :
     alternatization m v = ∑ σ : Perm ι, σ.sign • m.domDomCongr σ v := by
@@ -1376,7 +1376,7 @@ def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (σ : Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)), Eq.{max (succ (max u1 u2)) (succ u4) (succ (max u5 u6))} (MultilinearMap.{u3, u4, max u5 u6, max u1 u2} R' (Sum.{u1, u2} ιa ιb) (fun (_x : Sum.{u1, u2} ιa ιb) => Mᵢ) (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_17) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_18) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16)) (AlternatingMap.domCoprod.summand.{u1, u2, u3, u4, u5, u6} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b) a b (Quotient.mk''.{succ (max u1 u2)} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (QuotientGroup.leftRel.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} ιa ιb)) (MonoidHom.range.{max u1 u2, max u1 u2} (Prod.{u1, u2} (Equiv.Perm.{succ u1} ιa) (Equiv.Perm.{succ u2} ιb)) (Prod.group.{u1, u2} (Equiv.Perm.{succ u1} ιa) (Equiv.Perm.{succ u2} ιb) (Equiv.Perm.permGroup.{u1} ιa) (Equiv.Perm.permGroup.{u2} ιb)) (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.sumCongrHom.{u1, u2} ιa ιb))) σ)) (SMul.smul.{0, max (max u1 u2) u4 u5 u6} (Units.{0} Int Int.monoid) (MultilinearMap.{u3, u4, max u5 u6, max u1 u2} R' (Sum.{u1, u2} ιa ιb) (fun (_x : Sum.{u1, u2} ιa ιb) => Mᵢ) (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_17) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_18) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16)) (MultilinearMap.hasSmul.{u4, max u5 u6, max u1 u2, 0, u3} (Sum.{u1, u2} ιa ιb) (fun (_x : Sum.{u1, u2} ιa ιb) => Mᵢ) (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_17) (TensorProduct.addCommMonoid.{u3, u5, u6} R' 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+  forall {ιa : Type.{u3}} {ιb : Type.{u1}} [_inst_10 : Fintype.{u3} ιa] [_inst_11 : Fintype.{u1} ιb] {R' : Type.{u6}} {Mᵢ : Type.{u5}} {N₁ : Type.{u4}} {N₂ : Type.{u2}} [_inst_12 : CommSemiring.{u6} R'] [_inst_13 : AddCommGroup.{u4} N₁] [_inst_14 : Module.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u2} N₂] [_inst_16 : Module.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u5} Mᵢ] [_inst_18 : Module.{u6, u5} R' Mᵢ (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u3} ιa] [_inst_20 : DecidableEq.{succ u1} ιb] (a : AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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(MultilinearMap.domDomCongr.{u6, u5, max u4 u2, max u3 u1, max u3 u1} R' Mᵢ (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17 (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) _inst_18 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb) (Sum.{u3, u1} ιa ιb) σ (MultilinearMap.domCoprod.{u6, u3, u1, u4, u2, u5} R' ιa ιb _inst_12 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 Mᵢ _inst_17 _inst_18 (AlternatingMap.toMultilinearMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa a) (AlternatingMap.toMultilinearMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb b))))
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_mk' AlternatingMap.domCoprod.summand_mk''ₓ'. -/
 theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
     (σ : Equiv.Perm (Sum ιa ιb)) :
@@ -1554,7 +1554,7 @@ open Equiv
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : MultilinearMap.{u3, u4, u5, u1} R' ιa (fun (_x : ιa) => Mᵢ) N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : ιa) => _inst_17) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (fun (i : ιa) => _inst_18) _inst_14) (b : MultilinearMap.{u3, u4, u6, u2} R' ιb (fun (_x : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16), Eq.{max (succ (max u1 u2)) (succ u4) (succ (max u5 u6))} (MultilinearMap.{u3, u4, max u5 u6, max u1 u2} R' (Sum.{u1, u2} ιa ιb) (fun (_x : Sum.{u1, u2} ιa ιb) => Mᵢ) (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_17) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_18) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16)) (MultilinearMap.domCoprod.{u3, 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(MultilinearMap.domDomCongr.{u3, u4, u6, u2, u2} R' Mᵢ N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17 (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_18 _inst_16 ιb ιb σb b))))))
 but is expected to have type
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+  forall {ιa : Type.{u6}} {ιb : Type.{u5}} [_inst_10 : Fintype.{u6} ιa] [_inst_11 : Fintype.{u5} ιb] {R' : Type.{u4}} {Mᵢ : Type.{u3}} {N₁ : Type.{u2}} {N₂ : Type.{u1}} [_inst_12 : CommSemiring.{u4} R'] [_inst_13 : AddCommGroup.{u2} N₁] [_inst_14 : Module.{u4, u2} R' N₁ (CommSemiring.toSemiring.{u4} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u1} N₂] [_inst_16 : Module.{u4, u1} R' N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u3} Mᵢ] [_inst_18 : Module.{u4, u3} R' Mᵢ (CommSemiring.toSemiring.{u4} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u6} ιa] [_inst_20 : DecidableEq.{succ u5} ιb] (a : MultilinearMap.{u4, u3, u2, u6} R' ιa (fun (_x : ιa) => Mᵢ) N₁ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιa) => _inst_17) (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (fun (i : ιa) => _inst_18) _inst_14) (b : MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (_x : 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(AddCommGroup.toAddGroup.{max (max (max (max u6 u5) u3) u2) u1} (MultilinearMap.{u4, u3, max u1 u2, max u6 u5} R' (Sum.{u6, u5} ιa ιb) (fun (x._@.Mathlib.LinearAlgebra.Multilinear.TensorProduct._hyg.176 : Sum.{u6, u5} ιa ιb) => Mᵢ) (TensorProduct.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : Sum.{u6, u5} ιa ιb) => _inst_17) (TensorProduct.addCommMonoid.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (fun (i : Sum.{u6, u5} ιa ιb) => _inst_18) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16)) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u4, u3, max u2 u1, max u6 u5} R' (Sum.{u6, u5} ιa ιb) (fun (x._@.Mathlib.LinearAlgebra.Multilinear.TensorProduct._hyg.176 : Sum.{u6, u5} ιa ιb) => Mᵢ) (TensorProduct.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : Sum.{u6, u5} ιa ιb) => _inst_17) (TensorProduct.addCommGroup.{u4, u2, u1} R' _inst_12 N₁ N₂ _inst_13 _inst_15 _inst_14 _inst_16) (fun (i : Sum.{u6, u5} ιa ιb) => _inst_18) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16))))))) (FunLike.coe.{succ u5, succ u5, 1} (MonoidHom.{u5, 0} (Equiv.Perm.{succ u5} ιb) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u5} (Equiv.Perm.{succ u5} ιb) (DivInvMonoid.toMonoid.{u5} (Equiv.Perm.{succ u5} ιb) (Group.toDivInvMonoid.{u5} (Equiv.Perm.{succ u5} ιb) (Equiv.Perm.permGroup.{u5} ιb)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u5} ιb) (fun (_x : Equiv.Perm.{succ u5} ιb) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u5} ιb) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u5, u5, 0} (MonoidHom.{u5, 0} (Equiv.Perm.{succ u5} ιb) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u5} (Equiv.Perm.{succ u5} ιb) (DivInvMonoid.toMonoid.{u5} (Equiv.Perm.{succ u5} ιb) (Group.toDivInvMonoid.{u5} (Equiv.Perm.{succ u5} ιb) (Equiv.Perm.permGroup.{u5} ιb)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u5} ιb) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u5} (Equiv.Perm.{succ u5} ιb) (Monoid.toMulOneClass.{u5} (Equiv.Perm.{succ u5} ιb) (DivInvMonoid.toMonoid.{u5} (Equiv.Perm.{succ u5} ιb) (Group.toDivInvMonoid.{u5} (Equiv.Perm.{succ u5} ιb) (Equiv.Perm.permGroup.{u5} ιb))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u5, u5, 0} (MonoidHom.{u5, 0} (Equiv.Perm.{succ u5} ιb) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u5} (Equiv.Perm.{succ u5} ιb) (DivInvMonoid.toMonoid.{u5} (Equiv.Perm.{succ u5} ιb) (Group.toDivInvMonoid.{u5} (Equiv.Perm.{succ u5} ιb) (Equiv.Perm.permGroup.{u5} ιb)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u5} ιb) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u5} (Equiv.Perm.{succ u5} ιb) (DivInvMonoid.toMonoid.{u5} (Equiv.Perm.{succ u5} ιb) (Group.toDivInvMonoid.{u5} (Equiv.Perm.{succ u5} ιb) (Equiv.Perm.permGroup.{u5} ιb)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u5, 0} (Equiv.Perm.{succ u5} ιb) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u5} (Equiv.Perm.{succ u5} ιb) (DivInvMonoid.toMonoid.{u5} (Equiv.Perm.{succ u5} ιb) (Group.toDivInvMonoid.{u5} (Equiv.Perm.{succ u5} ιb) (Equiv.Perm.permGroup.{u5} ιb)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u5} ιb (fun (a : ιb) (b : ιb) => _inst_20 a b) _inst_11) σb) (MultilinearMap.domCoprod.{u4, u6, u5, u2, u1, u3} R' ιa ιb _inst_12 N₁ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) _inst_14 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 Mᵢ _inst_17 _inst_18 (MultilinearMap.domDomCongr.{u4, u3, u2, u6, u6} R' Mᵢ N₁ (CommSemiring.toSemiring.{u4} R' _inst_12) _inst_17 (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) _inst_18 _inst_14 ιa ιa σa a) (MultilinearMap.domDomCongr.{u4, u3, u1, u5, u5} R' Mᵢ N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) _inst_17 (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_18 _inst_16 ιb ιb σb b))))))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_alternization_coe MultilinearMap.domCoprod_alternization_coeₓ'. -/
 /-- A helper lemma for `multilinear_map.dom_coprod_alternization`. -/
 theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableEq ιb]

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

@@ -633,7 +633,7 @@ def compAlternatingMap (g : N →ₗ[R] N₂) : AlternatingMap R M N ι →+ Alt
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {N₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} N₂] [_inst_11 : Module.{u1, u5} R N₂ _inst_1 _inst_10] (g : LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Eq.{max (max (succ u4) (succ u2)) (succ u5)} ((ι -> M) -> N₂) (coeFn.{max (succ u2) (succ u5) (succ u4), max (max (succ u4) (succ u2)) (succ u5)} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (fun (_x : AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) => (ι -> M) -> N₂) (AlternatingMap.coeFun.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (coeFn.{max (succ (max u2 u5 u4)) (succ (max u2 u3 u4)), max (succ (max u2 u3 u4)) (succ (max u2 u5 u4))} (AddMonoidHom.{max u2 u3 u4, max u2 u5 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (fun (_x : AddMonoidHom.{max u2 u3 u4, max u2 u5 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) => (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) -> (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)) (AddMonoidHom.hasCoeToFun.{max u2 u3 u4, max u2 u5 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (LinearMap.compAlternatingMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι N₂ _inst_10 _inst_11 g) f)) (Function.comp.{max (succ u4) (succ u2), succ u3, succ u5} (ι -> M) N N₂ (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (fun (_x : LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) => N -> N₂) (LinearMap.hasCoeToFun.{u1, u1, u3, u5} R R N N₂ _inst_1 _inst_1 _inst_4 _inst_10 _inst_5 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) g) (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u5, u2} R M _inst_1 _inst_2] {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u5, u4} R N _inst_1 _inst_4] {ι : Type.{u1}} {N₂ : Type.{u3}} [_inst_10 : AddCommMonoid.{u3} N₂] [_inst_11 : Module.{u5, u3} R N₂ _inst_1 _inst_10] (g : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (f : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Eq.{max (max (succ u2) (succ u1)) (succ u3)} ((ι -> M) -> N₂) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (ι -> M) (fun (_x : ι -> M) => N₂) (AlternatingMap.funLike.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (FunLike.coe.{max (max 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_inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))))) (LinearMap.compAlternatingMap.{u5, u2, u4, u1, u3} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι N₂ _inst_10 _inst_11 g) f)) (Function.comp.{max (succ u2) (succ u1), succ u4, succ u3} (ι -> M) N N₂ (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => N₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R N N₂ _inst_1 _inst_1 _inst_4 _inst_10 _inst_5 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u1), max (succ u2) (succ u1), succ u4} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f))
 Case conversion may be inaccurate. Consider using '#align linear_map.coe_comp_alternating_map LinearMap.coe_compAlternatingMapₓ'. -/
 @[simp]
 theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) :
@@ -645,7 +645,7 @@ theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : AlternatingMap R M N
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {N₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} N₂] [_inst_11 : Module.{u1, u5} R N₂ _inst_1 _inst_10] (g : LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (m : ι -> M), Eq.{succ u5} N₂ (coeFn.{max (succ u2) (succ u5) (succ u4), max (max (succ u4) (succ u2)) (succ u5)} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (fun (_x : AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) => (ι -> M) -> N₂) (AlternatingMap.coeFun.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (coeFn.{max (succ (max u2 u5 u4)) (succ (max u2 u3 u4)), max (succ (max u2 u3 u4)) (succ (max u2 u5 u4))} (AddMonoidHom.{max u2 u3 u4, max u2 u5 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (fun (_x : AddMonoidHom.{max u2 u3 u4, max u2 u5 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) => (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) -> (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)) (AddMonoidHom.hasCoeToFun.{max u2 u3 u4, max u2 u5 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max u2 u5 u4} (AlternatingMap.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u1, u2, u5, u4} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (LinearMap.compAlternatingMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι N₂ _inst_10 _inst_11 g) f) m) (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (fun (_x : LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) => N -> N₂) (LinearMap.hasCoeToFun.{u1, u1, u3, u5} R R N N₂ _inst_1 _inst_1 _inst_4 _inst_10 _inst_5 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) g (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f m))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u5, u2} R M _inst_1 _inst_2] {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u5, u4} R N _inst_1 _inst_4] {ι : Type.{u1}} {N₂ : Type.{u3}} [_inst_10 : AddCommMonoid.{u3} N₂] [_inst_11 : Module.{u5, u3} R N₂ _inst_1 _inst_10] (g : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (f : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (m : ι -> M), Eq.{succ u3} N₂ (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (ι -> M) (fun (_x : ι -> M) => N₂) (AlternatingMap.funLike.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ 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_inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) _x) (AddHomClass.toFunLike.{max (max (max u4 u3) u1) u2, max (max u4 u1) u2, max (max u3 u1) u2} (AddMonoidHom.{max (max u1 u4) u2, max (max u1 u3) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddZeroClass.toAdd.{max (max u4 u1) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι)))) (AddZeroClass.toAdd.{max (max u3 u1) u2} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AddMonoidHomClass.toAddHomClass.{max (max (max u4 u3) u1) u2, max (max u4 u1) u2, max (max u3 u1) u2} (AddMonoidHom.{max (max u1 u4) u2, max (max u1 u3) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι))) (AddMonoidHom.addMonoidHomClass.{max (max u4 u1) u2, max (max u3 u1) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))))) (LinearMap.compAlternatingMap.{u5, u2, u4, u1, u3} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι N₂ _inst_10 _inst_11 g) f) m) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => N₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R N N₂ _inst_1 _inst_1 _inst_4 _inst_10 _inst_5 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u1), max (succ u2) (succ u1), succ u4} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f m))
+  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u5, u2} R M _inst_1 _inst_2] {N : Type.{u4}} [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u5, u4} R N _inst_1 _inst_4] {ι : Type.{u1}} {N₂ : Type.{u3}} [_inst_10 : AddCommMonoid.{u3} N₂] [_inst_11 : Module.{u5, u3} R N₂ _inst_1 _inst_10] (g : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (f : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (m : ι -> M), Eq.{succ u3} N₂ (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (ι -> M) (fun (_x : ι -> M) => N₂) (AlternatingMap.funLike.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ 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_inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) _x) (AddHomClass.toFunLike.{max (max (max u4 u3) u1) u2, max (max u4 u1) u2, max (max u3 u1) u2} (AddMonoidHom.{max (max u1 u4) u2, max (max u1 u3) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddZeroClass.toAdd.{max (max u4 u1) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι)))) (AddZeroClass.toAdd.{max (max u3 u1) u2} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AddMonoidHomClass.toAddHomClass.{max (max (max u4 u3) u1) u2, max (max u4 u1) u2, max (max u3 u1) u2} (AddMonoidHom.{max (max u1 u4) u2, max (max u1 u3) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι))) (AddMonoidHom.addMonoidHomClass.{max (max u4 u1) u2, max (max u3 u1) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.addCommMonoid.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι) (AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))))) (LinearMap.compAlternatingMap.{u5, u2, u4, u1, u3} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι N₂ _inst_10 _inst_11 g) f) m) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => N₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R N N₂ _inst_1 _inst_1 _inst_4 _inst_10 _inst_5 _inst_11 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u1), max (succ u2) (succ u1), succ u4} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f m))
 Case conversion may be inaccurate. Consider using '#align linear_map.comp_alternating_map_apply LinearMap.compAlternatingMap_applyₓ'. -/
 @[simp]
 theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) (m : ι → M) :
@@ -669,7 +669,7 @@ theorem subtype_compAlternatingMap_codRestrict (f : AlternatingMap R M N ι) (p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {N₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} N₂] [_inst_11 : Module.{u1, u5} R N₂ _inst_1 _inst_10] (g : LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N N₂ _inst_4 _inst_10 _inst_5 _inst_11) (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (p : Submodule.{u1, u5} R N₂ _inst_1 _inst_10 _inst_11) (h : forall (c : N), Membership.Mem.{u5, u5} N₂ (Submodule.{u1, u5} R N₂ _inst_1 _inst_10 _inst_11) (SetLike.hasMem.{u5, u5} (Submodule.{u1, u5} R N₂ _inst_1 _inst_10 _inst_11) N₂ (Submodule.setLike.{u1, u5} R N₂ _inst_1 _inst_10 _inst_11)) (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u1, u3, u5} R R 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 but is expected to have type
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(AlternatingMap.addCommMonoid.{u5, u2, u3, u1} R _inst_1 M _inst_2 _inst_3 N₂ _inst_10 _inst_11 ι)))))) (LinearMap.compAlternatingMap.{u5, u2, u4, u1, u3} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι N₂ _inst_10 _inst_11 g) f) p (fun (v : ι -> M) => h (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u1), max (succ u2) (succ u1), succ u4} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f v)))
 Case conversion may be inaccurate. Consider using '#align linear_map.comp_alternating_map_cod_restrict LinearMap.compAlternatingMap_codRestrictₓ'. -/
 @[simp]
 theorem compAlternatingMap_codRestrict (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι)
@@ -700,7 +700,7 @@ def compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) : Alterna
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {M₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u1, u5} R M₂ _inst_1 _inst_10] (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), Eq.{max (max (succ u4) (succ u5)) (succ u3)} ((ι -> M₂) -> N) (coeFn.{max (succ u5) (succ u3) (succ u4), max (max (succ u4) (succ u5)) (succ u3)} (AlternatingMap.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) => (ι -> M₂) -> N) (AlternatingMap.coeFun.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 f g)) (Function.comp.{max (succ u4) (succ u5), max (succ u4) (succ u2), succ u3} (ι -> M₂) (ι -> M) N (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f) (Function.comp.{succ u4, succ u5, succ u2} ι M₂ M (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) => M₂ -> M) (LinearMap.hasCoeToFun.{u1, u1, u5, u2} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) g)))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u5, u4} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u5, u3} R N _inst_1 _inst_4] {ι : Type.{u2}} {M₂ : Type.{u1}} [_inst_10 : AddCommMonoid.{u1} M₂] [_inst_11 : Module.{u5, u1} R M₂ _inst_1 _inst_10] (f : AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g : LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((ι -> M₂) -> N) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlternatingMap.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (ι -> M₂) (fun (_x : ι -> M₂) => N) (AlternatingMap.funLike.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 f g)) (Function.comp.{max (succ u1) (succ u2), max (succ u4) (succ u2), succ u3} (ι -> M₂) (ι -> M) N (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), succ u3} (AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f) ((fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.7564 : M₂ -> M) (x._@.Mathlib.LinearAlgebra.Alternating._hyg.7566 : ι -> M₂) => Function.comp.{succ u2, succ u1, succ u4} ι M₂ M x._@.Mathlib.LinearAlgebra.Alternating._hyg.7564 x._@.Mathlib.LinearAlgebra.Alternating._hyg.7566) (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u1, u4} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g)))
+  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u5, u4} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u5, u3} R N _inst_1 _inst_4] {ι : Type.{u2}} {M₂ : Type.{u1}} [_inst_10 : AddCommMonoid.{u1} M₂] [_inst_11 : Module.{u5, u1} R M₂ _inst_1 _inst_10] (f : AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g : LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((ι -> M₂) -> N) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlternatingMap.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (ι -> M₂) (fun (_x : ι -> M₂) => N) (AlternatingMap.funLike.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 f g)) (Function.comp.{max (succ u1) (succ u2), max (succ u4) (succ u2), succ u3} (ι -> M₂) (ι -> M) N (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), succ u3} (AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f) ((fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.7564 : M₂ -> M) (x._@.Mathlib.LinearAlgebra.Alternating._hyg.7566 : ι -> M₂) => Function.comp.{succ u2, succ u1, succ u4} ι M₂ M x._@.Mathlib.LinearAlgebra.Alternating._hyg.7564 x._@.Mathlib.LinearAlgebra.Alternating._hyg.7566) (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u1, u4} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g)))
 Case conversion may be inaccurate. Consider using '#align alternating_map.coe_comp_linear_map AlternatingMap.coe_compLinearMapₓ'. -/
 theorem coe_compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
     ⇑(f.compLinearMap g) = f ∘ (· ∘ ·) g :=
@@ -711,7 +711,7 @@ theorem coe_compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {M₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u1, u5} R M₂ _inst_1 _inst_10] (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (v : ι -> M₂), Eq.{succ u3} N (coeFn.{max (succ u5) (succ u3) (succ u4), max (max (succ u4) (succ u5)) (succ u3)} (AlternatingMap.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) => (ι -> M₂) -> N) (AlternatingMap.coeFun.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 f g) v) (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (fun (i : ι) => coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) => M₂ -> M) (LinearMap.hasCoeToFun.{u1, u1, u5, u2} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) g (v i)))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u5, u4} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u5, u3} R N _inst_1 _inst_4] {ι : Type.{u2}} {M₂ : Type.{u1}} [_inst_10 : AddCommMonoid.{u1} M₂] [_inst_11 : Module.{u5, u1} R M₂ _inst_1 _inst_10] (f : AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g : LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (v : ι -> M₂), Eq.{succ u3} N (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlternatingMap.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (ι -> M₂) (fun (_x : ι -> M₂) => N) (AlternatingMap.funLike.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 f g) v) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), succ u3} (AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (fun (i : ι) => FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u1, u4} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g (v i)))
+  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u5, u4} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u5, u3} R N _inst_1 _inst_4] {ι : Type.{u2}} {M₂ : Type.{u1}} [_inst_10 : AddCommMonoid.{u1} M₂] [_inst_11 : Module.{u5, u1} R M₂ _inst_1 _inst_10] (f : AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g : LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (v : ι -> M₂), Eq.{succ u3} N (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlternatingMap.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (ι -> M₂) (fun (_x : ι -> M₂) => N) (AlternatingMap.funLike.{u5, u1, u3, u2} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 f g) v) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), succ u3} (AlternatingMap.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u5, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f (fun (i : ι) => FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (LinearMap.{u5, u5, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u1, u4} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) g (v i)))
 Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_apply AlternatingMap.compLinearMap_applyₓ'. -/
 @[simp]
 theorem compLinearMap_apply (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) (v : ι → M₂) :
@@ -788,7 +788,7 @@ theorem compLinearMap_id (f : AlternatingMap R M N ι) : f.compLinearMap LinearM
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {M₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u1, u5} R M₂ _inst_1 _inst_10] (f : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), (Function.Surjective.{succ u5, succ u2} M₂ M (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) => M₂ -> M) (LinearMap.hasCoeToFun.{u1, u1, u5, u2} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (Function.Injective.{max (succ u2) (succ u3) (succ u4), max (succ u5) (succ u3) (succ u4)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (fun (g : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => AlternatingMap.compLinearMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g f))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u3}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u5, u3} R M _inst_1 _inst_2] {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u5, u2} R N _inst_1 _inst_4] {ι : Type.{u1}} {M₂ : Type.{u4}} [_inst_10 : AddCommMonoid.{u4} M₂] [_inst_11 : Module.{u5, u4} R M₂ _inst_1 _inst_10] (f : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), (Function.Surjective.{succ u4, succ u3} M₂ M (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f)) -> (Function.Injective.{max (max (succ u3) (succ u2)) (succ u1), max (max (succ u2) (succ u1)) (succ u4)} (AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u4, u2, u1} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (fun (g : AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g f))
+  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u3}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u5, u3} R M _inst_1 _inst_2] {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u5, u2} R N _inst_1 _inst_4] {ι : Type.{u1}} {M₂ : Type.{u4}} [_inst_10 : AddCommMonoid.{u4} M₂] [_inst_11 : Module.{u5, u4} R M₂ _inst_1 _inst_10] (f : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), (Function.Surjective.{succ u4, succ u3} M₂ M (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f)) -> (Function.Injective.{max (max (succ u3) (succ u2)) (succ u1), max (max (succ u2) (succ u1)) (succ u4)} (AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (AlternatingMap.{u5, u4, u2, u1} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (fun (g : AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g f))
 Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_injective AlternatingMap.compLinearMap_injectiveₓ'. -/
 /-- Composing with a surjective linear map is injective. -/
 theorem compLinearMap_injective (f : M₂ →ₗ[R] M) (hf : Function.Surjective f) :
@@ -800,7 +800,7 @@ theorem compLinearMap_injective (f : M₂ →ₗ[R] M) (hf : Function.Surjective
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} {M₂ : Type.{u5}} [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u1, u5} R M₂ _inst_1 _inst_10] (f : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), (Function.Surjective.{succ u5, succ u2} M₂ M (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) => M₂ -> M) (LinearMap.hasCoeToFun.{u1, u1, u5, u2} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (forall (g₁ : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g₂ : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Iff (Eq.{max (succ u5) (succ u3) (succ u4)} (AlternatingMap.{u1, u5, u3, u4} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g₁ f) (AlternatingMap.compLinearMap.{u1, u2, u3, u4, u5} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g₂ f)) (Eq.{max (succ u2) (succ u3) (succ u4)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) g₁ g₂))
 but is expected to have type
-  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u3}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u5, u3} R M _inst_1 _inst_2] {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u5, u2} R N _inst_1 _inst_4] {ι : Type.{u1}} {M₂ : Type.{u4}} [_inst_10 : AddCommMonoid.{u4} M₂] [_inst_11 : Module.{u5, u4} R M₂ _inst_1 _inst_10] (f : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), (Function.Surjective.{succ u4, succ u3} M₂ M (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f)) -> (forall (g₁ : AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g₂ : AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u4)} (AlternatingMap.{u5, u4, u2, u1} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g₁ f) (AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g₂ f)) (Eq.{max (max (succ u3) (succ u2)) (succ u1)} (AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) g₁ g₂))
+  forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u3}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u5, u3} R M _inst_1 _inst_2] {N : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u5, u2} R N _inst_1 _inst_4] {ι : Type.{u1}} {M₂ : Type.{u4}} [_inst_10 : AddCommMonoid.{u4} M₂] [_inst_11 : Module.{u5, u4} R M₂ _inst_1 _inst_10] (f : LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3), (Function.Surjective.{succ u4, succ u3} M₂ M (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M₂ M _inst_10 _inst_2 _inst_11 _inst_3) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂) => M) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u3} R R M₂ M _inst_1 _inst_1 _inst_10 _inst_2 _inst_11 _inst_3 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) f)) -> (forall (g₁ : AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (g₂ : AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u4)} (AlternatingMap.{u5, u4, u2, u1} R _inst_1 M₂ _inst_10 _inst_11 N _inst_4 _inst_5 ι) (AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g₁ f) (AlternatingMap.compLinearMap.{u5, u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι M₂ _inst_10 _inst_11 g₂ f)) (Eq.{max (max (succ u3) (succ u2)) (succ u1)} (AlternatingMap.{u5, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) g₁ g₂))
 Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_inj AlternatingMap.compLinearMap_injₓ'. -/
 theorem compLinearMap_inj (f : M₂ →ₗ[R] M) (hf : Function.Surjective f)
     (g₁ g₂ : AlternatingMap R M N ι) : g₁.compLinearMap f = g₂.compLinearMap f ↔ g₁ = g₂ :=
@@ -1538,7 +1538,7 @@ def domCoprod' :
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb), Eq.{max (succ u4) (succ (max u5 u6)) (succ (max u1 u2))} (AlternatingMap.{u3, u4, max u5 u6, max u1 u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u1, u2} ιa ιb)) (coeFn.{max (succ (max (max u4 u5 u1) u4 u6 u2)) (succ (max u4 (max u5 u6) u1 u2)), max (succ (max (max u4 u5 u1) u4 u6 u2)) (succ (max u4 (max u5 u6) u1 u2))} (LinearMap.{u3, u3, max (max u4 u5 u1) u4 u6 u2, max u4 (max u5 u6) u1 u2} R' R' (CommSemiring.toSemiring.{u3} R' _inst_12) (CommSemiring.toSemiring.{u3} R' _inst_12) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12))) (TensorProduct.{u3, max u4 u5 u1, max u4 u6 u2} R' _inst_12 (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u3, u4, u5, u1, u3} R' 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_inst_14 _inst_16) (Sum.{u1, u2} ιa ιb) R' (CommSemiring.toSemiring.{u3} R' _inst_12) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (AlternatingMap.domCoprod'._proof_3.{u3, u5, u6} R' N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16))) => (TensorProduct.{u3, max u4 u5 u1, max u4 u6 u2} R' _inst_12 (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u3, u4, u5, u1, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_14 (AlternatingMap.domCoprod'._proof_1.{u3, u5} R' N₁ _inst_12 _inst_13 _inst_14)) (AlternatingMap.module.{u3, u4, u6, u2, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_16 (AlternatingMap.domCoprod'._proof_2.{u3, u6} R' N₂ _inst_12 _inst_15 _inst_16))) -> (AlternatingMap.{u3, u4, max u5 u6, max u1 u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ 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(AlternatingMap.addCommMonoid.{u3, u4, max u5 u6, max u1 u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u1, u2} ιa ιb)) (TensorProduct.module.{u3, max u4 u5 u1, max u4 u6 u2} R' _inst_12 (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u3, u4, u5, u1, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_14 (AlternatingMap.domCoprod'._proof_1.{u3, u5} R' N₁ _inst_12 _inst_13 _inst_14)) (AlternatingMap.module.{u3, u4, u6, u2, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_16 (AlternatingMap.domCoprod'._proof_2.{u3, u6} 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_inst_16)) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12)))) (AlternatingMap.domCoprod'.{u1, u2, u3, u4, u5, u6} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b)) (TensorProduct.tmul.{u3, max u4 u5 u1, max u4 u6 u2} R' _inst_12 (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u3, u4, u5, u1, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_14 (AlternatingMap.domCoprod'._proof_1.{u3, u5} R' N₁ _inst_12 _inst_13 _inst_14)) (AlternatingMap.module.{u3, u4, u6, u2, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_16 (AlternatingMap.domCoprod'._proof_2.{u3, u6} R' N₂ _inst_12 _inst_15 _inst_16)) a b)) (AlternatingMap.domCoprod.{u1, u2, u3, u4, u5, u6} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b) a b)
 but is expected to have type
-  forall {ιa : Type.{u3}} {ιb : Type.{u1}} [_inst_10 : Fintype.{u3} ιa] [_inst_11 : Fintype.{u1} ιb] {R' : Type.{u6}} {Mᵢ : Type.{u5}} {N₁ : Type.{u4}} {N₂ : Type.{u2}} [_inst_12 : CommSemiring.{u6} R'] [_inst_13 : AddCommGroup.{u4} N₁] [_inst_14 : Module.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u2} N₂] [_inst_16 : Module.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u5} Mᵢ] [_inst_18 : Module.{u6, u5} R' Mᵢ (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u3} ιa] [_inst_20 : DecidableEq.{succ u1} ιb] (a : AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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_inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (fun (_x : TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) => AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, max (max (max (max u2 u4) u5) u1) u3, max (max (max (max u2 u4) u5) u1) u3} R' R' (TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) (CommSemiring.toSemiring.{u6} R' _inst_12) (CommSemiring.toSemiring.{u6} R' _inst_12) (TensorProduct.addCommMonoid.{u6, max (max u3 u5) u4, max (max u1 u5) u2} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.addCommMonoid.{u6, u5, max u4 u2, max u3 u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ 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(AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} 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_inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16))))) (RingHom.id.{u6} R' (Semiring.toNonAssocSemiring.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)))) (AlternatingMap.domCoprod'.{u3, u1, u6, u5, u4, u2} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b)) (TensorProduct.tmul.{u6, max (max u4 u5) u3, max (max u2 u5) u1} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) 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N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16)))) a b)) (AlternatingMap.domCoprod.{u3, u1, u6, u5, u4, u2} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b) a b)
+  forall {ιa : Type.{u3}} {ιb : Type.{u1}} [_inst_10 : Fintype.{u3} ιa] [_inst_11 : Fintype.{u1} ιb] {R' : Type.{u6}} {Mᵢ : Type.{u5}} {N₁ : Type.{u4}} {N₂ : Type.{u2}} [_inst_12 : CommSemiring.{u6} R'] [_inst_13 : AddCommGroup.{u4} N₁] [_inst_14 : Module.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u2} N₂] [_inst_16 : Module.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u5} Mᵢ] [_inst_18 : Module.{u6, u5} R' Mᵢ (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u3} ιa] [_inst_20 : DecidableEq.{succ u1} ιb] (a : AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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_inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (fun (_x : TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) => AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, max (max (max (max u2 u4) u5) u1) u3, max (max (max (max u2 u4) u5) u1) u3} R' R' (TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) (CommSemiring.toSemiring.{u6} R' _inst_12) (CommSemiring.toSemiring.{u6} R' _inst_12) (TensorProduct.addCommMonoid.{u6, max (max u3 u5) u4, max (max u1 u5) u2} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.addCommMonoid.{u6, u5, max u4 u2, max u3 u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, max (max u3 u5) u4, max (max u1 u5) u2} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.module.{u6, u5, max u4 u2, max u3 u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb) R' (CommSemiring.toSemiring.{u6} R' _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (smulCommClass_self.{u6, max u4 u2} R' (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, max u4 u2} R' (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (SubNegZeroMonoid.toNegZeroClass.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (SubtractionMonoid.toSubNegZeroMonoid.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (SubtractionCommMonoid.toSubtractionMonoid.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (AddCommGroup.toDivisionAddCommMonoid.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommGroup.{u6, u4, u2} R' _inst_12 N₁ N₂ _inst_13 _inst_15 _inst_14 _inst_16)))))) (Module.toMulActionWithZero.{u6, max u4 u2} R' (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u6} R' _inst_12) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16))))) (RingHom.id.{u6} R' (Semiring.toNonAssocSemiring.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)))) (AlternatingMap.domCoprod'.{u3, u1, u6, u5, u4, u2} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b)) (TensorProduct.tmul.{u6, max (max u4 u5) u3, max (max u2 u5) u1} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16)))) a b)) (AlternatingMap.domCoprod.{u3, u1, u6, u5, u4, u2} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b) a b)
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod'_apply AlternatingMap.domCoprod'_applyₓ'. -/
 @[simp]
 theorem domCoprod'_apply (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
@@ -1759,7 +1759,7 @@ def curryLeftLinearMap {n : ℕ} :
 lean 3 declaration is
   forall {R' : Type.{u1}} {M'' : Type.{u2}} {N'' : Type.{u3}} [_inst_10 : CommSemiring.{u1} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_13 : AddCommMonoid.{u3} N''] [_inst_15 : Module.{u1, u2} R' M'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11] [_inst_17 : Module.{u1, u3} R' N'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_13] {n : Nat} (f : AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ (Nat.succ n)))) (m : M''), Eq.{max (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (coeFn.{max (succ u2) (succ (max u2 u3)), max (succ u2) (succ (max u2 u3))} (LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) => M'' -> (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u3} R' R' M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) (AlternatingMap.curryLeft.{u1, u2, u3} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n (coeFn.{max (succ u2) (succ (max u2 u3)), max (succ u2) (succ (max u2 u3))} (LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) => M'' -> (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u3} R' R' M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) (AlternatingMap.curryLeft.{u1, u2, u3} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 (Nat.succ n) f) m)) m) (OfNat.ofNat.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) 0 (OfNat.mk.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) 0 (Zero.zero.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.zero.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)))))
 but is expected to have type
-  forall {R' : Type.{u3}} {M'' : Type.{u2}} {N'' : Type.{u1}} [_inst_10 : CommSemiring.{u3} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_13 : AddCommMonoid.{u1} N''] [_inst_15 : Module.{u3, u2} R' M'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11] [_inst_17 : Module.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13] {n : Nat} (f : AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ (Nat.succ n)))) (m : M''), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) m) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10))) M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u2 u1} R' R' M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)))) (AlternatingMap.curryLeft.{u3, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10))) M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u2 u1} R' R' M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)))) (AlternatingMap.curryLeft.{u3, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) f) m)) m) (OfNat.ofNat.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) m) 0 (Zero.toOfNat0.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) m) (AlternatingMap.zero.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n))))
+  forall {R' : Type.{u3}} {M'' : Type.{u2}} {N'' : Type.{u1}} [_inst_10 : CommSemiring.{u3} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_13 : AddCommMonoid.{u1} N''] [_inst_15 : Module.{u3, u2} R' M'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11] [_inst_17 : Module.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13] {n : Nat} (f : AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ (Nat.succ n)))) (m : M''), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) m) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10))) M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u2 u1} R' R' M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)))) (AlternatingMap.curryLeft.{u3, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10))) M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, max u2 u1} R' R' M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)))) (AlternatingMap.curryLeft.{u3, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) f) m)) m) (OfNat.ofNat.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) m) 0 (Zero.toOfNat0.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) m) (AlternatingMap.zero.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n))))
 Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_same AlternatingMap.curryLeft_sameₓ'. -/
 /-- Currying with the same element twice gives the zero map. -/
 @[simp]
@@ -1772,7 +1772,7 @@ theorem curryLeft_same {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ.succ
 lean 3 declaration is
   forall {R' : Type.{u1}} {M'' : Type.{u2}} {N'' : Type.{u3}} {N₂'' : Type.{u4}} [_inst_10 : CommSemiring.{u1} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_13 : AddCommMonoid.{u3} N''] [_inst_14 : AddCommMonoid.{u4} N₂''] [_inst_15 : Module.{u1, u2} R' M'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11] [_inst_17 : Module.{u1, u3} R' N'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_13] [_inst_18 : Module.{u1, u4} R' N₂'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_14] {n : Nat} (g : LinearMap.{u1, u1, u3, u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) N'' N₂'' _inst_13 _inst_14 _inst_17 _inst_18) (f : AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (m : M''), Eq.{max (succ u2) (succ u4)} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (coeFn.{max (succ u2) (succ (max u2 u4)), max (succ u2) (succ (max u2 u4))} (LinearMap.{u1, u1, u2, max u2 u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_18 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N₂'' _inst_10 _inst_14 _inst_18))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_18 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N₂'' _inst_10 _inst_14 _inst_18))) => M'' -> (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u4} R' R' M'' (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_18 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N₂'' _inst_10 _inst_14 _inst_18)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) (AlternatingMap.curryLeft.{u1, u2, u4} R' M'' N₂'' _inst_10 _inst_11 _inst_14 _inst_15 _inst_18 n (coeFn.{max (succ (max u2 u4)) (succ (max u2 u3)), max (succ (max u2 u3)) (succ (max u2 u4))} (AddMonoidHom.{max u2 u3, max u2 u4} 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(AddCommMonoid.toAddMonoid.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n))) (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n)))))) (fun (_x : AddMonoidHom.{max u2 u3, max u2 u4} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n))) (AddMonoid.toAddZeroClass.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (AddCommMonoid.toAddMonoid.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))))) (AddMonoid.toAddZeroClass.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n))) (AddCommMonoid.toAddMonoid.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n))) (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n)))))) => (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) -> (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin 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_inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n))) (AddCommMonoid.toAddMonoid.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n))) (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin (Nat.succ n)))))) (LinearMap.compAlternatingMap.{u1, u2, u3, 0, u4} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) N₂'' _inst_14 _inst_18 g) f)) m) (coeFn.{max (succ (max u2 u4)) (succ (max u2 u3)), max (succ (max u2 u3)) (succ (max u2 u4))} (AddMonoidHom.{max u2 u3, max u2 u4} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddMonoid.toAddZeroClass.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)))) (AddMonoid.toAddZeroClass.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n))))) (fun (_x : AddMonoidHom.{max u2 u3, max u2 u4} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddMonoid.toAddZeroClass.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)))) (AddMonoid.toAddZeroClass.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n))))) => (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) -> (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n))) (AddMonoidHom.hasCoeToFun.{max u2 u3, max u2 u4} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddMonoid.toAddZeroClass.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)))) (AddMonoid.toAddZeroClass.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u4} (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n))))) (LinearMap.compAlternatingMap.{u1, u2, u3, 0, u4} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) N₂'' _inst_14 _inst_18 g) (coeFn.{max (succ u2) (succ (max u2 u3)), max (succ u2) (succ (max u2 u3))} (LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) => M'' -> (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u3} R' R' M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) (AlternatingMap.curryLeft.{u1, u2, u3} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f) m))
 but is expected to have type
-  forall {R' : Type.{u4}} {M'' : Type.{u1}} {N'' : Type.{u3}} {N₂'' : Type.{u2}} [_inst_10 : CommSemiring.{u4} R'] [_inst_11 : AddCommMonoid.{u1} M''] [_inst_13 : AddCommMonoid.{u3} N''] [_inst_14 : AddCommMonoid.{u2} N₂''] [_inst_15 : Module.{u4, u1} R' M'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11] [_inst_17 : Module.{u4, u3} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13] [_inst_18 : Module.{u4, u2} R' N₂'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_14] {n : Nat} (g : LinearMap.{u4, u4, u3, u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) N'' N₂'' _inst_13 _inst_14 _inst_17 _inst_18) (f : AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (m : M''), Eq.{max (succ u1) (succ u2)} ((fun 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n)))) (AddMonoidHom.addMonoidHomClass.{max u3 u1, max u2 u1} (AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.{u4, u1, u2, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddMonoid.toAddZeroClass.{max u1 u3} (AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AddCommMonoid.toAddMonoid.{max u1 u3} (AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.addCommMonoid.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)))) (AddMonoid.toAddZeroClass.{max u1 u2} (AlternatingMap.{u4, u1, u2, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AddCommMonoid.toAddMonoid.{max u1 u2} (AlternatingMap.{u4, u1, u2, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n)) (AlternatingMap.addCommMonoid.{u4, u1, u2, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N₂'' _inst_14 _inst_18 (Fin n))))))) (LinearMap.compAlternatingMap.{u4, u1, u3, 0, u2} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) N₂'' _inst_14 _inst_18 g) (FunLike.coe.{max (succ u1) (succ u3), succ u1, max (succ u1) (succ u3)} (LinearMap.{u4, u4, u1, max u3 u1} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M'' (AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u1, u3, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u3} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u3} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u3} N'' (AddCommMonoid.toAddMonoid.{u3} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u3} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u1 u3} R' R' M'' (AlternatingMap.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u4, u1, u3, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u1, u3, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u3} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u3} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u3} N'' (AddCommMonoid.toAddMonoid.{u3} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u3} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) (AlternatingMap.curryLeft.{u4, u1, u3} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f) m))
 Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_comp_alternating_map AlternatingMap.curryLeft_compAlternatingMapₓ'. -/
 @[simp]
 theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
@@ -1785,7 +1785,7 @@ theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
 lean 3 declaration is
   forall {R' : Type.{u1}} {M'' : Type.{u2}} {M₂'' : Type.{u3}} {N'' : Type.{u4}} [_inst_10 : CommSemiring.{u1} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_12 : AddCommMonoid.{u3} M₂''] [_inst_13 : AddCommMonoid.{u4} N''] [_inst_15 : Module.{u1, u2} R' M'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11] [_inst_16 : Module.{u1, u3} R' M₂'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_12] [_inst_17 : Module.{u1, u4} R' N'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_13] {n : Nat} (g : LinearMap.{u1, u1, u3, u2} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) (f : AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (m : M₂''), Eq.{max (succ u3) (succ u4)} (AlternatingMap.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) (coeFn.{max (succ u3) (succ (max u3 u4)), max (succ u3) (succ (max u3 u4))} (LinearMap.{u1, u1, u3, max u3 u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M₂'' (AlternatingMap.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_12 (AlternatingMap.addCommMonoid.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_16 (AlternatingMap.module.{u1, u3, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N'' _inst_10 _inst_13 _inst_17))) (fun (_x : LinearMap.{u1, u1, u3, max u3 u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M₂'' (AlternatingMap.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_12 (AlternatingMap.addCommMonoid.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_16 (AlternatingMap.module.{u1, u3, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N'' _inst_10 _inst_13 _inst_17))) => M₂'' -> (AlternatingMap.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n))) (LinearMap.hasCoeToFun.{u1, u1, u3, max u3 u4} R' R' M₂'' (AlternatingMap.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_12 (AlternatingMap.addCommMonoid.{u1, u3, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_16 (AlternatingMap.module.{u1, u3, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N'' _inst_10 _inst_13 _inst_17)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) (AlternatingMap.curryLeft.{u1, u3, u4} R' M₂'' N'' _inst_10 _inst_12 _inst_13 _inst_16 _inst_17 n (AlternatingMap.compLinearMap.{u1, u2, u4, 0, u3} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) M₂'' _inst_12 _inst_16 f g)) m) (AlternatingMap.compLinearMap.{u1, u2, u4, 0, u3} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) M₂'' _inst_12 _inst_16 (coeFn.{max (succ u2) (succ (max u2 u4)), max (succ u2) (succ (max u2 u4))} (LinearMap.{u1, u1, u2, max u2 u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N'' _inst_10 _inst_13 _inst_17))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u4} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N'' _inst_10 _inst_13 _inst_17))) => M'' -> (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u4} R' R' M'' (AlternatingMap.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u4, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u4, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u4, u1} R' N'' _inst_10 _inst_13 _inst_17)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) (AlternatingMap.curryLeft.{u1, u2, u4} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f) (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u1, u1, u3, u2} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) (fun (_x : LinearMap.{u1, u1, u3, u2} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) => M₂'' -> M'') (LinearMap.hasCoeToFun.{u1, u1, u3, u2} R' R' M₂'' M'' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_12 _inst_11 _inst_16 _inst_15 (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)))) g m)) g)
 but is expected to have type
-  forall {R' : Type.{u4}} {M'' : Type.{u2}} {M₂'' : Type.{u3}} {N'' : Type.{u1}} [_inst_10 : CommSemiring.{u4} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_12 : AddCommMonoid.{u3} M₂''] [_inst_13 : AddCommMonoid.{u1} N''] [_inst_15 : Module.{u4, u2} R' M'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11] [_inst_16 : Module.{u4, u3} R' M₂'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12] [_inst_17 : Module.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13] {n : Nat} (g : LinearMap.{u4, u4, u3, u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) (f : AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (m : M₂''), Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂'') => AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) m) (FunLike.coe.{max (succ u3) (succ u1), succ u3, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u3, max u1 u3} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' (AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_12 (AlternatingMap.addCommMonoid.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_16 (AlternatingMap.module.{u4, u3, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17))))) M₂'' (fun (_x : M₂'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂'') => AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u3 u1} R' R' M₂'' (AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12 (AlternatingMap.addCommMonoid.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_16 (AlternatingMap.module.{u4, u3, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) (AlternatingMap.curryLeft.{u4, u3, u1} R' M₂'' N'' _inst_10 _inst_12 _inst_13 _inst_16 _inst_17 n (AlternatingMap.compLinearMap.{u4, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) M₂'' _inst_12 _inst_16 f g)) m) (AlternatingMap.compLinearMap.{u4, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) M₂'' _inst_12 _inst_16 (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u4, u4, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M'' (AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u2, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M'') => AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u2, max u2 u1} R' R' M'' (AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u2, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) (AlternatingMap.curryLeft.{u4, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) M₂'' (fun (_x : M₂'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂'') => M'') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R' R' M₂'' M'' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12 _inst_11 _inst_16 _inst_15 (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) g m)) g)
+  forall {R' : Type.{u4}} {M'' : Type.{u2}} {M₂'' : Type.{u3}} {N'' : Type.{u1}} [_inst_10 : CommSemiring.{u4} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_12 : AddCommMonoid.{u3} M₂''] [_inst_13 : AddCommMonoid.{u1} N''] [_inst_15 : Module.{u4, u2} R' M'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11] [_inst_16 : Module.{u4, u3} R' M₂'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12] [_inst_17 : Module.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13] {n : Nat} (g : LinearMap.{u4, u4, u3, u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) (f : AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (m : M₂''), Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂'') => AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) m) (FunLike.coe.{max (succ u3) (succ u1), succ u3, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u3, max u1 u3} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' (AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_12 (AlternatingMap.addCommMonoid.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_16 (AlternatingMap.module.{u4, u3, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17))))) M₂'' (fun (_x : M₂'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂'') => AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u3 u1} R' R' M₂'' (AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12 (AlternatingMap.addCommMonoid.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' 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(Fin (Nat.succ n)) M₂'' _inst_12 _inst_16 f g)) m) (AlternatingMap.compLinearMap.{u4, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) M₂'' _inst_12 _inst_16 (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u4, u4, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M'' (AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u2, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u2, max u2 u1} R' R' M'' (AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u2, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) (AlternatingMap.curryLeft.{u4, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) M₂'' (fun (_x : M₂'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂'') => M'') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R' R' M₂'' M'' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12 _inst_11 _inst_16 _inst_15 (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) g m)) g)
 Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_comp_linear_map AlternatingMap.curryLeft_compLinearMapₓ'. -/
 @[simp]
 theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')

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

@@ -1230,7 +1230,7 @@ def alternatization : MultilinearMap R (fun i : ι => M) N' →+ AlternatingMap
 lean 3 declaration is
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 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] {M : Type.{u3}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u4, u3} R M _inst_1 _inst_2] {N' : Type.{u2}} [_inst_8 : AddCommGroup.{u2} N'] [_inst_9 : Module.{u4, u2} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8)] {ι : Type.{u1}} [_inst_10 : Fintype.{u1} ι] [_inst_11 : DecidableEq.{succ u1} ι] (m : MultilinearMap.{u4, u3, u2, u1} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9), Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((ι -> M) -> N') (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (AlternatingMap.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (ι -> M) (fun (_x : ι -> M) => N') (AlternatingMap.funLike.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) 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_inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9)))))) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.Perm.{succ u1} ι) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} ι) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} ι (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10) σ) (MultilinearMap.domDomCongr.{u4, u3, u2, u1, u1} R M N' _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_3 _inst_9 ι ι σ m))))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_def MultilinearMap.alternatization_defₓ'. -/
 theorem alternatization_def (m : MultilinearMap R (fun i : ι => M) N') :
     ⇑(alternatization m) = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
@@ -1241,7 +1241,7 @@ theorem alternatization_def (m : MultilinearMap R (fun i : ι => M) N') :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} [_inst_10 : Fintype.{u4} ι] [_inst_11 : DecidableEq.{succ u4} ι] (m : MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9), Eq.{max (succ u4) (succ u2) (succ u3)} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) ((fun (a : Sort.{max (succ u2) (succ u3) (succ u4)}) (b : Sort.{max (succ u4) (succ u2) (succ u3)}) [self : HasLiftT.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} a b] => self.0) (AlternatingMap.{u1, u2, u3, u4} R 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N' (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommGroup.toAddGroup.{u3} N' _inst_8) (Module.toDistribMulAction.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9)))) (coeFn.{succ u4, succ u4} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u4} ι) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int 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 but is expected to have type
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(x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max (max u3 u2) u1} (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max (max u3 u2) u1} (AlternatingMap.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u3 u2) u1} (AlternatingMap.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u3 u2) u1} (AlternatingMap.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))))) (MultilinearMap.alternatization.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι _inst_10 (fun (a : ι) (b : ι) => _inst_11 a b)) m)) (Finset.sum.{max (max u3 u2) u1, u1} (MultilinearMap.{u4, u3, u2, u1} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (Equiv.Perm.{succ u1} ι) (MultilinearMap.addCommMonoid.{u4, u3, u2, u1} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (Finset.univ.{u1} (Equiv.Perm.{succ u1} ι) (equivFintype.{u1, u1} ι ι (fun (a : ι) (b : ι) => _inst_11 a b) (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10 _inst_10)) (fun (σ : Equiv.Perm.{succ u1} ι) => HSMul.hSMul.{0, max (max u1 u2) u3, max (max u3 u2) u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) σ) (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.{u4, u3, u2, u1} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (instHSMul.{0, max (max u3 u2) u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) σ) (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (Units.instSMulUnits.{0, max (max u3 u2) u1} Int (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) Int.instMonoidInt (SubNegMonoid.SMulInt.{max (max u3 u2) u1} (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max (max u3 u2) u1} (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max (max u3 u2) u1} (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9)))))) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.Perm.{succ u1} ι) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} ι) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} ι (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10) σ) (MultilinearMap.domDomCongr.{u4, u3, u2, u1, u1} R M N' _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_3 _inst_9 ι ι σ m)))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_coe MultilinearMap.alternatization_coeₓ'. -/
 theorem alternatization_coe (m : MultilinearMap R (fun i : ι => M) N') :
     ↑m.alternatization = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
@@ -1252,7 +1252,7 @@ theorem alternatization_coe (m : MultilinearMap R (fun i : ι => M) N') :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} [_inst_10 : Fintype.{u4} ι] [_inst_11 : DecidableEq.{succ u4} ι] (m : MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (v : ι -> M), Eq.{succ u3} N' (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) => (ι -> M) -> N') (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (coeFn.{max (succ (max u2 u3 u4)) (succ (max u4 u2 u3)), max (succ (max u4 u2 u3)) (succ (max u2 u3 u4))} (AddMonoidHom.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max u4 u2 u3} 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(AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (fun (_x : AddMonoidHom.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : 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 but is expected to have type
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_inst_11 a b) _inst_10 _inst_10)) (fun (σ : Equiv.Perm.{succ u1} ι) => HSMul.hSMul.{0, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) σ) ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) (instHSMul.{0, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) σ) ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) (Units.instSMulUnits.{0, u2} Int ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) Int.instMonoidInt (SubNegMonoid.SMulInt.{u2} ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) (AddGroup.toSubNegMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') v) (AddCommGroup.toAddGroup.{u2} ((fun 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(Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} ι (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10) σ) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), succ u2} (MultilinearMap.{u4, u3, u2, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (ι -> M) (fun (f : ι -> M) => (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N') f) (MultilinearMap.instFunLikeMultilinearMapForAll.{u4, u3, u2, u1} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.domDomCongr.{u4, u3, u2, u1, u1} R M N' _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_3 _inst_9 ι ι σ m) v)))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_apply MultilinearMap.alternatization_applyₓ'. -/
 theorem alternatization_apply (m : MultilinearMap R (fun i : ι => M) N') (v : ι → M) :
     alternatization m v = ∑ σ : Perm ι, σ.sign • m.domDomCongr σ v := by
@@ -1267,7 +1267,7 @@ namespace AlternatingMap
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} [_inst_10 : DecidableEq.{succ u4} ι] [_inst_11 : Fintype.{u4} ι] (a : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι), Eq.{max (succ u2) (succ u3) (succ u4)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (coeFn.{max (succ (max u2 u3 u4)) (succ (max u4 u2 u3)), max (succ (max u4 u2 u3)) (succ (max u2 u3 u4))} (AddMonoidHom.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, 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 but is expected to have type
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_inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddZeroClass.toAdd.{max (max u4 u1) u2} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddMonoid.toAddZeroClass.{max (max u2 u1) u4} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) 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(x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9)))))) (AddZeroClass.toAdd.{max (max u4 u1) u2} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (AddMonoidHomClass.toAddHomClass.{max (max u4 u1) u2, max (max u4 u1) u2, max (max u4 u1) u2} (AddMonoidHom.{max (max u4 u1) u2, max (max u4 u1) u2} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max (max u2 u1) u4} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max (max u2 u1) u4} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max (max u2 u1) u4} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max (max u2 u1) u4} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max (max u2 u1) u4} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max (max u2 u1) u4} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max (max u2 u1) u4} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max (max u2 u1) u4} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι))))) (AddMonoidHom.addMonoidHomClass.{max (max u4 u1) u2, max (max u4 u1) u2} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max (max u2 u1) u4} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max (max u2 u1) u4} (MultilinearMap.{u3, u2, u1, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) 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_inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))))) (MultilinearMap.alternatization.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι _inst_11 (fun (a : ι) (b : ι) => _inst_10 a b)) (AlternatingMap.toMultilinearMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι a)) (HSMul.hSMul.{0, max (max u2 u1) u4, max (max u2 u1) u4} Nat (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (instHSMul.{0, max (max u2 u1) u4} Nat (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddMonoid.SMul.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u2 u1) u4} (AlternatingMap.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u1} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u3, u2, u1, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (Nat.factorial (Fintype.card.{u4} ι _inst_11)) a)
 Case conversion may be inaccurate. Consider using '#align alternating_map.coe_alternatization AlternatingMap.coe_alternatizationₓ'. -/
 /-- Alternatizing a multilinear map that is already alternating results in a scale factor of `n!`,
 where `n` is the number of inputs. -/
@@ -1290,7 +1290,7 @@ variable {N'₂ : Type _} [AddCommGroup N'₂] [Module R N'₂] [DecidableEq ι]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} {N'₂ : Type.{u5}} [_inst_10 : AddCommGroup.{u5} N'₂] [_inst_11 : Module.{u1, u5} R N'₂ _inst_1 (AddCommGroup.toAddCommMonoid.{u5} N'₂ _inst_10)] [_inst_12 : DecidableEq.{succ u4} ι] [_inst_13 : Fintype.{u4} ι] (g : LinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N' N'₂ (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (AddCommGroup.toAddCommMonoid.{u5} N'₂ _inst_10) _inst_9 _inst_11) (f : MultilinearMap.{u1, u2, u3, u4} R ι (fun (_x : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9), Eq.{max (succ u2) (succ u5) (succ u4)} (AlternatingMap.{u1, u2, u5, 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(AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (MultilinearMap.alternatization.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι _inst_13 (fun (a : ι) (b : ι) => _inst_12 a b)) f))
 but is expected to have type
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_inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AddZeroClass.toAdd.{max (max u1 u4) u2} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max (max u2 u4) u1} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max (max u2 u4) u1} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max (max u2 u4) u1} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9)))))) (AddZeroClass.toAdd.{max (max u1 u4) u2} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u4) u2, max (max u1 u4) u2, max (max u1 u4) u2} (AddMonoidHom.{max (max u1 u4) u2, max (max u1 u4) u2} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max (max u2 u4) u1} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max (max u2 u4) u1} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max (max u2 u4) u1} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' 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_inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι))))) (AddMonoidHom.addMonoidHomClass.{max (max u1 u4) u2, max (max u1 u4) u2} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max (max u2 u4) u1} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max (max u2 u4) u1} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max (max u2 u4) u1} (MultilinearMap.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u5, u2, u4, u1} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max (max u2 u4) u1} (AlternatingMap.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u4} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))))) (MultilinearMap.alternatization.{u5, u2, u4, u1} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι _inst_13 (fun (a : ι) (b : ι) => _inst_12 a b)) f))
 Case conversion may be inaccurate. Consider using '#align linear_map.comp_multilinear_map_alternatization LinearMap.compMultilinearMap_alternatizationₓ'. -/
 /-- Composition with a linear map before and after alternatization are equivalent. -/
 theorem compMultilinearMap_alternatization (g : N' →ₗ[R] N'₂)
@@ -1376,7 +1376,7 @@ def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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_inst_17) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (fun (i : Sum.{u3, u1} ιa ιb) => _inst_18) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16)) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u6, u5, max u4 u2, max u3 u1} R' (Sum.{u3, u1} ιa ιb) (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.13403 : Sum.{u3, u1} ιa ιb) => Mᵢ) (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u6} R' _inst_12) (fun (i : Sum.{u3, u1} ιa ιb) => _inst_17) (TensorProduct.addCommGroup.{u6, u4, u2} R' _inst_12 N₁ N₂ _inst_13 _inst_15 _inst_14 _inst_16) (fun (i : 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u1} ιa ιb)) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{max u3 u1, max u3 u1, 0} (MonoidHom.{max u3 u1, 0} (Equiv.Perm.{succ (max u3 u1)} (Sum.{u3, u1} ιa ιb)) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{max u3 u1} (Equiv.Perm.{succ (max u3 u1)} (Sum.{u3, u1} ιa ιb)) (DivInvMonoid.toMonoid.{max u3 u1} (Equiv.Perm.{succ (max u3 u1)} (Sum.{u3, u1} ιa ιb)) (Group.toDivInvMonoid.{max u3 u1} (Equiv.Perm.{succ (max u3 u1)} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.permGroup.{max u3 u1} (Sum.{u3, u1} ιa ιb))))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ (max u3 u1)} (Sum.{u3, u1} ιa ιb)) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{max u3 u1} (Equiv.Perm.{succ (max u3 u1)} (Sum.{u3, u1} ιa ιb)) (Monoid.toMulOneClass.{max u3 u1} (Equiv.Perm.{succ (max u3 u1)} (Sum.{u3, u1} ιa ιb)) (DivInvMonoid.toMonoid.{max u3 u1} (Equiv.Perm.{succ (max u3 u1)} (Sum.{u3, u1} ιa ιb)) (Group.toDivInvMonoid.{max u3 u1} (Equiv.Perm.{succ (max u3 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(MultilinearMap.domDomCongr.{u6, u5, max u4 u2, max u3 u1, max u3 u1} R' Mᵢ (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17 (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) _inst_18 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb) (Sum.{u3, u1} ιa ιb) σ (MultilinearMap.domCoprod.{u6, u3, u1, u4, u2, u5} R' ιa ιb _inst_12 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 Mᵢ _inst_17 _inst_18 (AlternatingMap.toMultilinearMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa a) (AlternatingMap.toMultilinearMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb b))))
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_mk' AlternatingMap.domCoprod.summand_mk''ₓ'. -/
 theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
     (σ : Equiv.Perm (Sum ιa ιb)) :
@@ -1391,7 +1391,7 @@ theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : Altern
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (σ : Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) {v : (Sum.{u1, u2} ιa ιb) -> Mᵢ} {i : Sum.{u1, u2} ιa ιb} {j : Sum.{u1, u2} ιa ιb}, (Eq.{succ u4} Mᵢ (v i) (v j)) -> (Ne.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb) i j) -> (Eq.{succ (max u5 u6)} (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (HAdd.hAdd.{max u5 u6, max u5 u6, max u5 u6} (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) 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 but is expected to have type
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ιb)) (Equiv.Perm.ModSumCongr.{u3, u1} ιa ιb) (Equiv.Perm.ModSumCongr.{u3, u1} ιa ιb) (instHSMul.{max u3 u1, max u3 u1} (Equiv.Perm.{max (succ u3) (succ u1)} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.ModSumCongr.{u3, u1} ιa ιb) (MulAction.toSMul.{max u3 u1, max u3 u1} (Equiv.Perm.{max (succ u3) (succ u1)} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.ModSumCongr.{u3, u1} ιa ιb) (DivInvMonoid.toMonoid.{max u3 u1} (Equiv.Perm.{max (succ u3) (succ u1)} (Sum.{u3, u1} ιa ιb)) (Group.toDivInvMonoid.{max u3 u1} (Equiv.Perm.{max (succ u3) (succ u1)} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.permGroup.{max u3 u1} (Sum.{u3, u1} ιa ιb)))) (MulAction.quotient.{max u3 u1, max u3 u1} (Equiv.Perm.{max (succ u1) (succ u3)} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.{max (succ u3) (succ u1)} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.permGroup.{max u3 u1} (Sum.{u3, u1} ιa ιb)) (DivInvMonoid.toMonoid.{max u3 u1} (Equiv.Perm.{max (succ u3) (succ u1)} (Sum.{u3, u1} ιa ιb)) (Group.toDivInvMonoid.{max u3 u1} (Equiv.Perm.{max (succ u3) (succ u1)} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.permGroup.{max u3 u1} (Sum.{u3, u1} ιa ιb)))) (Monoid.toMulAction.{max u3 u1} (Equiv.Perm.{max (succ u3) (succ u1)} (Sum.{u3, u1} ιa ιb)) (DivInvMonoid.toMonoid.{max u3 u1} (Equiv.Perm.{max (succ u3) (succ u1)} (Sum.{u3, u1} ιa ιb)) (Group.toDivInvMonoid.{max u3 u1} (Equiv.Perm.{max (succ u3) (succ u1)} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.permGroup.{max u3 u1} (Sum.{u3, u1} ιa ιb))))) (MonoidHom.range.{max u3 u1, max u3 u1} (Prod.{u3, u1} (Equiv.Perm.{succ u3} ιa) (Equiv.Perm.{succ u1} ιb)) (Prod.instGroupProd.{u3, u1} (Equiv.Perm.{succ u3} ιa) (Equiv.Perm.{succ u1} ιb) (Equiv.Perm.permGroup.{u3} ιa) (Equiv.Perm.permGroup.{u1} ιb)) (Equiv.Perm.{max (succ u1) (succ u3)} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.permGroup.{max u3 u1} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.sumCongrHom.{u3, u1} ιa ιb)) (MulAction.left_quotientAction.{max u3 u1} (Equiv.Perm.{max (succ u1) (succ u3)} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.permGroup.{max u3 u1} (Sum.{u3, u1} ιa ιb)) (MonoidHom.range.{max u3 u1, max u3 u1} (Prod.{u3, u1} (Equiv.Perm.{succ u3} ιa) (Equiv.Perm.{succ u1} ιb)) (Prod.instGroupProd.{u3, u1} (Equiv.Perm.{succ u3} ιa) (Equiv.Perm.{succ u1} ιb) (Equiv.Perm.permGroup.{u3} ιa) (Equiv.Perm.permGroup.{u1} ιb)) (Equiv.Perm.{max (succ u1) (succ u3)} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.permGroup.{max u3 u1} (Sum.{u3, u1} ιa ιb)) (Equiv.Perm.sumCongrHom.{u3, u1} ιa ιb)))))) (Equiv.swap.{max (succ u3) (succ u1)} (Sum.{u3, u1} ιa ιb) (fun (a : Sum.{u3, u1} ιa ιb) (b : Sum.{u3, u1} ιa ιb) => Sum.instDecidableEqSum.{u3, u1} ιa ιb (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b) a b) i j) σ)) v)) (OfNat.ofNat.{max u4 u2} ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : (Sum.{u3, u1} ιa ιb) -> Mᵢ) => TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) v) 0 (Zero.toOfNat0.{max u4 u2} ((fun 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 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_add_swap_smul_eq_zero AlternatingMap.domCoprod.summand_add_swap_smul_eq_zeroₓ'. -/
 /-- Swapping elements in `σ` with equal values in `v` results in an addition that cancels -/
 theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁ ιa)
@@ -1415,7 +1415,7 @@ theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (σ : Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) {v : (Sum.{u1, u2} ιa ιb) -> Mᵢ} {i : Sum.{u1, u2} ιa ιb} {j : Sum.{u1, u2} ιa ιb}, (Eq.{succ u4} Mᵢ (v i) (v j)) -> (Ne.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb) i j) -> (Eq.{succ (max u1 u2)} (Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) (SMul.smul.{max u1 u2, max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) (MulAction.toHasSmul.{max u1 u2, max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) (DivInvMonoid.toMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Group.toDivInvMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} ιa ιb)))) (MulAction.quotient.{max u1 u2, max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.{max (succ u1) 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 but is expected to have type
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+  forall {ιa : Type.{u3}} {ιb : Type.{u1}} [_inst_10 : Fintype.{u3} ιa] [_inst_11 : Fintype.{u1} ιb] {R' : Type.{u6}} {Mᵢ : Type.{u5}} {N₁ : Type.{u4}} {N₂ : Type.{u2}} [_inst_12 : CommSemiring.{u6} R'] [_inst_13 : AddCommGroup.{u4} N₁] [_inst_14 : Module.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u2} N₂] [_inst_16 : Module.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u5} Mᵢ] [_inst_18 : Module.{u6, u5} R' Mᵢ (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u3} ιa] [_inst_20 : DecidableEq.{succ u1} ιb] (a : AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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_inst_15 _inst_14 _inst_16)))))))))
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariantₓ'. -/
 /-- Swapping elements in `σ` with equal values in `v` result in zero if the swap has no effect
 on the quotient. -/
@@ -1554,7 +1554,7 @@ open Equiv
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : MultilinearMap.{u3, u4, u5, u1} R' ιa (fun (_x : ιa) => Mᵢ) N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : ιa) => _inst_17) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (fun (i : ιa) => _inst_18) _inst_14) (b : MultilinearMap.{u3, u4, u6, u2} R' ιb (fun (_x : 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(AddMonoid.toAddZeroClass.{u5} N₁ (AddCommMonoid.toAddMonoid.{u5} N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)))) (Module.toMulActionWithZero.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14)))) (SubNegMonoid.SMulInt.{u5} N₁ (AddGroup.toSubNegMonoid.{u5} N₁ (AddCommGroup.toAddGroup.{u5} N₁ _inst_13))) (AddGroup.int_smulCommClass'.{u3, u5} R' N₁ (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12))) (AddCommGroup.toAddGroup.{u5} N₁ _inst_13) (Module.toDistribMulAction.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14)))) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (Units.smulCommClass_right.{u3, 0, max u5 u6} R' Int (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ 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(TensorProduct.leftHasSMul.{u3, 0, u5, u6} R' _inst_12 Int Int.monoid N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16 (Module.toDistribMulAction.{0, u5} Int N₁ Int.semiring (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.intModule.{u5} N₁ _inst_13)) (AddGroup.int_smulCommClass'.{u3, u5} R' N₁ (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12))) (AddCommGroup.toAddGroup.{u5} N₁ _inst_13) (Module.toDistribMulAction.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14))) (AddGroup.int_smulCommClass'.{u3, max u5 u6} R' (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12))) (AddCommGroup.toAddGroup.{max u5 u6} (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommGroup.{u3, u5, u6} R' _inst_12 N₁ N₂ _inst_13 _inst_15 _inst_14 _inst_16)) (TensorProduct.distribMulAction.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16)))) (coeFn.{succ u2, succ u2} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} ιb) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} ιb) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} ιb) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} ιb) (Equiv.Perm.permGroup.{u2} ιb)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} ιb) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} ιb) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ 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(MultilinearMap.domDomCongr.{u3, u4, u6, u2, u2} R' Mᵢ N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17 (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_18 _inst_16 ιb ιb σb b))))))
 but is expected to have type
-  forall {ιa : Type.{u6}} {ιb : Type.{u5}} [_inst_10 : Fintype.{u6} ιa] [_inst_11 : Fintype.{u5} ιb] {R' : Type.{u4}} {Mᵢ : Type.{u3}} {N₁ : Type.{u2}} {N₂ : Type.{u1}} [_inst_12 : CommSemiring.{u4} R'] [_inst_13 : AddCommGroup.{u2} N₁] [_inst_14 : Module.{u4, u2} R' N₁ (CommSemiring.toSemiring.{u4} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u1} N₂] [_inst_16 : Module.{u4, u1} R' N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u3} Mᵢ] [_inst_18 : Module.{u4, u3} R' Mᵢ (CommSemiring.toSemiring.{u4} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u6} ιa] [_inst_20 : DecidableEq.{succ u5} ιb] (a : MultilinearMap.{u4, u3, u2, u6} R' ιa (fun (_x : ιa) => Mᵢ) N₁ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιa) => _inst_17) (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (fun (i : ιa) => _inst_18) _inst_14) (b : MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (_x : 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+  forall {ιa : Type.{u6}} {ιb : Type.{u5}} [_inst_10 : Fintype.{u6} ιa] [_inst_11 : Fintype.{u5} ιb] {R' : Type.{u4}} {Mᵢ : Type.{u3}} {N₁ : Type.{u2}} {N₂ : Type.{u1}} [_inst_12 : CommSemiring.{u4} R'] [_inst_13 : AddCommGroup.{u2} N₁] [_inst_14 : Module.{u4, u2} R' N₁ (CommSemiring.toSemiring.{u4} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u1} N₂] [_inst_16 : Module.{u4, u1} R' N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u3} Mᵢ] [_inst_18 : Module.{u4, u3} R' Mᵢ (CommSemiring.toSemiring.{u4} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u6} ιa] [_inst_20 : DecidableEq.{succ u5} ιb] (a : MultilinearMap.{u4, u3, u2, u6} R' ιa (fun (_x : ιa) => Mᵢ) N₁ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιa) => _inst_17) (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (fun (i : ιa) => _inst_18) _inst_14) (b : MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (_x : 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(Equiv.Perm.permGroup.{u5} ιb)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u5} ιb (fun (a : ιb) (b : ιb) => _inst_20 a b) _inst_11) σb) (MultilinearMap.domCoprod.{u4, u6, u5, u2, u1, u3} R' ιa ιb _inst_12 N₁ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) _inst_14 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 Mᵢ _inst_17 _inst_18 (MultilinearMap.domDomCongr.{u4, u3, u2, u6, u6} R' Mᵢ N₁ (CommSemiring.toSemiring.{u4} R' _inst_12) _inst_17 (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) _inst_18 _inst_14 ιa ιa σa a) (MultilinearMap.domDomCongr.{u4, u3, u1, u5, u5} R' Mᵢ N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) _inst_17 (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_18 _inst_16 ιb ιb σb b))))))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_alternization_coe MultilinearMap.domCoprod_alternization_coeₓ'. -/
 /-- A helper lemma for `multilinear_map.dom_coprod_alternization`. -/
 theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableEq ιb]
@@ -1574,7 +1574,7 @@ open AlternatingMap
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : MultilinearMap.{u3, u4, u5, u1} R' ιa (fun (_x : ιa) => Mᵢ) N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : ιa) => _inst_17) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (fun (i : ιa) => _inst_18) _inst_14) (b : MultilinearMap.{u3, u4, u6, u2} R' ιb (fun (_x : 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(AlternatingMap.addCommGroup.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ _inst_15 _inst_16 ιb)))))) (MultilinearMap.alternatization.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ _inst_15 _inst_16 ιb _inst_11 (fun (a : ιb) (b : ιb) => _inst_20 a b)) b))
 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddZeroClass.toAdd.{max (max u5 u1) u3} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AddMonoid.toAddZeroClass.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (SubNegMonoid.toAddMonoid.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AddGroup.toSubNegMonoid.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AddCommGroup.toAddGroup.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) _inst_15 (fun (i : ιb) => _inst_18) _inst_16)))))) (AddZeroClass.toAdd.{max (max u5 u1) u3} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddMonoid.toAddZeroClass.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (SubNegMonoid.toAddMonoid.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddGroup.toSubNegMonoid.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddCommGroup.toAddGroup.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommGroup.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ _inst_15 _inst_16 ιb)))))) (AddMonoidHomClass.toAddHomClass.{max (max u5 u1) u3, max (max u5 u1) u3, max (max u5 u1) u3} (AddMonoidHom.{max (max u5 u1) u3, max (max u5 u1) u3} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddMonoid.toAddZeroClass.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (SubNegMonoid.toAddMonoid.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AddGroup.toSubNegMonoid.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AddCommGroup.toAddGroup.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) _inst_15 (fun (i : ιb) => _inst_18) _inst_16))))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (SubNegMonoid.toAddMonoid.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddGroup.toSubNegMonoid.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddCommGroup.toAddGroup.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommGroup.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ _inst_15 _inst_16 ιb)))))) (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddMonoid.toAddZeroClass.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (SubNegMonoid.toAddMonoid.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AddGroup.toSubNegMonoid.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AddCommGroup.toAddGroup.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) _inst_15 (fun (i : ιb) => _inst_18) _inst_16))))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (SubNegMonoid.toAddMonoid.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddGroup.toSubNegMonoid.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddCommGroup.toAddGroup.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommGroup.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ _inst_15 _inst_16 ιb))))) (AddMonoidHom.addMonoidHomClass.{max (max u5 u1) u3, max (max u5 u1) u3} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddMonoid.toAddZeroClass.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (SubNegMonoid.toAddMonoid.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AddGroup.toSubNegMonoid.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (AddCommGroup.toAddGroup.{max (max u3 u1) u5} (MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) (fun (i : ιb) => _inst_18) _inst_16) (MultilinearMap.instAddCommGroupMultilinearMapToAddCommMonoid.{u4, u3, u1, u5} R' ιb (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.12949 : ιb) => Mᵢ) N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιb) => _inst_17) _inst_15 (fun (i : ιb) => _inst_18) _inst_16))))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (SubNegMonoid.toAddMonoid.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddGroup.toSubNegMonoid.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AddCommGroup.toAddGroup.{max (max u3 u1) u5} (AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommGroup.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ _inst_15 _inst_16 ιb)))))))) (MultilinearMap.alternatization.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ _inst_15 _inst_16 ιb _inst_11 (fun (a : ιb) (b : ιb) => _inst_20 a b)) b))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_alternization MultilinearMap.domCoprod_alternizationₓ'. -/
 /-- Computing the `multilinear_map.alternatization` of the `multilinear_map.dom_coprod` is the same
 as computing the `alternating_map.dom_coprod` of the `multilinear_map.alternatization`s.
@@ -1619,7 +1619,7 @@ theorem MultilinearMap.domCoprod_alternization [DecidableEq ιa] [DecidableEq ι
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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_inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b) a b))
 but is expected to have type
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(TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u6, u5} ιa ιb)) (AddCommGroup.toAddGroup.{max (max (max (max u6 u5) u3) u2) u1} (AlternatingMap.{u4, u3, max u1 u2, max u5 u6} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u6, u5} ιa ιb)) (AlternatingMap.addCommGroup.{u4, u3, max u2 u1, max u6 u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommGroup.{u4, u2, u1} R' _inst_12 N₁ N₂ _inst_13 _inst_15 _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u6, u5} ιa ιb))))))) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (Nat.factorial (Fintype.card.{u6} ιa _inst_10)) (Nat.factorial (Fintype.card.{u5} ιb _inst_11))) (AlternatingMap.domCoprod.{u6, u5, u4, u3, u2, u1} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => 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+  forall {ιa : Type.{u6}} {ιb : Type.{u5}} [_inst_10 : Fintype.{u6} ιa] [_inst_11 : Fintype.{u5} ιb] {R' : Type.{u4}} {Mᵢ : Type.{u3}} {N₁ : Type.{u2}} {N₂ : Type.{u1}} [_inst_12 : CommSemiring.{u4} R'] [_inst_13 : AddCommGroup.{u2} N₁] [_inst_14 : Module.{u4, u2} R' N₁ (CommSemiring.toSemiring.{u4} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u1} N₂] [_inst_16 : Module.{u4, u1} R' N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u3} Mᵢ] [_inst_18 : Module.{u4, u3} R' Mᵢ (CommSemiring.toSemiring.{u4} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u6} ιa] [_inst_20 : DecidableEq.{succ u5} ιb] (a : AlternatingMap.{u4, u3, u2, u6} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u4, u3, u1, u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (AddCommGroup.toAddCommMonoid.{max u2 u1} (TensorProduct.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommGroup.{u4, u2, u1} R' _inst_12 N₁ N₂ _inst_13 _inst_15 _inst_14 _inst_16)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u6, u5} ιa ιb)) (AlternatingMap.addCommGroup.{u4, u3, max u2 u1, max u6 u5} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommGroup.{u4, u2, u1} R' 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(AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u6, u5} ιa ιb)) (AlternatingMap.{u4, u3, max u1 u2, max u5 u6} R' (CommSemiring.toSemiring.{u4} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u4, u2, u1} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15) _inst_14 _inst_16) 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_inst_20 a b) a b))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_alternization_eq MultilinearMap.domCoprod_alternization_eqₓ'. -/
 /-- Taking the `multilinear_map.alternatization` of the `multilinear_map.dom_coprod` of two
 `alternating_map`s gives a scaled version of the `alternating_map.coprod` of those maps.

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -202,7 +202,7 @@ instance : Coe (AlternatingMap R M N ι) (MultilinearMap R (fun i : ι => M) N)
 lean 3 declaration is
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 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u1, u4} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u2}} (f : AlternatingMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (forall (ᾰ : ι -> M), (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.419 : ι -> M) => N) ᾰ) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), succ u3} (MultilinearMap.{u1, u4, u3, u2} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.259 : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (ι -> M) (fun (f : ι -> M) => (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.419 : ι -> M) => N) f) (MultilinearMap.instFunLikeMultilinearMapForAll.{u1, u4, u3, u2} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (AlternatingMap.toMultilinearMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι f)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), succ u3} (AlternatingMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u1, u4} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u2}} (f : AlternatingMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (forall (ᾰ : ι -> M), (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N) ᾰ) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), succ u3} (MultilinearMap.{u1, u4, u3, u2} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.259 : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (ι -> M) (fun (f : ι -> M) => (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : ι -> M) => N) f) (MultilinearMap.instFunLikeMultilinearMapForAll.{u1, u4, u3, u2} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (AlternatingMap.toMultilinearMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι f)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), succ u3} (AlternatingMap.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (ι -> M) (fun (_x : ι -> M) => N) (AlternatingMap.funLike.{u1, u4, u3, u2} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f)
 Case conversion may be inaccurate. Consider using '#align alternating_map.coe_multilinear_map AlternatingMap.coe_multilinearMapₓ'. -/
 @[simp, norm_cast]
 theorem coe_multilinearMap : ⇑(f : MultilinearMap R (fun i : ι => M) N) = f :=
@@ -236,7 +236,7 @@ theorem [anonymous] : f.toMultilinearMap = f :=
 lean 3 declaration is
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(AddCommMonoid.toAddMonoid.{u3} N _inst_4)))) (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => (fun (i : ι) => M) i) (fun (a : ι) (b : ι) => _inst_1 a b) m i x)) (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => (fun (i : ι) => M) i) (fun (a : ι) (b : ι) => _inst_1 a b) m i y)))) (h₂ : forall [_inst_1_1 : DecidableEq.{succ u4} ι] (m : forall (i : ι), (fun (i : ι) => M) i) (i : ι) (c : R) (x : M), Eq.{succ u3} N (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => (fun (i : ι) => M) i) (fun (a : ι) (b : ι) => _inst_1_1 a b) m i (SMul.smul.{u1, u2} R ((fun (i : ι) => M) i) (SMulZeroClass.toHasSmul.{u1, u2} R ((fun (i : ι) => M) i) (AddZeroClass.toHasZero.{u2} ((fun (i : ι) => M) i) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => M) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M) i) ((fun (i : ι) => _inst_2) i)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R ((fun (i : ι) => M) i) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} ((fun (i : ι) => M) i) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => M) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M) i) ((fun (i : ι) => _inst_2) i)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R ((fun (i : ι) => M) i) (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} ((fun (i : ι) => M) i) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => M) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M) i) ((fun (i : ι) => _inst_2) i)))) (Module.toMulActionWithZero.{u1, u2} R ((fun (i : ι) => M) i) _inst_1 ((fun (i : ι) => _inst_2) i) ((fun (i : ι) => _inst_3) i))))) c x))) (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_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4))) (Module.toMulActionWithZero.{u1, u3} R N _inst_1 _inst_4 _inst_5)))) c (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => (fun (i : ι) => M) i) (fun (a : ι) (b : ι) => _inst_1_1 a b) m i x)))) (h₃ : forall (v : ι -> M) (i : ι) (j : ι), (Eq.{succ u2} M (v i) (v j)) -> (Ne.{succ u4} ι i j) -> (Eq.{succ u3} N (f v) (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_4)))))))), Eq.{max (succ u4) (succ u2) (succ u3)} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) ((fun (a : Sort.{max (succ u2) (succ u3) (succ u4)}) (b : Sort.{max (succ u4) (succ u2) (succ u3)}) [self : HasLiftT.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} a b] => self.0) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (HasLiftT.mk.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (CoeTCₓ.coe.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (coeBase.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (AlternatingMap.coe.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι)))) (AlternatingMap.mk.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι f h₁ h₂ h₃)) (MultilinearMap.mk.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5 f h₁ h₂)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : (ι -> M) -> N) (h₁ : forall [_inst_1 : DecidableEq.{succ u4} ι] (m : ι -> M) (i : ι) (x : M) (y : M), Eq.{succ u3} N (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => M) (fun (a : ι) (b : ι) => _inst_1 a b) m i (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) x y))) (HAdd.hAdd.{u3, u3, u3} N N N (instHAdd.{u3} N (AddZeroClass.toAdd.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))) (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => M) (fun (a : ι) (b : ι) => _inst_1 a b) m i x)) (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => M) (fun (a : ι) (b : ι) => _inst_1 a b) m i y)))) (h₂ : forall [_inst_1_1 : DecidableEq.{succ u4} ι] (m : ι -> M) (i : ι) (c : R) (x : M), Eq.{succ u3} N (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => M) (fun (a : ι) (b : ι) => _inst_1_1 a b) m i (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) c x))) (HSMul.hSMul.{u1, u3, u3} R N N (instHSMul.{u1, u3} R N (SMulZeroClass.toSMul.{u1, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)) (Module.toMulActionWithZero.{u1, u3} R N _inst_1 _inst_4 _inst_5))))) c (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => M) (fun (a : ι) (b : ι) => _inst_1_1 a b) m i x)))) (h₃ : forall (v : ι -> M) (i : ι) (j : ι), (Eq.{succ u2} M (v i) (v j)) -> (Ne.{succ u4} ι i j) -> (Eq.{succ u3} N (MultilinearMap.toFun.{u1, u2, u3, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.259 : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5 (MultilinearMap.mk.{u1, u2, u3, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.259 : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5 f (fun [inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.93.Mathlib.LinearAlgebra.Alternating._hyg.2122 : DecidableEq.{succ u4} ι] => h₁ (fun (a : ι) (b : ι) => inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.93.Mathlib.LinearAlgebra.Alternating._hyg.2122 a b)) (fun [inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.139.Mathlib.LinearAlgebra.Alternating._hyg.2124 : DecidableEq.{succ u4} ι] => h₂ (fun (a : ι) (b : ι) => inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.139.Mathlib.LinearAlgebra.Alternating._hyg.2124 a b))) v) (OfNat.ofNat.{u3} N 0 (Zero.toOfNat0.{u3} N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))))), Eq.{max (max (succ u2) (succ u3)) (succ u4)} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (AlternatingMap.toMultilinearMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι (AlternatingMap.mk.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι (MultilinearMap.mk.{u1, u2, u3, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.259 : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5 f (fun [inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.93.Mathlib.LinearAlgebra.Alternating._hyg.2122 : DecidableEq.{succ u4} ι] => h₁ (fun (a : ι) (b : ι) => inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.93.Mathlib.LinearAlgebra.Alternating._hyg.2122 a b)) (fun [inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.139.Mathlib.LinearAlgebra.Alternating._hyg.2124 : DecidableEq.{succ u4} ι] => h₂ (fun (a : ι) (b : ι) => inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.139.Mathlib.LinearAlgebra.Alternating._hyg.2124 a b))) h₃)) (MultilinearMap.mk.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5 f h₁ h₂)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : (ι -> M) -> N) (h₁ : forall [_inst_1 : DecidableEq.{succ u4} ι] (m : ι -> M) (i : ι) (x : M) (y : M), Eq.{succ u3} N (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => M) (fun (a : ι) (b : ι) => _inst_1 a b) m i (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) x y))) (HAdd.hAdd.{u3, u3, u3} N N N (instHAdd.{u3} N (AddZeroClass.toAdd.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))) (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => M) (fun (a : ι) (b : ι) => _inst_1 a b) m i x)) (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => M) (fun (a : ι) (b : ι) => _inst_1 a b) m i y)))) (h₂ : forall [_inst_1_1 : DecidableEq.{succ u4} ι] (m : ι -> M) (i : ι) (c : R) (x : M), Eq.{succ u3} N (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => M) (fun (a : ι) (b : ι) => _inst_1_1 a b) m i (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) c x))) (HSMul.hSMul.{u1, u3, u3} R N N (instHSMul.{u1, u3} R N (SMulZeroClass.toSMul.{u1, u3} R N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)) (Module.toMulActionWithZero.{u1, u3} R N _inst_1 _inst_4 _inst_5))))) c (f (Function.update.{succ u4, succ u2} ι (fun (i : ι) => M) (fun (a : ι) (b : ι) => _inst_1_1 a b) m i x)))) (h₃ : forall (v : ι -> M) (i : ι) (j : ι), (Eq.{succ u2} M (v i) (v j)) -> (Ne.{succ u4} ι i j) -> (Eq.{succ u3} N (MultilinearMap.toFun.{u1, u2, u3, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.259 : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5 (MultilinearMap.mk.{u1, u2, u3, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.259 : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5 f (fun [inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.92.Mathlib.LinearAlgebra.Alternating._hyg.2122 : DecidableEq.{succ u4} ι] => h₁ (fun (a : ι) (b : ι) => inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.92.Mathlib.LinearAlgebra.Alternating._hyg.2122 a b)) (fun [inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.138.Mathlib.LinearAlgebra.Alternating._hyg.2124 : DecidableEq.{succ u4} ι] => h₂ (fun (a : ι) (b : ι) => inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.138.Mathlib.LinearAlgebra.Alternating._hyg.2124 a b))) v) (OfNat.ofNat.{u3} N 0 (Zero.toOfNat0.{u3} N (AddMonoid.toZero.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_4)))))), Eq.{max (max (succ u2) (succ u3)) (succ u4)} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5) (AlternatingMap.toMultilinearMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι (AlternatingMap.mk.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι (MultilinearMap.mk.{u1, u2, u3, u4} R ι (fun (x._@.Mathlib.LinearAlgebra.Alternating._hyg.259 : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5 f (fun [inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.92.Mathlib.LinearAlgebra.Alternating._hyg.2122 : DecidableEq.{succ u4} ι] => h₁ (fun (a : ι) (b : ι) => inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.92.Mathlib.LinearAlgebra.Alternating._hyg.2122 a b)) (fun [inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.138.Mathlib.LinearAlgebra.Alternating._hyg.2124 : DecidableEq.{succ u4} ι] => h₂ (fun (a : ι) (b : ι) => inst._@.Mathlib.LinearAlgebra.Multilinear.Basic.138.Mathlib.LinearAlgebra.Alternating._hyg.2124 a b))) h₃)) (MultilinearMap.mk.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N _inst_1 (fun (i : ι) => _inst_2) _inst_4 (fun (i : ι) => _inst_3) _inst_5 f h₁ h₂)
 Case conversion may be inaccurate. Consider using '#align alternating_map.coe_multilinear_map_mk AlternatingMap.coe_multilinearMap_mkₓ'. -/
 @[simp]
 theorem coe_multilinearMap_mk (f : (ι → M) → N) (h₁ h₂ h₃) :
@@ -1230,7 +1230,7 @@ def alternatization : MultilinearMap R (fun i : ι => M) N' →+ AlternatingMap
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} [_inst_10 : Fintype.{u4} ι] [_inst_11 : DecidableEq.{succ u4} ι] (m : MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9), Eq.{max (max (succ u4) (succ u2)) (succ u3)} ((ι -> M) -> N') (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) => (ι -> M) -> N') (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (coeFn.{max (succ (max u2 u3 u4)) (succ (max u4 u2 u3)), max (succ (max u4 u2 u3)) (succ (max u2 u3 u4))} (AddMonoidHom.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.addCommGroup.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_def MultilinearMap.alternatization_defₓ'. -/
 theorem alternatization_def (m : MultilinearMap R (fun i : ι => M) N') :
     ⇑(alternatization m) = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
@@ -1241,7 +1241,7 @@ theorem alternatization_def (m : MultilinearMap R (fun i : ι => M) N') :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} [_inst_10 : Fintype.{u4} ι] [_inst_11 : DecidableEq.{succ u4} ι] (m : MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9), Eq.{max (succ u4) (succ u2) (succ u3)} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) ((fun (a : Sort.{max (succ u2) (succ u3) (succ u4)}) (b : Sort.{max (succ u4) (succ u2) (succ u3)}) [self : HasLiftT.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} a b] => self.0) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (HasLiftT.mk.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (CoeTCₓ.coe.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (coeBase.{max (succ u2) (succ u3) (succ u4), max (succ u4) (succ u2) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.coe.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι)))) (coeFn.{max (succ (max u2 u3 u4)) (succ (max u4 u2 u3)), max (succ (max u4 u2 u3)) (succ (max u2 u3 u4))} (AddMonoidHom.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max u4 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(AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (fun (_x : AddMonoidHom.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.addCommGroup.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) => (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) -> (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι)) (AddMonoidHom.hasCoeToFun.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max u4 u2 u3} (MultilinearMap.{u1, 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ι) (AddCommGroup.toAddGroup.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (MultilinearMap.alternatization.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι _inst_10 (fun (a : ι) (b : ι) => _inst_11 a b)) m)) (Finset.sum.{max u4 u2 u3, u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (Equiv.Perm.{succ u4} ι) (MultilinearMap.addCommMonoid.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (Finset.univ.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.fintype.{u4, u4} ι ι (fun (a : ι) (b : ι) => _inst_11 a b) (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10 _inst_10)) (fun (σ : Equiv.Perm.{succ u4} ι) => SMul.smul.{0, max u4 u2 u3} (Units.{0} Int Int.monoid) (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.hasSmul.{u2, u3, u4, 0, u1} ι (fun (i : ι) => M) N' (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (Units.{0} Int Int.monoid) R (DivInvMonoid.toMonoid.{0} (Units.{0} Int Int.monoid) (Group.toDivInvMonoid.{0} (Units.{0} Int Int.monoid) (Units.group.{0} Int Int.monoid))) _inst_1 (fun (i : ι) => _inst_3) (Units.distribMulAction.{0, u3} Int N' Int.monoid (AddCommMonoid.toAddMonoid.{u3} N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)) (Module.toDistribMulAction.{0, u3} Int N' Int.semiring (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (AddCommGroup.intModule.{u3} N' _inst_8))) _inst_9 (Units.smulCommClass_right.{u1, 0, u3} R Int N' Int.monoid (SMulZeroClass.toHasSmul.{u1, u3} R N' (AddZeroClass.toHasZero.{u3} N' (AddMonoid.toAddZeroClass.{u3} N' (AddCommMonoid.toAddMonoid.{u3} N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)))) (SMulWithZero.toSmulZeroClass.{u1, u3} R N' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} N' (AddMonoid.toAddZeroClass.{u3} N' (AddCommMonoid.toAddMonoid.{u3} N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)))) (MulActionWithZero.toSMulWithZero.{u1, u3} R N' (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} N' (AddMonoid.toAddZeroClass.{u3} N' (AddCommMonoid.toAddMonoid.{u3} N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)))) (Module.toMulActionWithZero.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9)))) (SubNegMonoid.SMulInt.{u3} N' (AddGroup.toSubNegMonoid.{u3} N' (AddCommGroup.toAddGroup.{u3} N' _inst_8))) (AddGroup.int_smulCommClass'.{u1, u3} R N' (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommGroup.toAddGroup.{u3} N' _inst_8) (Module.toDistribMulAction.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9)))) (coeFn.{succ u4, succ u4} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u4} ι) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u4} ι (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10) σ) (MultilinearMap.domDomCongr.{u1, u2, u3, u4, u4} R M N' _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_3 _inst_9 ι ι σ m)))
 but is expected to have type
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} ι) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} ι) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} ι) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} ι) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} ι) (Equiv.Perm.permGroup.{u1} ι)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} ι (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10) σ) (MultilinearMap.domDomCongr.{u4, u3, u2, u1, u1} R M N' _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_3 _inst_9 ι ι σ m)))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_coe MultilinearMap.alternatization_coeₓ'. -/
 theorem alternatization_coe (m : MultilinearMap R (fun i : ι => M) N') :
     ↑m.alternatization = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
@@ -1252,7 +1252,7 @@ theorem alternatization_coe (m : MultilinearMap R (fun i : ι => M) N') :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N' : Type.{u3}} [_inst_8 : AddCommGroup.{u3} N'] [_inst_9 : Module.{u1, u3} R N' _inst_1 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8)] {ι : Type.{u4}} [_inst_10 : Fintype.{u4} ι] [_inst_11 : DecidableEq.{succ u4} ι] (m : MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (v : ι -> M), Eq.{succ u3} N' (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) => (ι -> M) -> N') (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (coeFn.{max (succ (max u2 u3 u4)) (succ (max u4 u2 u3)), max (succ (max u4 u2 u3)) (succ (max u2 u3 u4))} (AddMonoidHom.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.addCommGroup.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (fun (_x : AddMonoidHom.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.addCommGroup.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) => (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) -> (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι)) (AddMonoidHom.hasCoeToFun.{max u4 u2 u3, max u2 u3 u4} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddMonoid.toAddZeroClass.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (SubNegMonoid.toAddMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddGroup.toSubNegMonoid.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (AddCommGroup.toAddGroup.{max u4 u2 u3} (MultilinearMap.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.addCommGroup.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) _inst_8 (fun (i : ι) => _inst_3) _inst_9))))) (AddMonoid.toAddZeroClass.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (SubNegMonoid.toAddMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddGroup.toSubNegMonoid.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AddCommGroup.toAddGroup.{max u2 u3 u4} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_9 ι) (AlternatingMap.addCommGroup.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι)))))) (MultilinearMap.alternatization.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N' _inst_8 _inst_9 ι _inst_10 (fun (a : ι) (b : ι) => _inst_11 a b)) m) v) (Finset.sum.{u3, u4} N' (Equiv.Perm.{succ u4} ι) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (Finset.univ.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.fintype.{u4, u4} ι ι (fun (a : ι) (b : ι) => _inst_11 a b) (fun (a : ι) (b : ι) => _inst_11 a b) _inst_10 _inst_10)) (fun (σ : Equiv.Perm.{succ u4} ι) => SMul.smul.{0, u3} (Units.{0} Int Int.monoid) N' (Units.hasSmul.{0, u3} Int N' Int.monoid (SubNegMonoid.SMulInt.{u3} N' (AddGroup.toSubNegMonoid.{u3} N' (AddCommGroup.toAddGroup.{u3} N' _inst_8)))) (coeFn.{succ u4, succ u4} (MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Group.toDivInvMonoid.{u4} (Equiv.Perm.{succ u4} ι) (Equiv.Perm.permGroup.{u4} ι)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u4, 0} (Equiv.Perm.{succ u4} ι) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u4} (Equiv.Perm.{succ u4} ι) (DivInvMonoid.toMonoid.{u4} 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_inst_8) (fun (i : ι) => _inst_3) _inst_9) => (ι -> M) -> N') (MultilinearMap.hasCoeToFun.{u1, u2, u3, u4} R ι (fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.domDomCongr.{u1, u2, u3, u4, u4} R M N' _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} N' _inst_8) _inst_3 _inst_9 ι ι σ m) v)))
 but is expected to have type
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(fun (i : ι) => M) N' _inst_1 (fun (i : ι) => _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) (fun (i : ι) => _inst_3) _inst_9) (MultilinearMap.domDomCongr.{u4, u3, u2, u1, u1} R M N' _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} N' _inst_8) _inst_3 _inst_9 ι ι σ m) v)))
 Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_apply MultilinearMap.alternatization_applyₓ'. -/
 theorem alternatization_apply (m : MultilinearMap R (fun i : ι => M) N') (v : ι → M) :
     alternatization m v = ∑ σ : Perm ι, σ.sign • m.domDomCongr σ v := by
@@ -1376,7 +1376,7 @@ def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (σ : Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)), Eq.{max (succ (max u1 u2)) (succ u4) (succ (max u5 u6))} (MultilinearMap.{u3, u4, max u5 u6, max u1 u2} R' (Sum.{u1, u2} ιa ιb) (fun (_x : Sum.{u1, u2} ιa ιb) => Mᵢ) (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_17) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_18) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16)) (AlternatingMap.domCoprod.summand.{u1, u2, u3, u4, u5, u6} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b) a b (Quotient.mk''.{succ (max u1 u2)} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (QuotientGroup.leftRel.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} ιa ιb)) (MonoidHom.range.{max u1 u2, max u1 u2} (Prod.{u1, u2} (Equiv.Perm.{succ u1} ιa) (Equiv.Perm.{succ u2} ιb)) (Prod.group.{u1, u2} (Equiv.Perm.{succ u1} ιa) (Equiv.Perm.{succ u2} ιb) (Equiv.Perm.permGroup.{u1} ιa) (Equiv.Perm.permGroup.{u2} ιb)) (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.sumCongrHom.{u1, u2} ιa ιb))) σ)) (SMul.smul.{0, max (max u1 u2) u4 u5 u6} (Units.{0} Int Int.monoid) (MultilinearMap.{u3, u4, max u5 u6, max u1 u2} R' (Sum.{u1, u2} ιa ιb) (fun (_x : Sum.{u1, u2} ιa ιb) => Mᵢ) 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(MultilinearMap.domDomCongr.{u6, u5, max u4 u2, max u3 u1, max u3 u1} R' Mᵢ (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17 (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) _inst_18 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb) (Sum.{u3, u1} ιa ιb) σ (MultilinearMap.domCoprod.{u6, u3, u1, u4, u2, u5} R' ιa ιb _inst_12 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 Mᵢ _inst_17 _inst_18 (AlternatingMap.toMultilinearMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa a) (AlternatingMap.toMultilinearMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb b))))
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_mk' AlternatingMap.domCoprod.summand_mk''ₓ'. -/
 theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
     (σ : Equiv.Perm (Sum ιa ιb)) :
@@ -1391,7 +1391,7 @@ theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : Altern
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_add_swap_smul_eq_zero AlternatingMap.domCoprod.summand_add_swap_smul_eq_zeroₓ'. -/
 /-- Swapping elements in `σ` with equal values in `v` results in an addition that cancels -/
 theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁ ιa)
@@ -1415,7 +1415,7 @@ theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁
 lean 3 declaration is
   forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (σ : Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) {v : (Sum.{u1, u2} ιa ιb) -> Mᵢ} {i : Sum.{u1, u2} ιa ιb} {j : Sum.{u1, u2} ιa ιb}, (Eq.{succ u4} Mᵢ (v i) (v j)) -> (Ne.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb) i j) -> (Eq.{succ (max u1 u2)} (Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) (SMul.smul.{max u1 u2, max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) (MulAction.toHasSmul.{max u1 u2, max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) (DivInvMonoid.toMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Group.toDivInvMonoid.{max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.permGroup.{max u1 u2} (Sum.{u1, u2} ιa ιb)))) (MulAction.quotient.{max u1 u2, max u1 u2} (Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)) (Equiv.Perm.{max (succ u1) 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 but is expected to have type
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+  forall {ιa : Type.{u3}} {ιb : Type.{u1}} [_inst_10 : Fintype.{u3} ιa] [_inst_11 : Fintype.{u1} ιb] {R' : Type.{u6}} {Mᵢ : Type.{u5}} {N₁ : Type.{u4}} {N₂ : Type.{u2}} [_inst_12 : CommSemiring.{u6} R'] [_inst_13 : AddCommGroup.{u4} N₁] [_inst_14 : Module.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u2} N₂] [_inst_16 : Module.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u5} Mᵢ] [_inst_18 : Module.{u6, u5} R' Mᵢ (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u3} ιa] [_inst_20 : DecidableEq.{succ u1} ιb] (a : AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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_inst_15 _inst_14 _inst_16)))))))))
 Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariantₓ'. -/
 /-- Swapping elements in `σ` with equal values in `v` result in zero if the swap has no effect
 on the quotient. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Zhangir Azerbayev
 
 ! This file was ported from Lean 3 source module linear_algebra.alternating
-! leanprover-community/mathlib commit 284fdd2962e67d2932fa3a79ce19fcf92d38e228
+! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.LinearAlgebra.Multilinear.TensorProduct
 /-!
 # Alternating Maps
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We construct the bundled function `alternating_map`, which extends `multilinear_map` with all the
 arguments of the same type.
 

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

@@ -67,11 +67,13 @@ section
 
 variable (R M N ι)
 
+#print AlternatingMap /-
 /-- An alternating map is a multilinear map that vanishes when two of its arguments are equal.
 -/
 structure AlternatingMap extends MultilinearMap R (fun i : ι => M) N where
   map_eq_zero_of_eq' : ∀ (v : ι → M) (i j : ι) (h : v i = v j) (hij : i ≠ j), to_fun v = 0
 #align alternating_map AlternatingMap
+-/
 
 end
 
@@ -95,6 +97,7 @@ open Function
 
 section Coercions
 
+#print AlternatingMap.funLike /-
 instance funLike : FunLike (AlternatingMap R M N ι) (ι → M) fun _ => N
     where
   coe := AlternatingMap.toFun
@@ -103,6 +106,7 @@ instance funLike : FunLike (AlternatingMap R M N ι) (ι → M) fun _ => N
     cases g
     congr
 #align alternating_map.fun_like AlternatingMap.funLike
+-/
 
 -- shortcut instance
 instance : CoeFun (AlternatingMap R M N ι) fun _ => (ι → M) → N :=
@@ -110,6 +114,12 @@ instance : CoeFun (AlternatingMap R M N ι) fun _ => (ι → M) → N :=
 
 initialize_simps_projections AlternatingMap (toFun → apply)
 
+/- warning: alternating_map.to_fun_eq_coe -> AlternatingMap.toFun_eq_coe is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_4] {ι : Type.{u4}} (f : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι), Eq.{max (max (succ u4) (succ u2)) (succ u3)} ((forall (i : ι), (fun (i : ι) => M) i) -> N) (AlternatingMap.toFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι f) (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u4) (succ u2)) (succ u3)} (AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) (fun (_x : AlternatingMap.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) => (ι -> M) -> N) (AlternatingMap.coeFun.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι) f)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align alternating_map.to_fun_eq_coe AlternatingMap.toFun_eq_coeₓ'. -/
 @[simp]
 theorem toFun_eq_coe : f.toFun = f :=
   rfl
@@ -118,30 +128,66 @@ theorem toFun_eq_coe : f.toFun = f :=
 @[simp]
 theorem coe_mk (f : (ι → M) → N) (h₁ h₂ h₃) : ⇑(⟨f, h₁, h₂, h₃⟩ : AlternatingMap R M N ι) = f :=
   rfl
-#align alternating_map.coe_mk AlternatingMap.coe_mk
-
+#align alternating_map.coe_mk AlternatingMap.coe_mkₓ
+
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 theorem congr_fun {f g : AlternatingMap R M N ι} (h : f = g) (x : ι → M) : f x = g x :=
   congr_arg (fun h : AlternatingMap R M N ι => h x) h
 #align alternating_map.congr_fun AlternatingMap.congr_fun
 
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 theorem congr_arg (f : AlternatingMap R M N ι) {x y : ι → M} (h : x = y) : f x = f y :=
   congr_arg (fun x : ι → M => f x) h
 #align alternating_map.congr_arg AlternatingMap.congr_arg
 
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 theorem coe_injective : Injective (coeFn : AlternatingMap R M N ι → (ι → M) → N) :=
   FunLike.coe_injective
 #align alternating_map.coe_injective AlternatingMap.coe_injective
 
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 @[simp, norm_cast]
 theorem coe_inj {f g : AlternatingMap R M N ι} : (f : (ι → M) → N) = g ↔ f = g :=
   coe_injective.eq_iff
 #align alternating_map.coe_inj AlternatingMap.coe_inj
 
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 @[ext]
 theorem ext {f f' : AlternatingMap R M N ι} (H : ∀ x, f x = f' x) : f = f' :=
   FunLike.ext _ _ H
 #align alternating_map.ext AlternatingMap.ext
 
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 theorem ext_iff {f g : AlternatingMap R M N ι} : f = g ↔ ∀ x, f x = g x :=
   ⟨fun h x => h ▸ rfl, fun h => ext h⟩
 #align alternating_map.ext_iff AlternatingMap.ext_iff
@@ -149,21 +195,46 @@ theorem ext_iff {f g : AlternatingMap R M N ι} : f = g ↔ ∀ x, f x = g x :=
 instance : Coe (AlternatingMap R M N ι) (MultilinearMap R (fun i : ι => M) N) :=
   ⟨fun x => x.toMultilinearMap⟩
 
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 @[simp, norm_cast]
 theorem coe_multilinearMap : ⇑(f : MultilinearMap R (fun i : ι => M) N) = f :=
   rfl
 #align alternating_map.coe_multilinear_map AlternatingMap.coe_multilinearMap
 
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 theorem coe_multilinearMap_injective :
     Function.Injective (coe : AlternatingMap R M N ι → MultilinearMap R (fun i : ι => M) N) :=
   fun x y h => ext <| MultilinearMap.congr_fun h
 #align alternating_map.coe_multilinear_map_injective AlternatingMap.coe_multilinearMap_injective
 
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 @[simp]
-theorem toMultilinearMap_eq_coe : f.toMultilinearMap = f :=
+theorem [anonymous] : f.toMultilinearMap = f :=
   rfl
-#align alternating_map.to_multilinear_map_eq_coe AlternatingMap.toMultilinearMap_eq_coe
-
+#align alternating_map.to_multilinear_map_eq_coe [anonymous]
+
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 @[simp]
 theorem coe_multilinearMap_mk (f : (ι → M) → N) (h₁ h₂ h₃) :
     ((⟨f, h₁, h₂, h₃⟩ : AlternatingMap R M N ι) : MultilinearMap R (fun i : ι => M) N) =
@@ -180,48 +251,98 @@ These are expressed in terms of `⇑f` instead of `f.to_fun`.
 -/
 
 
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 @[simp]
 theorem map_add [DecidableEq ι] (i : ι) (x y : M) :
     f (update v i (x + y)) = f (update v i x) + f (update v i y) :=
   f.toMultilinearMap.map_add' v i x y
 #align alternating_map.map_add AlternatingMap.map_add
 
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 @[simp]
 theorem map_sub [DecidableEq ι] (i : ι) (x y : M') :
     g' (update v' i (x - y)) = g' (update v' i x) - g' (update v' i y) :=
   g'.toMultilinearMap.map_sub v' i x y
 #align alternating_map.map_sub AlternatingMap.map_sub
 
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 @[simp]
 theorem map_neg [DecidableEq ι] (i : ι) (x : M') : g' (update v' i (-x)) = -g' (update v' i x) :=
   g'.toMultilinearMap.map_neg v' i x
 #align alternating_map.map_neg AlternatingMap.map_neg
 
+#print AlternatingMap.map_smul /-
 @[simp]
 theorem map_smul [DecidableEq ι] (i : ι) (r : R) (x : M) :
     f (update v i (r • x)) = r • f (update v i x) :=
   f.toMultilinearMap.map_smul' v i r x
 #align alternating_map.map_smul AlternatingMap.map_smul
+-/
 
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 @[simp]
 theorem map_eq_zero_of_eq (v : ι → M) {i j : ι} (h : v i = v j) (hij : i ≠ j) : f v = 0 :=
   f.map_eq_zero_of_eq' v i j h hij
 #align alternating_map.map_eq_zero_of_eq AlternatingMap.map_eq_zero_of_eq
 
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 theorem map_coord_zero {m : ι → M} (i : ι) (h : m i = 0) : f m = 0 :=
   f.toMultilinearMap.map_coord_zero i h
 #align alternating_map.map_coord_zero AlternatingMap.map_coord_zero
 
+/- warning: alternating_map.map_update_zero -> AlternatingMap.map_update_zero is a dubious translation:
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 @[simp]
 theorem map_update_zero [DecidableEq ι] (m : ι → M) (i : ι) : f (update m i 0) = 0 :=
   f.toMultilinearMap.map_update_zero m i
 #align alternating_map.map_update_zero AlternatingMap.map_update_zero
 
+/- warning: alternating_map.map_zero -> AlternatingMap.map_zero is a dubious translation:
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 @[simp]
 theorem map_zero [Nonempty ι] : f 0 = 0 :=
   f.toMultilinearMap.map_zero
 #align alternating_map.map_zero AlternatingMap.map_zero
 
+/- warning: alternating_map.map_eq_zero_of_not_injective -> AlternatingMap.map_eq_zero_of_not_injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alternating_map.map_eq_zero_of_not_injective AlternatingMap.map_eq_zero_of_not_injectiveₓ'. -/
 theorem map_eq_zero_of_not_injective (v : ι → M) (hv : ¬Function.Injective v) : f v = 0 :=
   by
   rw [Function.Injective] at hv
@@ -247,17 +368,35 @@ instance : SMul S (AlternatingMap R M N ι) :=
     { (c • f : MultilinearMap R (fun i : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }⟩
 
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 @[simp]
 theorem smul_apply (c : S) (m : ι → M) : (c • f) m = c • f m :=
   rfl
 #align alternating_map.smul_apply AlternatingMap.smul_apply
 
+/- warning: alternating_map.coe_smul -> AlternatingMap.coe_smul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alternating_map.coe_smul AlternatingMap.coe_smulₓ'. -/
 @[norm_cast]
 theorem coe_smul (c : S) :
     ((c • f : AlternatingMap R M N ι) : MultilinearMap R (fun i : ι => M) N) = c • f :=
   rfl
 #align alternating_map.coe_smul AlternatingMap.coe_smul
 
+/- warning: alternating_map.coe_fn_smul -> AlternatingMap.coeFn_smul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alternating_map.coe_fn_smul AlternatingMap.coeFn_smulₓ'. -/
 theorem coeFn_smul (c : S) (f : AlternatingMap R M N ι) : ⇑(c • f) = c • f :=
   rfl
 #align alternating_map.coe_fn_smul AlternatingMap.coeFn_smul
@@ -274,11 +413,23 @@ instance : Add (AlternatingMap R M N ι) :=
       map_eq_zero_of_eq' := fun v i j h hij => by
         simp [a.map_eq_zero_of_eq v h hij, b.map_eq_zero_of_eq v h hij] }⟩
 
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 @[simp]
 theorem add_apply : (f + f') v = f v + f' v :=
   rfl
 #align alternating_map.add_apply AlternatingMap.add_apply
 
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 @[norm_cast]
 theorem coe_add : (↑(f + f') : MultilinearMap R (fun i : ι => M) N) = f + f' :=
   rfl
@@ -288,11 +439,23 @@ instance : Zero (AlternatingMap R M N ι) :=
   ⟨{ (0 : MultilinearMap R (fun i : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by simp }⟩
 
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 @[simp]
 theorem zero_apply : (0 : AlternatingMap R M N ι) v = 0 :=
   rfl
 #align alternating_map.zero_apply AlternatingMap.zero_apply
 
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 @[norm_cast]
 theorem coe_zero : ((0 : AlternatingMap R M N ι) : MultilinearMap R (fun i : ι => M) N) = 0 :=
   rfl
@@ -309,11 +472,23 @@ instance : Neg (AlternatingMap R M N' ι) :=
     { -(f : MultilinearMap R (fun i : ι => M) N') with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }⟩
 
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 @[simp]
 theorem neg_apply (m : ι → M) : (-g) m = -g m :=
   rfl
 #align alternating_map.neg_apply AlternatingMap.neg_apply
 
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 @[norm_cast]
 theorem coe_neg : ((-g : AlternatingMap R M N' ι) : MultilinearMap R (fun i : ι => M) N') = -g :=
   rfl
@@ -325,11 +500,23 @@ instance : Sub (AlternatingMap R M N' ι) :=
       map_eq_zero_of_eq' := fun v i j h hij => by
         simp [f.map_eq_zero_of_eq v h hij, g.map_eq_zero_of_eq v h hij] }⟩
 
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 @[simp]
 theorem sub_apply (m : ι → M) : (g - g₂) m = g m - g₂ m :=
   rfl
 #align alternating_map.sub_apply AlternatingMap.sub_apply
 
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+Case conversion may be inaccurate. Consider using '#align alternating_map.coe_sub AlternatingMap.coe_subₓ'. -/
 @[norm_cast]
 theorem coe_sub : (↑(g - g₂) : MultilinearMap R (fun i : ι => M) N') = g - g₂ :=
   rfl
@@ -372,6 +559,7 @@ section
 
 variable (R M)
 
+#print AlternatingMap.ofSubsingleton /-
 /-- The evaluation map from `ι → M` to `M` at a given `i` is alternating when `ι` is subsingleton.
 -/
 @[simps]
@@ -382,7 +570,9 @@ def ofSubsingleton [Subsingleton ι] (i : ι) : AlternatingMap R M M ι :=
     toFun := Function.eval i
     map_eq_zero_of_eq' := fun v i j hv hij => (hij <| Subsingleton.elim _ _).elim }
 #align alternating_map.of_subsingleton AlternatingMap.ofSubsingleton
+-/
 
+#print AlternatingMap.constOfIsEmpty /-
 /-- The constant map is alternating when `ι` is empty. -/
 @[simps (config := { fullyApplied := false })]
 def constOfIsEmpty [IsEmpty ι] (m : N) : AlternatingMap R M N ι :=
@@ -392,9 +582,11 @@ def constOfIsEmpty [IsEmpty ι] (m : N) : AlternatingMap R M N ι :=
     toFun := Function.const _ m
     map_eq_zero_of_eq' := fun v => isEmptyElim }
 #align alternating_map.const_of_is_empty AlternatingMap.constOfIsEmpty
+-/
 
 end
 
+#print AlternatingMap.codRestrict /-
 /-- Restrict the codomain of an alternating map to a submodule. -/
 @[simps]
 def codRestrict (f : AlternatingMap R M N ι) (p : Submodule R N) (h : ∀ v, f v ∈ p) :
@@ -405,6 +597,7 @@ def codRestrict (f : AlternatingMap R M N ι) (p : Submodule R N) (h : ∀ v, f
     toFun := fun v => ⟨f v, h v⟩
     map_eq_zero_of_eq' := fun v i j hv hij => Subtype.ext <| map_eq_zero_of_eq _ _ hv hij }
 #align alternating_map.cod_restrict AlternatingMap.codRestrict
+-/
 
 end AlternatingMap
 
@@ -417,6 +610,7 @@ namespace LinearMap
 
 variable {N₂ : Type _} [AddCommMonoid N₂] [Module R N₂]
 
+#print LinearMap.compAlternatingMap /-
 /-- Composing a alternating map with a linear map on the left gives again an alternating map. -/
 def compAlternatingMap (g : N →ₗ[R] N₂) : AlternatingMap R M N ι →+ AlternatingMap R M N₂ ι
     where
@@ -430,25 +624,50 @@ def compAlternatingMap (g : N →ₗ[R] N₂) : AlternatingMap R M N ι →+ Alt
     ext
     simp
 #align linear_map.comp_alternating_map LinearMap.compAlternatingMap
+-/
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.coe_comp_alternating_map LinearMap.coe_compAlternatingMapₓ'. -/
 @[simp]
 theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) :
     ⇑(g.compAlternatingMap f) = g ∘ f :=
   rfl
 #align linear_map.coe_comp_alternating_map LinearMap.coe_compAlternatingMap
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.comp_alternating_map_apply LinearMap.compAlternatingMap_applyₓ'. -/
 @[simp]
 theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) (m : ι → M) :
     g.compAlternatingMap f m = g (f m) :=
   rfl
 #align linear_map.comp_alternating_map_apply LinearMap.compAlternatingMap_apply
 
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(AlternatingMap.codRestrict.{u4, u3, u2, u1} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι f p h)) f
+Case conversion may be inaccurate. Consider using '#align linear_map.subtype_comp_alternating_map_cod_restrict LinearMap.subtype_compAlternatingMap_codRestrictₓ'. -/
 @[simp]
 theorem subtype_compAlternatingMap_codRestrict (f : AlternatingMap R M N ι) (p : Submodule R N)
     (h) : p.Subtype.compAlternatingMap (f.codRestrict p h) = f :=
   AlternatingMap.ext fun v => rfl
 #align linear_map.subtype_comp_alternating_map_cod_restrict LinearMap.subtype_compAlternatingMap_codRestrict
 
+/- warning: linear_map.comp_alternating_map_cod_restrict -> LinearMap.compAlternatingMap_codRestrict 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.comp_alternating_map_cod_restrict LinearMap.compAlternatingMap_codRestrictₓ'. -/
 @[simp]
 theorem compAlternatingMap_codRestrict (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι)
     (p : Submodule R N₂) (h) :
@@ -465,24 +684,44 @@ variable {M₂ : Type _} [AddCommMonoid M₂] [Module R M₂]
 
 variable {M₃ : Type _} [AddCommMonoid M₃] [Module R M₃]
 
+#print AlternatingMap.compLinearMap /-
 /-- Composing a alternating map with the same linear map on each argument gives again an
 alternating map. -/
 def compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) : AlternatingMap R M₂ N ι :=
   { (f : MultilinearMap R (fun _ : ι => M) N).compLinearMap fun _ => g with
     map_eq_zero_of_eq' := fun v i j h hij => f.map_eq_zero_of_eq _ (LinearMap.congr_arg h) hij }
 #align alternating_map.comp_linear_map AlternatingMap.compLinearMap
+-/
 
+/- warning: alternating_map.coe_comp_linear_map -> AlternatingMap.coe_compLinearMap is a dubious translation:
+lean 3 declaration is
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 theorem coe_compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
     ⇑(f.compLinearMap g) = f ∘ (· ∘ ·) g :=
   rfl
 #align alternating_map.coe_comp_linear_map AlternatingMap.coe_compLinearMap
 
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+Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_apply AlternatingMap.compLinearMap_applyₓ'. -/
 @[simp]
 theorem compLinearMap_apply (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) (v : ι → M₂) :
     f.compLinearMap g v = f fun i => g (v i) :=
   rfl
 #align alternating_map.comp_linear_map_apply AlternatingMap.compLinearMap_apply
 
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 /-- Composing an alternating map twice with the same linear map in each argument is
 the same as composing with their composition. -/
 theorem compLinearMap_assoc (f : AlternatingMap R M N ι) (g₁ : M₂ →ₗ[R] M) (g₂ : M₃ →ₗ[R] M₂) :
@@ -490,6 +729,12 @@ theorem compLinearMap_assoc (f : AlternatingMap R M N ι) (g₁ : M₂ →ₗ[R]
   rfl
 #align alternating_map.comp_linear_map_assoc AlternatingMap.compLinearMap_assoc
 
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+Case conversion may be inaccurate. Consider using '#align alternating_map.zero_comp_linear_map AlternatingMap.zero_compLinearMapₓ'. -/
 @[simp]
 theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : AlternatingMap R M N ι).compLinearMap g = 0 :=
   by
@@ -497,6 +742,12 @@ theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : AlternatingMap R M N ι
   simp only [comp_linear_map_apply, zero_apply]
 #align alternating_map.zero_comp_linear_map AlternatingMap.zero_compLinearMap
 
+/- warning: alternating_map.add_comp_linear_map -> AlternatingMap.add_compLinearMap is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alternating_map.add_comp_linear_map AlternatingMap.add_compLinearMapₓ'. -/
 @[simp]
 theorem add_compLinearMap (f₁ f₂ : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
     (f₁ + f₂).compLinearMap g = f₁.compLinearMap g + f₂.compLinearMap g :=
@@ -505,6 +756,12 @@ theorem add_compLinearMap (f₁ f₂ : AlternatingMap R M N ι) (g : M₂ →ₗ
   simp only [comp_linear_map_apply, add_apply]
 #align alternating_map.add_comp_linear_map AlternatingMap.add_compLinearMap
 
+/- warning: alternating_map.comp_linear_map_zero -> AlternatingMap.compLinearMap_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_zero AlternatingMap.compLinearMap_zeroₓ'. -/
 @[simp]
 theorem compLinearMap_zero [Nonempty ι] (f : AlternatingMap R M N ι) :
     f.compLinearMap (0 : M₂ →ₗ[R] M) = 0 := by
@@ -512,18 +769,36 @@ theorem compLinearMap_zero [Nonempty ι] (f : AlternatingMap R M N ι) :
   simp_rw [comp_linear_map_apply, LinearMap.zero_apply, ← Pi.zero_def, map_zero, zero_apply]
 #align alternating_map.comp_linear_map_zero AlternatingMap.compLinearMap_zero
 
+/- warning: alternating_map.comp_linear_map_id -> AlternatingMap.compLinearMap_id is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_id AlternatingMap.compLinearMap_idₓ'. -/
 /-- Composing an alternating map with the identity linear map in each argument. -/
 @[simp]
 theorem compLinearMap_id (f : AlternatingMap R M N ι) : f.compLinearMap LinearMap.id = f :=
   ext fun _ => rfl
 #align alternating_map.comp_linear_map_id AlternatingMap.compLinearMap_id
 
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+Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_map_injective AlternatingMap.compLinearMap_injectiveₓ'. -/
 /-- Composing with a surjective linear map is injective. -/
 theorem compLinearMap_injective (f : M₂ →ₗ[R] M) (hf : Function.Surjective f) :
     Function.Injective fun g : AlternatingMap R M N ι => g.compLinearMap f := fun g₁ g₂ h =>
   ext fun x => by simpa [Function.surjInv_eq hf] using ext_iff.mp h (Function.surjInv hf ∘ x)
 #align alternating_map.comp_linear_map_injective AlternatingMap.compLinearMap_injective
 
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 theorem compLinearMap_inj (f : M₂ →ₗ[R] M) (hf : Function.Surjective f)
     (g₁ g₂ : AlternatingMap R M N ι) : g₁.compLinearMap f = g₂.compLinearMap f ↔ g₁ = g₂ :=
   (compLinearMap_injective _ hf).eq_iff
@@ -533,9 +808,10 @@ section DomLcongr
 
 variable (ι R N) (S : Type _) [Semiring S] [Module S N] [SMulCommClass R S N]
 
+#print AlternatingMap.domLCongr /-
 /-- Construct a linear equivalence between maps from a linear equivalence between domains. -/
 @[simps apply]
-def domLcongr (e : M ≃ₗ[R] M₂) : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M₂ N ι
+def domLCongr (e : M ≃ₗ[R] M₂) : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M₂ N ι
     where
   toFun f := f.compLinearMap e.symm
   invFun g := g.compLinearMap e
@@ -543,32 +819,57 @@ def domLcongr (e : M ≃ₗ[R] M₂) : AlternatingMap R M N ι ≃ₗ[S] Alterna
   map_smul' _ _ := rfl
   left_inv f := AlternatingMap.ext fun v => f.congr_arg <| funext fun i => e.symm_apply_apply _
   right_inv f := AlternatingMap.ext fun v => f.congr_arg <| funext fun i => e.apply_symm_apply _
-#align alternating_map.dom_lcongr AlternatingMap.domLcongr
+#align alternating_map.dom_lcongr AlternatingMap.domLCongr
+-/
 
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+Case conversion may be inaccurate. Consider using '#align alternating_map.dom_lcongr_refl AlternatingMap.domLCongr_reflₓ'. -/
 @[simp]
-theorem domLcongr_refl : domLcongr R N ι S (LinearEquiv.refl R M) = LinearEquiv.refl S _ :=
+theorem domLCongr_refl : domLCongr R N ι S (LinearEquiv.refl R M) = LinearEquiv.refl S _ :=
   LinearEquiv.ext fun _ => AlternatingMap.ext fun v => rfl
-#align alternating_map.dom_lcongr_refl AlternatingMap.domLcongr_refl
-
+#align alternating_map.dom_lcongr_refl AlternatingMap.domLCongr_refl
+
+/- warning: alternating_map.dom_lcongr_symm -> AlternatingMap.domLCongr_symm 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 alternating_map.dom_lcongr_symm AlternatingMap.domLCongr_symmₓ'. -/
 @[simp]
-theorem domLcongr_symm (e : M ≃ₗ[R] M₂) : (domLcongr R N ι S e).symm = domLcongr R N ι S e.symm :=
+theorem domLCongr_symm (e : M ≃ₗ[R] M₂) : (domLCongr R N ι S e).symm = domLCongr R N ι S e.symm :=
   rfl
-#align alternating_map.dom_lcongr_symm AlternatingMap.domLcongr_symm
-
-theorem domLcongr_trans (e : M ≃ₗ[R] M₂) (f : M₂ ≃ₗ[R] M₃) :
-    (domLcongr R N ι S e).trans (domLcongr R N ι S f) = domLcongr R N ι S (e.trans f) :=
+#align alternating_map.dom_lcongr_symm AlternatingMap.domLCongr_symm
+
+/- warning: alternating_map.dom_lcongr_trans -> AlternatingMap.domLCongr_trans is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align alternating_map.dom_lcongr_trans AlternatingMap.domLCongr_transₓ'. -/
+theorem domLCongr_trans (e : M ≃ₗ[R] M₂) (f : M₂ ≃ₗ[R] M₃) :
+    (domLCongr R N ι S e).trans (domLCongr R N ι S f) = domLCongr R N ι S (e.trans f) :=
   rfl
-#align alternating_map.dom_lcongr_trans AlternatingMap.domLcongr_trans
+#align alternating_map.dom_lcongr_trans AlternatingMap.domLCongr_trans
 
 end DomLcongr
 
+/- warning: alternating_map.comp_linear_equiv_eq_zero_iff -> AlternatingMap.compLinearEquiv_eq_zero_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alternating_map.comp_linear_equiv_eq_zero_iff AlternatingMap.compLinearEquiv_eq_zero_iffₓ'. -/
 /-- Composing an alternating map with the same linear equiv on each argument gives the zero map
 if and only if the alternating map is the zero map. -/
 @[simp]
-theorem comp_linearEquiv_eq_zero_iff (f : AlternatingMap R M N ι) (g : M₂ ≃ₗ[R] M) :
+theorem compLinearEquiv_eq_zero_iff (f : AlternatingMap R M N ι) (g : M₂ ≃ₗ[R] M) :
     f.compLinearMap (g : M₂ →ₗ[R] M) = 0 ↔ f = 0 :=
-  (domLcongr R N ι ℕ g.symm).map_eq_zero_iff
-#align alternating_map.comp_linear_equiv_eq_zero_iff AlternatingMap.comp_linearEquiv_eq_zero_iff
+  (domLCongr R N ι ℕ g.symm).map_eq_zero_iff
+#align alternating_map.comp_linear_equiv_eq_zero_iff AlternatingMap.compLinearEquiv_eq_zero_iff
 
 variable (f f' : AlternatingMap R M N ι)
 
@@ -589,10 +890,12 @@ section
 
 open BigOperators
 
+#print AlternatingMap.map_update_sum /-
 theorem map_update_sum {α : Type _} [DecidableEq ι] (t : Finset α) (i : ι) (g : α → M) (m : ι → M) :
     f (update m i (∑ a in t, g a)) = ∑ a in t, f (update m i (g a)) :=
   f.toMultilinearMap.map_update_sum t i g m
 #align alternating_map.map_update_sum AlternatingMap.map_update_sum
+-/
 
 end
 
@@ -604,17 +907,35 @@ Various properties of reordered and repeated inputs which follow from
 -/
 
 
+/- warning: alternating_map.map_update_self -> AlternatingMap.map_update_self is a dubious translation:
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 theorem map_update_self [DecidableEq ι] {i j : ι} (hij : i ≠ j) :
     f (Function.update v i (v j)) = 0 :=
   f.map_eq_zero_of_eq _ (by rw [Function.update_same, Function.update_noteq hij.symm]) hij
 #align alternating_map.map_update_self AlternatingMap.map_update_self
 
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 theorem map_update_update [DecidableEq ι] {i j : ι} (hij : i ≠ j) (m : M) :
     f (Function.update (Function.update v i m) j m) = 0 :=
   f.map_eq_zero_of_eq _
     (by rw [Function.update_same, Function.update_noteq hij, Function.update_same]) hij
 #align alternating_map.map_update_update AlternatingMap.map_update_update
 
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 theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equiv.swap i j) + f v = 0 :=
   by
   rw [Equiv.comp_swap_eq_update]
@@ -623,16 +944,25 @@ theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equi
     Function.update_comm hij (v i + v j) (v _) v, Function.update_comm hij.symm (v i) (v i) v]
 #align alternating_map.map_swap_add AlternatingMap.map_swap_add
 
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 theorem map_add_swap [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f v + f (v ∘ Equiv.swap i j) = 0 :=
   by
   rw [add_comm]
   exact f.map_swap_add v hij
 #align alternating_map.map_add_swap AlternatingMap.map_add_swap
 
+#print AlternatingMap.map_swap /-
 theorem map_swap [DecidableEq ι] {i j : ι} (hij : i ≠ j) : g (v ∘ Equiv.swap i j) = -g v :=
   eq_neg_of_add_eq_zero_left <| g.map_swap_add v hij
 #align alternating_map.map_swap AlternatingMap.map_swap
+-/
 
+#print AlternatingMap.map_perm /-
 theorem map_perm [DecidableEq ι] [Fintype ι] (v : ι → M) (σ : Equiv.Perm ι) :
     g (v ∘ σ) = σ.sign • g v :=
   by
@@ -641,7 +971,14 @@ theorem map_perm [DecidableEq ι] [Fintype ι] (v : ι → M) (σ : Equiv.Perm 
   · intro s x y hxy hI
     simpa [g.map_swap (v ∘ s) hxy, Equiv.Perm.sign_swap hxy] using hI
 #align alternating_map.map_perm AlternatingMap.map_perm
+-/
 
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 theorem map_congr_perm [DecidableEq ι] [Fintype ι] (σ : Equiv.Perm ι) : g v = σ.sign • g (v ∘ σ) :=
   by
   rw [g.map_perm, smul_smul]
@@ -650,6 +987,7 @@ theorem map_congr_perm [DecidableEq ι] [Fintype ι] (σ : Equiv.Perm ι) : g v
 
 section DomDomCongr
 
+#print AlternatingMap.domDomCongr /-
 /-- Transfer the arguments to a map along an equivalence between argument indices.
 
 This is the alternating version of `multilinear_map.dom_dom_congr`. -/
@@ -662,28 +1000,54 @@ def domDomCongr (σ : ι ≃ ι') (f : AlternatingMap R M N ι) : AlternatingMap
     map_eq_zero_of_eq' := fun v i j hv hij =>
       f.map_eq_zero_of_eq (v ∘ σ) (by simpa using hv) (σ.symm.Injective.Ne hij) }
 #align alternating_map.dom_dom_congr AlternatingMap.domDomCongr
+-/
 
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 @[simp]
 theorem domDomCongr_refl (f : AlternatingMap R M N ι) : f.domDomCongr (Equiv.refl ι) = f :=
   ext fun v => rfl
 #align alternating_map.dom_dom_congr_refl AlternatingMap.domDomCongr_refl
 
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 theorem domDomCongr_trans (σ₁ : ι ≃ ι') (σ₂ : ι' ≃ ι'') (f : AlternatingMap R M N ι) :
     f.domDomCongr (σ₁.trans σ₂) = (f.domDomCongr σ₁).domDomCongr σ₂ :=
   rfl
 #align alternating_map.dom_dom_congr_trans AlternatingMap.domDomCongr_trans
 
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 @[simp]
 theorem domDomCongr_zero (σ : ι ≃ ι') : (0 : AlternatingMap R M N ι).domDomCongr σ = 0 :=
   rfl
 #align alternating_map.dom_dom_congr_zero AlternatingMap.domDomCongr_zero
 
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 @[simp]
 theorem domDomCongr_add (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
     (f + g).domDomCongr σ = f.domDomCongr σ + g.domDomCongr σ :=
   rfl
 #align alternating_map.dom_dom_congr_add AlternatingMap.domDomCongr_add
 
+#print AlternatingMap.domDomCongrEquiv /-
 /-- `alternating_map.dom_dom_congr` as an equivalence.
 
 This is declared separately because it does not work with dot notation. -/
@@ -700,7 +1064,14 @@ def domDomCongrEquiv (σ : ι ≃ ι') : AlternatingMap R M N ι ≃+ Alternatin
     simp [Function.comp]
   map_add' := domDomCongr_add σ
 #align alternating_map.dom_dom_congr_equiv AlternatingMap.domDomCongrEquiv
+-/
 
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 /-- The results of applying `dom_dom_congr` to two maps are equal if and only if those maps are. -/
 @[simp]
 theorem domDomCongr_eq_iff (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
@@ -708,17 +1079,35 @@ theorem domDomCongr_eq_iff (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
   (domDomCongrEquiv σ : _ ≃+ AlternatingMap R M N ι').apply_eq_iff_eq
 #align alternating_map.dom_dom_congr_eq_iff AlternatingMap.domDomCongr_eq_iff
 
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+Case conversion may be inaccurate. Consider using '#align alternating_map.dom_dom_congr_eq_zero_iff AlternatingMap.domDomCongr_eq_zero_iffₓ'. -/
 @[simp]
 theorem domDomCongr_eq_zero_iff (σ : ι ≃ ι') (f : AlternatingMap R M N ι) :
     f.domDomCongr σ = 0 ↔ f = 0 :=
   (domDomCongrEquiv σ : AlternatingMap R M N ι ≃+ AlternatingMap R M N ι').map_eq_zero_iff
 #align alternating_map.dom_dom_congr_eq_zero_iff AlternatingMap.domDomCongr_eq_zero_iff
 
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+Case conversion may be inaccurate. Consider using '#align alternating_map.dom_dom_congr_perm AlternatingMap.domDomCongr_permₓ'. -/
 theorem domDomCongr_perm [Fintype ι] [DecidableEq ι] (σ : Equiv.Perm ι) :
     g.domDomCongr σ = σ.sign • g :=
   AlternatingMap.ext fun v => g.map_perm v σ
 #align alternating_map.dom_dom_congr_perm AlternatingMap.domDomCongr_perm
 
+/- warning: alternating_map.coe_dom_dom_congr -> AlternatingMap.coe_domDomCongr is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align alternating_map.coe_dom_dom_congr AlternatingMap.coe_domDomCongrₓ'. -/
 @[norm_cast]
 theorem coe_domDomCongr (σ : ι ≃ ι') :
     ↑(f.domDomCongr σ) = (f : MultilinearMap R (fun _ : ι => M) N).domDomCongr σ :=
@@ -727,8 +1116,14 @@ theorem coe_domDomCongr (σ : ι ≃ ι') :
 
 end DomDomCongr
 
+/- warning: alternating_map.map_linear_dependent -> AlternatingMap.map_linearDependent is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alternating_map.map_linear_dependent AlternatingMap.map_linearDependentₓ'. -/
 /-- If the arguments are linearly dependent then the result is `0`. -/
-theorem map_linear_dependent {K : Type _} [Ring K] {M : Type _} [AddCommGroup M] [Module K M]
+theorem map_linearDependent {K : Type _} [Ring K] {M : Type _} [AddCommGroup M] [Module K M]
     {N : Type _} [AddCommGroup N] [Module K N] [NoZeroSMulDivisors K N] (f : AlternatingMap K M N ι)
     (v : ι → M) (h : ¬LinearIndependent K v) : f v = 0 :=
   by
@@ -745,18 +1140,30 @@ theorem map_linear_dependent {K : Type _} [Ring K] {M : Type _} [AddCommGroup M]
   intro j hj
   obtain ⟨hij, _⟩ := finset.mem_erase.mp hj
   rw [f.map_smul, f.map_update_self _ hij.symm, smul_zero]
-#align alternating_map.map_linear_dependent AlternatingMap.map_linear_dependent
+#align alternating_map.map_linear_dependent AlternatingMap.map_linearDependent
 
 section Fin
 
 open Fin
 
+/- warning: alternating_map.map_vec_cons_add -> AlternatingMap.map_vecCons_add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alternating_map.map_vec_cons_add AlternatingMap.map_vecCons_addₓ'. -/
 /-- A version of `multilinear_map.cons_add` for `alternating_map`. -/
 theorem map_vecCons_add {n : ℕ} (f : AlternatingMap R M N (Fin n.succ)) (m : Fin n → M) (x y : M) :
     f (Matrix.vecCons (x + y) m) = f (Matrix.vecCons x m) + f (Matrix.vecCons y m) :=
   f.toMultilinearMap.cons_add _ _ _
 #align alternating_map.map_vec_cons_add AlternatingMap.map_vecCons_add
 
+/- warning: alternating_map.map_vec_cons_smul -> AlternatingMap.map_vecCons_smul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alternating_map.map_vec_cons_smul AlternatingMap.map_vecCons_smulₓ'. -/
 /-- A version of `multilinear_map.cons_smul` for `alternating_map`. -/
 theorem map_vecCons_smul {n : ℕ} (f : AlternatingMap R M N (Fin n.succ)) (m : Fin n → M) (c : R)
     (x : M) : f (Matrix.vecCons (c • x) m) = c • f (Matrix.vecCons x m) :=
@@ -787,6 +1194,12 @@ private theorem alternization_map_eq_zero_of_eq_aux (m : MultilinearMap R (fun i
       fun σ _ => swap_mul_involutive i j σ
 #align multilinear_map.alternization_map_eq_zero_of_eq_aux multilinear_map.alternization_map_eq_zero_of_eq_aux
 
+/- warning: multilinear_map.alternatization -> MultilinearMap.alternatization is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization MultilinearMap.alternatizationₓ'. -/
 /-- Produce an `alternating_map` out of a `multilinear_map`, by summing over all argument
 permutations. -/
 def alternatization : MultilinearMap R (fun i : ι => M) N' →+ AlternatingMap R M N' ι
@@ -810,16 +1223,34 @@ def alternatization : MultilinearMap R (fun i : ι => M) N' →+ AlternatingMap
       AlternatingMap.zero_apply, AlternatingMap.coe_mk, smul_apply, sum_apply]
 #align multilinear_map.alternatization MultilinearMap.alternatization
 
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+Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_def MultilinearMap.alternatization_defₓ'. -/
 theorem alternatization_def (m : MultilinearMap R (fun i : ι => M) N') :
     ⇑(alternatization m) = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
   rfl
 #align multilinear_map.alternatization_def MultilinearMap.alternatization_def
 
+/- warning: multilinear_map.alternatization_coe -> MultilinearMap.alternatization_coe is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_coe MultilinearMap.alternatization_coeₓ'. -/
 theorem alternatization_coe (m : MultilinearMap R (fun i : ι => M) N') :
     ↑m.alternatization = (∑ σ : Perm ι, σ.sign • m.domDomCongr σ : _) :=
   coe_injective rfl
 #align multilinear_map.alternatization_coe MultilinearMap.alternatization_coe
 
+/- warning: multilinear_map.alternatization_apply -> MultilinearMap.alternatization_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align multilinear_map.alternatization_apply MultilinearMap.alternatization_applyₓ'. -/
 theorem alternatization_apply (m : MultilinearMap R (fun i : ι => M) N') (v : ι → M) :
     alternatization m v = ∑ σ : Perm ι, σ.sign • m.domDomCongr σ v := by
   simp only [alternatization_def, smul_apply, sum_apply]
@@ -829,6 +1260,12 @@ end MultilinearMap
 
 namespace AlternatingMap
 
+/- warning: alternating_map.coe_alternatization -> AlternatingMap.coe_alternatization is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alternating_map.coe_alternatization AlternatingMap.coe_alternatizationₓ'. -/
 /-- Alternatizing a multilinear map that is already alternating results in a scale factor of `n!`,
 where `n` is the number of inputs. -/
 theorem coe_alternatization [DecidableEq ι] [Fintype ι] (a : AlternatingMap R M N' ι) :
@@ -846,6 +1283,12 @@ namespace LinearMap
 
 variable {N'₂ : Type _} [AddCommGroup N'₂] [Module R N'₂] [DecidableEq ι] [Fintype ι]
 
+/- warning: linear_map.comp_multilinear_map_alternatization -> LinearMap.compMultilinearMap_alternatization 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.comp_multilinear_map_alternatization LinearMap.compMultilinearMap_alternatizationₓ'. -/
 /-- Composition with a linear map before and after alternatization are equivalent. -/
 theorem compMultilinearMap_alternatization (g : N' →ₗ[R] N'₂)
     (f : MultilinearMap R (fun _ : ι => M) N') :
@@ -870,11 +1313,19 @@ variable {R' : Type _} {Mᵢ N₁ N₂ : Type _} [CommSemiring R'] [AddCommGroup
 
 namespace Equiv.Perm
 
+#print Equiv.Perm.ModSumCongr /-
 /-- Elements which are considered equivalent if they differ only by swaps within α or β  -/
 abbrev ModSumCongr (α β : Type _) :=
   _ ⧸ (Equiv.Perm.sumCongrHom α β).range
 #align equiv.perm.mod_sum_congr Equiv.Perm.ModSumCongr
+-/
 
+/- warning: equiv.perm.mod_sum_congr.swap_smul_involutive -> Equiv.Perm.ModSumCongr.swap_smul_involutive 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 equiv.perm.mod_sum_congr.swap_smul_involutive Equiv.Perm.ModSumCongr.swap_smul_involutiveₓ'. -/
 theorem ModSumCongr.swap_smul_involutive {α β : Type _} [DecidableEq (Sum α β)] (i j : Sum α β) :
     Function.Involutive (SMul.smul (Equiv.swap i j) : ModSumCongr α β → ModSumCongr α β) := fun σ =>
   by
@@ -890,8 +1341,14 @@ open Equiv
 
 variable [DecidableEq ιa] [DecidableEq ιb]
 
+/- warning: alternating_map.dom_coprod.summand -> AlternatingMap.domCoprod.summand is a dubious translation:
+lean 3 declaration is
+  forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb], (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) -> (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) -> (Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) -> (MultilinearMap.{u3, u4, max u5 u6, max u1 u2} R' (Sum.{u1, u2} ιa ιb) (fun (_x : Sum.{u1, u2} ιa ιb) => Mᵢ) (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_17) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_18) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16))
+but is expected to have type
+  forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb], (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) -> (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) -> (Equiv.Perm.ModSumCongr.{u1, u2} ιa ιb) -> (MultilinearMap.{u3, u4, max u6 u5, max u1 u2} R' (Sum.{u1, u2} ιa ιb) (fun (_x : Sum.{u1, u2} ιa ιb) => Mᵢ) (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_17) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_18) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16))
+Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand AlternatingMap.domCoprod.summandₓ'. -/
 /-- summand used in `alternating_map.dom_coprod` -/
-def DomCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
+def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
     (σ : Perm.ModSumCongr ιa ιb) : MultilinearMap R' (fun _ : Sum ιa ιb => Mᵢ) (N₁ ⊗[R'] N₂) :=
   Quotient.liftOn' σ
     (fun σ =>
@@ -910,22 +1367,34 @@ def DomCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap
     simp only [Sum.map_inr, perm.sum_congr_hom_apply, perm.sum_congr_apply, Sum.map_inl,
       Function.comp_apply, perm.coe_mul]
     rw [← a.map_congr_perm fun i => v (σ₁ _), ← b.map_congr_perm fun i => v (σ₁ _)]
-#align alternating_map.dom_coprod.summand AlternatingMap.DomCoprod.summand
-
-theorem DomCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
+#align alternating_map.dom_coprod.summand AlternatingMap.domCoprod.summand
+
+/- warning: alternating_map.dom_coprod.summand_mk' -> AlternatingMap.domCoprod.summand_mk'' is a dubious translation:
+lean 3 declaration is
+  forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (σ : Equiv.Perm.{max (succ u1) (succ u2)} (Sum.{u1, u2} ιa ιb)), Eq.{max (succ (max u1 u2)) (succ u4) (succ (max u5 u6))} (MultilinearMap.{u3, u4, max u5 u6, max u1 u2} R' (Sum.{u1, u2} ιa ιb) (fun (_x : Sum.{u1, u2} ιa ιb) => Mᵢ) (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_17) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (fun (i : Sum.{u1, u2} ιa ιb) => _inst_18) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16)) (AlternatingMap.domCoprod.summand.{u1, u2, u3, u4, u5, u6} ιa ιb _inst_10 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+Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_mk' AlternatingMap.domCoprod.summand_mk''ₓ'. -/
+theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
     (σ : Equiv.Perm (Sum ιa ιb)) :
-    DomCoprod.summand a b (Quotient.mk'' σ) =
+    domCoprod.summand a b (Quotient.mk'' σ) =
       σ.sign •
         (MultilinearMap.domCoprod ↑a ↑b : MultilinearMap R' (fun _ => Mᵢ) (N₁ ⊗ N₂)).domDomCongr
           σ :=
   rfl
-#align alternating_map.dom_coprod.summand_mk' AlternatingMap.DomCoprod.summand_mk''
-
+#align alternating_map.dom_coprod.summand_mk' AlternatingMap.domCoprod.summand_mk''
+
+/- warning: alternating_map.dom_coprod.summand_add_swap_smul_eq_zero -> AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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+Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_add_swap_smul_eq_zero AlternatingMap.domCoprod.summand_add_swap_smul_eq_zeroₓ'. -/
 /-- Swapping elements in `σ` with equal values in `v` results in an addition that cancels -/
-theorem DomCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁ ιa)
+theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁ ιa)
     (b : AlternatingMap R' Mᵢ N₂ ιb) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
     {i j : Sum ιa ιb} (hv : v i = v j) (hij : i ≠ j) :
-    DomCoprod.summand a b σ v + DomCoprod.summand a b (swap i j • σ) v = 0 :=
+    domCoprod.summand a b σ v + domCoprod.summand a b (swap i j • σ) v = 0 :=
   by
   apply σ.induction_on' fun σ => _
   dsimp only [Quotient.liftOn'_mk'', Quotient.map'_mk'', MulAction.Quotient.smul_mk,
@@ -937,14 +1406,20 @@ theorem DomCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁
   convert add_right_neg _ <;>
     · ext k
       rw [Equiv.apply_swap_eq_self hv]
-#align alternating_map.dom_coprod.summand_add_swap_smul_eq_zero AlternatingMap.DomCoprod.summand_add_swap_smul_eq_zero
-
+#align alternating_map.dom_coprod.summand_add_swap_smul_eq_zero AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero
+
+/- warning: alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant -> AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ιa : Type.{u3}} {ιb : Type.{u1}} [_inst_10 : Fintype.{u3} ιa] [_inst_11 : Fintype.{u1} ιb] {R' : Type.{u6}} {Mᵢ : Type.{u5}} {N₁ : Type.{u4}} {N₂ : Type.{u2}} [_inst_12 : CommSemiring.{u6} R'] [_inst_13 : AddCommGroup.{u4} N₁] [_inst_14 : Module.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u2} N₂] [_inst_16 : Module.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u5} Mᵢ] [_inst_18 : Module.{u6, u5} R' Mᵢ (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u3} ιa] [_inst_20 : DecidableEq.{succ u1} ιb] (a : AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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_inst_15 _inst_14 _inst_16)))))))))
+Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariantₓ'. -/
 /-- Swapping elements in `σ` with equal values in `v` result in zero if the swap has no effect
 on the quotient. -/
-theorem DomCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ N₁ ιa)
+theorem domCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ N₁ ιa)
     (b : AlternatingMap R' Mᵢ N₂ ιb) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
     {i j : Sum ιa ιb} (hv : v i = v j) (hij : i ≠ j) :
-    swap i j • σ = σ → DomCoprod.summand a b σ v = 0 :=
+    swap i j • σ = σ → domCoprod.summand a b σ v = 0 :=
   by
   apply σ.induction_on' fun σ => _
   dsimp only [Quotient.liftOn'_mk'', Quotient.map'_mk'', MultilinearMap.smul_apply,
@@ -972,8 +1447,14 @@ theorem DomCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ
     on_goal 1 => convert TensorProduct.tmul_zero _ _
     on_goal 2 => convert TensorProduct.zero_tmul _ _
     all_goals exact AlternatingMap.map_eq_zero_of_eq _ _ hv fun hij' => hij (hij' ▸ rfl)
-#align alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant AlternatingMap.DomCoprod.summand_eq_zero_of_smul_invariant
-
+#align alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant
+
+/- warning: alternating_map.dom_coprod -> AlternatingMap.domCoprod is a dubious translation:
+lean 3 declaration is
+  forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb], (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) -> (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) -> (AlternatingMap.{u3, u4, max u5 u6, max u1 u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u1, u2} ιa ιb))
+but is expected to have type
+  forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb], (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) -> (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) -> (AlternatingMap.{u3, u4, max u6 u5, max u2 u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u1, u2} ιa ιb))
+Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod AlternatingMap.domCoprodₓ'. -/
 /-- Like `multilinear_map.dom_coprod`, but ensures the result is also alternating.
 
 Note that this is usually defined (for instance, as used in Proposition 22.24 in [Gallier2011Notes])
@@ -999,9 +1480,9 @@ def domCoprod (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ
     AlternatingMap R' Mᵢ (N₁ ⊗[R'] N₂) (Sum ιa ιb) :=
   {
     ∑ σ : Perm.ModSumCongr ιa ιb,
-      DomCoprod.summand a b
+      domCoprod.summand a b
         σ with
-    toFun := fun v => (⇑(∑ σ : Perm.ModSumCongr ιa ιb, DomCoprod.summand a b σ)) v
+    toFun := fun v => (⇑(∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ)) v
     map_eq_zero_of_eq' := fun v i j hv hij => by
       dsimp only
       rw [MultilinearMap.sum_apply]
@@ -1013,12 +1494,19 @@ def domCoprod (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ
           Equiv.Perm.ModSumCongr.swap_smul_involutive i j σ }
 #align alternating_map.dom_coprod AlternatingMap.domCoprod
 
+/- warning: alternating_map.dom_coprod_coe -> AlternatingMap.domCoprod_coe is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ιa : Type.{u3}} {ιb : Type.{u1}} [_inst_10 : Fintype.{u3} ιa] [_inst_11 : Fintype.{u1} ιb] {R' : Type.{u6}} {Mᵢ : Type.{u5}} {N₁ : Type.{u4}} {N₂ : Type.{u2}} [_inst_12 : CommSemiring.{u6} R'] [_inst_13 : AddCommGroup.{u4} N₁] [_inst_14 : Module.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u2} N₂] [_inst_16 : Module.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u5} Mᵢ] [_inst_18 : Module.{u6, u5} R' Mᵢ (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u3} ιa] [_inst_20 : DecidableEq.{succ u1} ιb] (a : AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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+Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod_coe AlternatingMap.domCoprod_coeₓ'. -/
 theorem domCoprod_coe (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
     (↑(a.domCoprod b) : MultilinearMap R' (fun _ => Mᵢ) _) =
-      ∑ σ : Perm.ModSumCongr ιa ιb, DomCoprod.summand a b σ :=
+      ∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ :=
   MultilinearMap.ext fun _ => rfl
 #align alternating_map.dom_coprod_coe AlternatingMap.domCoprod_coe
 
+#print AlternatingMap.domCoprod' /-
 /-- A more bundled version of `alternating_map.dom_coprod` that maps
 `((ι₁ → N) → N₁) ⊗ ((ι₂ → N) → N₂)` to `(ι₁ ⊕ ι₂ → N) → N₁ ⊗ N₂`. -/
 def domCoprod' :
@@ -1041,7 +1529,14 @@ def domCoprod' :
         first |rw [← smul_add]|rw [smul_comm]
         congr
 #align alternating_map.dom_coprod' AlternatingMap.domCoprod'
+-/
 
+/- warning: alternating_map.dom_coprod'_apply -> AlternatingMap.domCoprod'_apply is a dubious translation:
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_inst_14 _inst_16) (Sum.{u1, u2} ιa ιb) R' (CommSemiring.toSemiring.{u3} R' _inst_12) (TensorProduct.module.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_14 _inst_16) (AlternatingMap.domCoprod'._proof_3.{u3, u5, u6} R' N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16))) => (TensorProduct.{u3, max u4 u5 u1, max u4 u6 u2} R' _inst_12 (AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u3, u4, u5, u1, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_14 (AlternatingMap.domCoprod'._proof_1.{u3, u5} R' N₁ _inst_12 _inst_13 _inst_14)) (AlternatingMap.module.{u3, u4, u6, u2, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_16 (AlternatingMap.domCoprod'._proof_2.{u3, u6} R' N₂ _inst_12 _inst_15 _inst_16))) -> (AlternatingMap.{u3, u4, max u5 u6, max u1 u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u3, u5, u6} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u6} N₂ 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+but is expected to have type
+  forall {ιa : Type.{u3}} {ιb : Type.{u1}} [_inst_10 : Fintype.{u3} ιa] [_inst_11 : Fintype.{u1} ιb] {R' : Type.{u6}} {Mᵢ : Type.{u5}} {N₁ : Type.{u4}} {N₂ : Type.{u2}} [_inst_12 : CommSemiring.{u6} R'] [_inst_13 : AddCommGroup.{u4} N₁] [_inst_14 : Module.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u2} N₂] [_inst_16 : Module.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u5} Mᵢ] [_inst_18 : Module.{u6, u5} R' Mᵢ (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u3} ιa] [_inst_20 : DecidableEq.{succ u1} ιb] (a : AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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(smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) (TensorProduct.addCommMonoid.{u6, max (max u3 u5) u4, max (max u1 u5) u2} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.addCommMonoid.{u6, u5, max u4 u2, max u3 u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, max (max u3 u5) u4, max (max u1 u5) u2} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.module.{u6, u5, max u4 u2, max u3 u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb) R' (CommSemiring.toSemiring.{u6} R' _inst_12) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (smulCommClass_self.{u6, max u4 u2} R' (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, max u4 u2} R' (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (SubNegZeroMonoid.toNegZeroClass.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (SubtractionMonoid.toSubNegZeroMonoid.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (SubtractionCommMonoid.toSubtractionMonoid.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (AddCommGroup.toDivisionAddCommMonoid.{max u4 u2} (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommGroup.{u6, u4, u2} R' _inst_12 N₁ N₂ _inst_13 _inst_15 _inst_14 _inst_16)))))) (Module.toMulActionWithZero.{u6, max u4 u2} R' (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (CommSemiring.toSemiring.{u6} R' _inst_12) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16)))))) (TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (fun (_x : TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) => AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, max (max (max (max u2 u4) u5) u1) u3, max (max (max (max u2 u4) u5) u1) u3} R' R' (TensorProduct.{u6, max (max u3 u4) u5, max (max u1 u2) u5} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.{u6, u5, max u2 u4, max u1 u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) (CommSemiring.toSemiring.{u6} R' _inst_12) (CommSemiring.toSemiring.{u6} R' _inst_12) (TensorProduct.addCommMonoid.{u6, max (max u3 u5) u4, max (max u1 u5) u2} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.addCommMonoid.{u6, u5, max u4 u2, max u3 u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 (TensorProduct.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.addCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R' _inst_12 N₁ N₂ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_14 _inst_16) (Sum.{u3, u1} ιa ιb)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, max (max u3 u5) u4, max (max u1 u5) u2} R' _inst_12 (AlternatingMap.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.addCommMonoid.{u6, u5, u4, u3} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa) (AlternatingMap.addCommMonoid.{u6, u5, u2, u1} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb) (AlternatingMap.module.{u6, u5, u4, u3, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14 ιa R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_14 (smulCommClass_self.{u6, u4} R' N₁ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u4} R' N₁ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u4} N₁ (SubNegZeroMonoid.toNegZeroClass.{u4} N₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} N₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} N₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} N₁ _inst_13))))) (Module.toMulActionWithZero.{u6, u4} R' N₁ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u4} N₁ _inst_13) _inst_14)))) (AlternatingMap.module.{u6, u5, u2, u1, u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16 ιb R' (CommSemiring.toSemiring.{u6} R' _inst_12) _inst_16 (smulCommClass_self.{u6, u2} R' N₂ (CommSemiring.toCommMonoid.{u6} R' _inst_12) (MulActionWithZero.toMulAction.{u6, u2} R' N₂ (Semiring.toMonoidWithZero.{u6} R' (CommSemiring.toSemiring.{u6} R' _inst_12)) (NegZeroClass.toZero.{u2} N₂ (SubNegZeroMonoid.toNegZeroClass.{u2} N₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} N₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} N₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} N₂ _inst_15))))) (Module.toMulActionWithZero.{u6, u2} R' N₂ (CommSemiring.toSemiring.{u6} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₂ _inst_15) _inst_16))))) (AlternatingMap.module.{u6, 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(AlternatingMap.domCoprod.{u3, u1, u6, u5, u4, u2} ιa ιb _inst_10 _inst_11 R' Mᵢ N₁ N₂ _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 (fun (a : ιa) (b : ιa) => _inst_19 a b) (fun (a : ιb) (b : ιb) => _inst_20 a b) a b)
+Case conversion may be inaccurate. Consider using '#align alternating_map.dom_coprod'_apply AlternatingMap.domCoprod'_applyₓ'. -/
 @[simp]
 theorem domCoprod'_apply (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
     domCoprod' (a ⊗ₜ[R'] b) = domCoprod a b :=
@@ -1052,6 +1547,12 @@ end AlternatingMap
 
 open Equiv
 
+/- warning: multilinear_map.dom_coprod_alternization_coe -> MultilinearMap.domCoprod_alternization_coe is a dubious translation:
+lean 3 declaration is
+  forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : MultilinearMap.{u3, u4, u5, u1} R' ιa (fun (_x : ιa) => Mᵢ) N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (fun (i : ιa) => _inst_17) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) (fun (i : ιa) => _inst_18) _inst_14) (b : MultilinearMap.{u3, u4, u6, u2} R' ιb (fun (_x : 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+but is expected to have type
+  forall {ιa : Type.{u6}} {ιb : Type.{u5}} [_inst_10 : Fintype.{u6} ιa] [_inst_11 : Fintype.{u5} ιb] {R' : Type.{u4}} {Mᵢ : Type.{u3}} {N₁ : Type.{u2}} {N₂ : Type.{u1}} [_inst_12 : CommSemiring.{u4} R'] [_inst_13 : AddCommGroup.{u2} N₁] [_inst_14 : Module.{u4, u2} R' N₁ (CommSemiring.toSemiring.{u4} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u1} N₂] [_inst_16 : Module.{u4, u1} R' N₂ (CommSemiring.toSemiring.{u4} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u1} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u3} Mᵢ] [_inst_18 : Module.{u4, u3} R' Mᵢ (CommSemiring.toSemiring.{u4} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u6} ιa] [_inst_20 : DecidableEq.{succ u5} ιb] (a : MultilinearMap.{u4, u3, u2, u6} R' ιa (fun (_x : ιa) => Mᵢ) N₁ (CommSemiring.toSemiring.{u4} R' _inst_12) (fun (i : ιa) => _inst_17) (AddCommGroup.toAddCommMonoid.{u2} N₁ _inst_13) (fun (i : ιa) => _inst_18) _inst_14) (b : MultilinearMap.{u4, u3, u1, u5} R' ιb (fun (_x : 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+Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_alternization_coe MultilinearMap.domCoprod_alternization_coeₓ'. -/
 /-- A helper lemma for `multilinear_map.dom_coprod_alternization`. -/
 theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableEq ιb]
     (a : MultilinearMap R' (fun _ : ιa => Mᵢ) N₁) (b : MultilinearMap R' (fun _ : ιb => Mᵢ) N₂) :
@@ -1066,6 +1567,12 @@ theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableE
 
 open AlternatingMap
 
+/- warning: multilinear_map.dom_coprod_alternization -> MultilinearMap.domCoprod_alternization 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 multilinear_map.dom_coprod_alternization MultilinearMap.domCoprod_alternizationₓ'. -/
 /-- Computing the `multilinear_map.alternatization` of the `multilinear_map.dom_coprod` is the same
 as computing the `alternating_map.dom_coprod` of the `multilinear_map.alternatization`s.
 -/
@@ -1105,6 +1612,12 @@ theorem MultilinearMap.domCoprod_alternization [DecidableEq ιa] [DecidableEq ι
     MultilinearMap.domCoprod_domDomCongr_sumCongr, perm.sign_sum_congr, mul_smul, mul_smul]
 #align multilinear_map.dom_coprod_alternization MultilinearMap.domCoprod_alternization
 
+/- warning: multilinear_map.dom_coprod_alternization_eq -> MultilinearMap.domCoprod_alternization_eq is a dubious translation:
+lean 3 declaration is
+  forall {ιa : Type.{u1}} {ιb : Type.{u2}} [_inst_10 : Fintype.{u1} ιa] [_inst_11 : Fintype.{u2} ιb] {R' : Type.{u3}} {Mᵢ : Type.{u4}} {N₁ : Type.{u5}} {N₂ : Type.{u6}} [_inst_12 : CommSemiring.{u3} R'] [_inst_13 : AddCommGroup.{u5} N₁] [_inst_14 : Module.{u3, u5} R' N₁ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13)] [_inst_15 : AddCommGroup.{u6} N₂] [_inst_16 : Module.{u3, u6} R' N₂ (CommSemiring.toSemiring.{u3} R' _inst_12) (AddCommGroup.toAddCommMonoid.{u6} N₂ _inst_15)] [_inst_17 : AddCommMonoid.{u4} Mᵢ] [_inst_18 : Module.{u3, u4} R' Mᵢ (CommSemiring.toSemiring.{u3} R' _inst_12) _inst_17] [_inst_19 : DecidableEq.{succ u1} ιa] [_inst_20 : DecidableEq.{succ u2} ιb] (a : AlternatingMap.{u3, u4, u5, u1} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₁ (AddCommGroup.toAddCommMonoid.{u5} N₁ _inst_13) _inst_14 ιa) (b : AlternatingMap.{u3, u4, u6, u2} R' (CommSemiring.toSemiring.{u3} R' _inst_12) Mᵢ _inst_17 _inst_18 N₂ 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_inst_20 a b) a b))
+Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_alternization_eq MultilinearMap.domCoprod_alternization_eqₓ'. -/
 /-- Taking the `multilinear_map.alternatization` of the `multilinear_map.dom_coprod` of two
 `alternating_map`s gives a scaled version of the `alternating_map.coprod` of those maps.
 -/
@@ -1134,6 +1647,12 @@ variable {R' : Type _} {N₁ N₂ : Type _} [CommSemiring R'] [AddCommMonoid N
 
 variable [Module R' N₁] [Module R' N₂]
 
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+Case conversion may be inaccurate. Consider using '#align basis.ext_alternating Basis.ext_alternatingₓ'. -/
 /-- Two alternating maps indexed by a `fintype` are equal if they are equal when all arguments
 are distinct basis vectors. -/
 theorem Basis.ext_alternating {f g : AlternatingMap R' N₁ N₂ ι} (e : Basis ι₁ R' N₁)
@@ -1161,6 +1680,7 @@ variable {R' : Type _} {M'' M₂'' N'' N₂'' : Type _} [CommSemiring R'] [AddCo
 
 namespace AlternatingMap
 
+#print AlternatingMap.curryLeft /-
 /-- Given an alternating map `f` in `n+1` variables, split the first variable to obtain
 a linear map into alternating maps in `n` variables, given by `x ↦ (m ↦ f (matrix.vec_cons x m))`.
 It can be thought of as a map $Hom(\bigwedge^{n+1} M, N) \to Hom(M, Hom(\bigwedge^n M, N))$.
@@ -1182,24 +1702,44 @@ def curryLeft {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ)) :
   map_add' m₁ m₂ := ext fun v => f.map_vecCons_add _ _ _
   map_smul' r m := ext fun v => f.map_vecCons_smul _ _ _
 #align alternating_map.curry_left AlternatingMap.curryLeft
+-/
 
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+Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_zero AlternatingMap.curryLeft_zeroₓ'. -/
 @[simp]
 theorem curryLeft_zero {n : ℕ} : curryLeft (0 : AlternatingMap R' M'' N'' (Fin n.succ)) = 0 :=
   rfl
 #align alternating_map.curry_left_zero AlternatingMap.curryLeft_zero
 
+/- warning: alternating_map.curry_left_add -> AlternatingMap.curryLeft_add is a dubious translation:
+lean 3 declaration is
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(Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17))))) (instHAdd.{max u2 u1} (LinearMap.{u3, u3, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10))) M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17))))) (LinearMap.instAddLinearMap.{u3, u3, u2, max u2 u1} R' R' M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u3, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_17 (smulCommClass_self.{u3, u1} R' N'' (CommSemiring.toCommMonoid.{u3} R' _inst_10) (MulActionWithZero.toMulAction.{u3, u1} R' N'' (Semiring.toMonoidWithZero.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10))))) (AlternatingMap.curryLeft.{u3, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f) (AlternatingMap.curryLeft.{u3, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n g))
+Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_add AlternatingMap.curryLeft_addₓ'. -/
 @[simp]
 theorem curryLeft_add {n : ℕ} (f g : AlternatingMap R' M'' N'' (Fin n.succ)) :
     curryLeft (f + g) = curryLeft f + curryLeft g :=
   rfl
 #align alternating_map.curry_left_add AlternatingMap.curryLeft_add
 
+/- warning: alternating_map.curry_left_smul -> AlternatingMap.curryLeft_smul is a dubious translation:
+lean 3 declaration is
+  forall {R' : Type.{u1}} {M'' : Type.{u2}} {N'' : Type.{u3}} [_inst_10 : CommSemiring.{u1} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_13 : AddCommMonoid.{u3} N''] [_inst_15 : Module.{u1, u2} R' M'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11] [_inst_17 : Module.{u1, u3} R' N'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_13] {n : Nat} (r : R') (f : AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))), Eq.{max (succ u2) (succ (max u2 u3))} (LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) (AlternatingMap.curryLeft.{u1, u2, u3} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n (SMul.smul.{u1, max u2 u3} R' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (AlternatingMap.smul.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) R' (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) (Module.toDistribMulAction.{u1, u3} R' N'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_13 _inst_17) (smulCommClass_self.{u1, u3} R' N'' (CommSemiring.toCommMonoid.{u1} R' _inst_10) (MulActionWithZero.toMulAction.{u1, u3} R' N'' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)) (AddZeroClass.toHasZero.{u3} N'' (AddMonoid.toAddZeroClass.{u3} N'' (AddCommMonoid.toAddMonoid.{u3} N'' _inst_13))) (Module.toMulActionWithZero.{u1, u3} R' N'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_13 _inst_17)))) r f)) (SMul.smul.{u1, max u2 u3} R' (LinearMap.{u1, u1, u2, max u2 u3} R' R' (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17))) (LinearMap.hasSmul.{u1, u1, u1, u2, max u2 u3} R' R' R' M'' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u1} R' _inst_10) (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (AlternatingMap.curryLeft._proof_1.{u3, u1} R' N'' _inst_10 _inst_13 _inst_17)) (RingHom.id.{u1} R' (Semiring.toNonAssocSemiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) (AlternatingMap.distribMulAction.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10))) (Module.toDistribMulAction.{u1, u3} R' N'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_13 _inst_17) (smulCommClass_self.{u1, u3} R' N'' (CommSemiring.toCommMonoid.{u1} R' _inst_10) (MulActionWithZero.toMulAction.{u1, u3} R' N'' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)) (AddZeroClass.toHasZero.{u3} N'' (AddMonoid.toAddZeroClass.{u3} N'' (AddCommMonoid.toAddMonoid.{u3} N'' _inst_13))) (Module.toMulActionWithZero.{u1, u3} R' N'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_13 _inst_17)))) (smulCommClass_self.{u1, max u2 u3} R' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toCommMonoid.{u1} R' _inst_10) (MulActionWithZero.toMulAction.{u1, max u2 u3} R' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)) (AddZeroClass.toHasZero.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AddMonoid.toAddZeroClass.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AddCommMonoid.toAddMonoid.{max u2 u3} (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n))))) (Module.toMulActionWithZero.{u1, max u2 u3} R' (AlternatingMap.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u1} R' _inst_10) (AlternatingMap.addCommMonoid.{u1, u2, u3, 0} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (AlternatingMap.module.{u1, u2, u3, 0, u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_17 (smulCommClass_self.{u1, u3} R' N'' (CommSemiring.toCommMonoid.{u1} R' _inst_10) (MulActionWithZero.toMulAction.{u1, u3} R' N'' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_10)) (AddZeroClass.toHasZero.{u3} N'' (AddMonoid.toAddZeroClass.{u3} N'' (AddCommMonoid.toAddMonoid.{u3} N'' _inst_13))) (Module.toMulActionWithZero.{u1, u3} R' N'' (CommSemiring.toSemiring.{u1} R' _inst_10) _inst_13 _inst_17)))))))) r (AlternatingMap.curryLeft.{u1, u2, u3} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f))
+but is expected to have type
+  forall {R' : Type.{u3}} {M'' : Type.{u2}} {N'' : Type.{u1}} [_inst_10 : CommSemiring.{u3} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_13 : AddCommMonoid.{u1} N''] [_inst_15 : Module.{u3, u2} R' M'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_11] [_inst_17 : Module.{u3, u1} R' N'' (CommSemiring.toSemiring.{u3} R' _inst_10) _inst_13] {n : Nat} (r : R') (f : AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))), Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u3} R' _inst_10) (CommSemiring.toSemiring.{u3} R' _inst_10) (RingHom.id.{u3} R' (Semiring.toNonAssocSemiring.{u3} R' (CommSemiring.toSemiring.{u3} R' _inst_10))) M'' (AlternatingMap.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u3, u2, u1, 0} R' (CommSemiring.toSemiring.{u3} R' 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+Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_smul AlternatingMap.curryLeft_smulₓ'. -/
 @[simp]
 theorem curryLeft_smul {n : ℕ} (r : R') (f : AlternatingMap R' M'' N'' (Fin n.succ)) :
     curryLeft (r • f) = r • curryLeft f :=
   rfl
 #align alternating_map.curry_left_smul AlternatingMap.curryLeft_smul
 
+#print AlternatingMap.curryLeftLinearMap /-
 /-- `alternating_map.curry_left` as a `linear_map`. This is a separate definition as dot notation
 does not work for this version. -/
 @[simps]
@@ -1210,7 +1750,14 @@ def curryLeftLinearMap {n : ℕ} :
   map_add' := curryLeft_add
   map_smul' := curryLeft_smul
 #align alternating_map.curry_left_linear_map AlternatingMap.curryLeftLinearMap
+-/
 
+/- warning: alternating_map.curry_left_same -> AlternatingMap.curryLeft_same is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_same AlternatingMap.curryLeft_sameₓ'. -/
 /-- Currying with the same element twice gives the zero map. -/
 @[simp]
 theorem curryLeft_same {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ.succ)) (m : M'') :
@@ -1218,6 +1765,12 @@ theorem curryLeft_same {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ.succ
   ext fun x => f.map_eq_zero_of_eq _ (by simp) Fin.zero_ne_one
 #align alternating_map.curry_left_same AlternatingMap.curryLeft_same
 
+/- warning: alternating_map.curry_left_comp_alternating_map -> AlternatingMap.curryLeft_compAlternatingMap 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 alternating_map.curry_left_comp_alternating_map AlternatingMap.curryLeft_compAlternatingMapₓ'. -/
 @[simp]
 theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
     (f : AlternatingMap R' M'' N'' (Fin n.succ)) (m : M'') :
@@ -1225,6 +1778,12 @@ theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
   rfl
 #align alternating_map.curry_left_comp_alternating_map AlternatingMap.curryLeft_compAlternatingMap
 
+/- warning: alternating_map.curry_left_comp_linear_map -> AlternatingMap.curryLeft_compLinearMap is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R' : Type.{u4}} {M'' : Type.{u2}} {M₂'' : Type.{u3}} {N'' : Type.{u1}} [_inst_10 : CommSemiring.{u4} R'] [_inst_11 : AddCommMonoid.{u2} M''] [_inst_12 : AddCommMonoid.{u3} M₂''] [_inst_13 : AddCommMonoid.{u1} N''] [_inst_15 : Module.{u4, u2} R' M'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11] [_inst_16 : Module.{u4, u3} R' M₂'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12] [_inst_17 : Module.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13] {n : Nat} (g : LinearMap.{u4, u4, u3, u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) (f : AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n))) (m : M₂''), Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂'') => AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) m) (FunLike.coe.{max (succ u3) (succ u1), succ u3, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u3, max u1 u3} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' (AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_12 (AlternatingMap.addCommMonoid.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_16 (AlternatingMap.module.{u4, u3, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17))))) M₂'' (fun (_x : M₂'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂'') => AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u3 u1} R' R' M₂'' (AlternatingMap.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12 (AlternatingMap.addCommMonoid.{u4, u3, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n)) _inst_16 (AlternatingMap.module.{u4, u3, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M₂'' _inst_12 _inst_16 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) (AlternatingMap.curryLeft.{u4, u3, u1} R' M₂'' N'' _inst_10 _inst_12 _inst_13 _inst_16 _inst_17 n (AlternatingMap.compLinearMap.{u4, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin (Nat.succ n)) M₂'' _inst_12 _inst_16 f g)) m) (AlternatingMap.compLinearMap.{u4, u2, u1, 0, u3} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) M₂'' _inst_12 _inst_16 (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u4, u4, u2, max u1 u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M'' (AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_11 (AlternatingMap.addCommMonoid.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u2, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17))))) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M'') => AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u2, max u2 u1} R' R' M'' (AlternatingMap.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_11 (AlternatingMap.addCommMonoid.{u4, u2, u1, 0} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n)) _inst_15 (AlternatingMap.module.{u4, u2, u1, 0, u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10) M'' _inst_11 _inst_15 N'' _inst_13 _inst_17 (Fin n) R' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_17 (smulCommClass_self.{u4, u1} R' N'' (CommSemiring.toCommMonoid.{u4} R' _inst_10) (MulActionWithZero.toMulAction.{u4, u1} R' N'' (Semiring.toMonoidWithZero.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)) (AddMonoid.toZero.{u1} N'' (AddCommMonoid.toAddMonoid.{u1} N'' _inst_13)) (Module.toMulActionWithZero.{u4, u1} R' N'' (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_13 _inst_17)))) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) (AlternatingMap.curryLeft.{u4, u2, u1} R' M'' N'' _inst_10 _inst_11 _inst_13 _inst_15 _inst_17 n f) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R' R' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10))) M₂'' M'' _inst_12 _inst_11 _inst_16 _inst_15) M₂'' (fun (_x : M₂'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂'') => M'') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R' R' M₂'' M'' (CommSemiring.toSemiring.{u4} R' _inst_10) (CommSemiring.toSemiring.{u4} R' _inst_10) _inst_12 _inst_11 _inst_16 _inst_15 (RingHom.id.{u4} R' (Semiring.toNonAssocSemiring.{u4} R' (CommSemiring.toSemiring.{u4} R' _inst_10)))) g m)) g)
+Case conversion may be inaccurate. Consider using '#align alternating_map.curry_left_comp_linear_map AlternatingMap.curryLeft_compLinearMapₓ'. -/
 @[simp]
 theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')
     (f : AlternatingMap R' M'' N'' (Fin n.succ)) (m : M₂'') :
@@ -1237,6 +1796,7 @@ theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')
         · simp
 #align alternating_map.curry_left_comp_linear_map AlternatingMap.curryLeft_compLinearMap
 
+#print AlternatingMap.constLinearEquivOfIsEmpty /-
 /-- The space of constant maps is equivalent to the space of maps that are alternating with respect
 to an empty family. -/
 @[simps]
@@ -1249,6 +1809,7 @@ def constLinearEquivOfIsEmpty [IsEmpty ι] : N'' ≃ₗ[R'] AlternatingMap R' M'
   left_inv _ := rfl
   right_inv f := ext fun x => AlternatingMap.congr_arg f <| Subsingleton.elim _ _
 #align alternating_map.const_linear_equiv_of_is_empty AlternatingMap.constLinearEquivOfIsEmpty
+-/
 
 end AlternatingMap
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Zhangir Azerbayev
 
 ! This file was ported from Lean 3 source module linear_algebra.alternating
-! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
+! leanprover-community/mathlib commit 284fdd2962e67d2932fa3a79ce19fcf92d38e228
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -95,8 +95,18 @@ open Function
 
 section Coercions
 
+instance funLike : FunLike (AlternatingMap R M N ι) (ι → M) fun _ => N
+    where
+  coe := AlternatingMap.toFun
+  coe_injective' f g h := by
+    cases f
+    cases g
+    congr
+#align alternating_map.fun_like AlternatingMap.funLike
+
+-- shortcut instance
 instance : CoeFun (AlternatingMap R M N ι) fun _ => (ι → M) → N :=
-  ⟨fun x => x.toFun⟩
+  ⟨FunLike.coe⟩
 
 initialize_simps_projections AlternatingMap (toFun → apply)
 
@@ -118,12 +128,8 @@ theorem congr_arg (f : AlternatingMap R M N ι) {x y : ι → M} (h : x = y) : f
   congr_arg (fun x : ι → M => f x) h
 #align alternating_map.congr_arg AlternatingMap.congr_arg
 
-theorem coe_injective : Injective (coeFn : AlternatingMap R M N ι → (ι → M) → N) := fun f g h =>
-  by
-  cases f
-  cases g
-  cases h
-  rfl
+theorem coe_injective : Injective (coeFn : AlternatingMap R M N ι → (ι → M) → N) :=
+  FunLike.coe_injective
 #align alternating_map.coe_injective AlternatingMap.coe_injective
 
 @[simp, norm_cast]
@@ -133,7 +139,7 @@ theorem coe_inj {f g : AlternatingMap R M N ι} : (f : (ι → M) → N) = g ↔
 
 @[ext]
 theorem ext {f f' : AlternatingMap R M N ι} (H : ∀ x, f x = f' x) : f = f' :=
-  coe_injective (funext H)
+  FunLike.ext _ _ H
 #align alternating_map.ext AlternatingMap.ext
 
 theorem ext_iff {f g : AlternatingMap R M N ι} : f = g ↔ ∀ x, f x = g x :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Zhangir Azerbayev
 
 ! This file was ported from Lean 3 source module linear_algebra.alternating
-! leanprover-community/mathlib commit 657df4339ae6ceada048c8a2980fb10e393143ec
+! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -61,7 +61,7 @@ variable {M' : Type _} [AddCommGroup M'] [Module R M']
 
 variable {N' : Type _} [AddCommGroup N'] [Module R N']
 
-variable {ι ι' ι'' : Type _} [DecidableEq ι] [DecidableEq ι'] [DecidableEq ι'']
+variable {ι ι' ι'' : Type _}
 
 section
 
@@ -161,7 +161,7 @@ theorem toMultilinearMap_eq_coe : f.toMultilinearMap = f :=
 @[simp]
 theorem coe_multilinearMap_mk (f : (ι → M) → N) (h₁ h₂ h₃) :
     ((⟨f, h₁, h₂, h₃⟩ : AlternatingMap R M N ι) : MultilinearMap R (fun i : ι => M) N) =
-      ⟨f, h₁, h₂⟩ :=
+      ⟨f, @h₁, @h₂⟩ :=
   rfl
 #align alternating_map.coe_multilinear_map_mk AlternatingMap.coe_multilinearMap_mk
 
@@ -175,23 +175,25 @@ These are expressed in terms of `⇑f` instead of `f.to_fun`.
 
 
 @[simp]
-theorem map_add (i : ι) (x y : M) : f (update v i (x + y)) = f (update v i x) + f (update v i y) :=
+theorem map_add [DecidableEq ι] (i : ι) (x y : M) :
+    f (update v i (x + y)) = f (update v i x) + f (update v i y) :=
   f.toMultilinearMap.map_add' v i x y
 #align alternating_map.map_add AlternatingMap.map_add
 
 @[simp]
-theorem map_sub (i : ι) (x y : M') :
+theorem map_sub [DecidableEq ι] (i : ι) (x y : M') :
     g' (update v' i (x - y)) = g' (update v' i x) - g' (update v' i y) :=
   g'.toMultilinearMap.map_sub v' i x y
 #align alternating_map.map_sub AlternatingMap.map_sub
 
 @[simp]
-theorem map_neg (i : ι) (x : M') : g' (update v' i (-x)) = -g' (update v' i x) :=
+theorem map_neg [DecidableEq ι] (i : ι) (x : M') : g' (update v' i (-x)) = -g' (update v' i x) :=
   g'.toMultilinearMap.map_neg v' i x
 #align alternating_map.map_neg AlternatingMap.map_neg
 
 @[simp]
-theorem map_smul (i : ι) (r : R) (x : M) : f (update v i (r • x)) = r • f (update v i x) :=
+theorem map_smul [DecidableEq ι] (i : ι) (r : R) (x : M) :
+    f (update v i (r • x)) = r • f (update v i x) :=
   f.toMultilinearMap.map_smul' v i r x
 #align alternating_map.map_smul AlternatingMap.map_smul
 
@@ -205,7 +207,7 @@ theorem map_coord_zero {m : ι → M} (i : ι) (h : m i = 0) : f m = 0 :=
 #align alternating_map.map_coord_zero AlternatingMap.map_coord_zero
 
 @[simp]
-theorem map_update_zero (m : ι → M) (i : ι) : f (update m i 0) = 0 :=
+theorem map_update_zero [DecidableEq ι] (m : ι → M) (i : ι) : f (update m i 0) = 0 :=
   f.toMultilinearMap.map_update_zero m i
 #align alternating_map.map_update_zero AlternatingMap.map_update_zero
 
@@ -581,7 +583,7 @@ section
 
 open BigOperators
 
-theorem map_update_sum {α : Type _} (t : Finset α) (i : ι) (g : α → M) (m : ι → M) :
+theorem map_update_sum {α : Type _} [DecidableEq ι] (t : Finset α) (i : ι) (g : α → M) (m : ι → M) :
     f (update m i (∑ a in t, g a)) = ∑ a in t, f (update m i (g a)) :=
   f.toMultilinearMap.map_update_sum t i g m
 #align alternating_map.map_update_sum AlternatingMap.map_update_sum
@@ -596,17 +598,18 @@ Various properties of reordered and repeated inputs which follow from
 -/
 
 
-theorem map_update_self {i j : ι} (hij : i ≠ j) : f (Function.update v i (v j)) = 0 :=
+theorem map_update_self [DecidableEq ι] {i j : ι} (hij : i ≠ j) :
+    f (Function.update v i (v j)) = 0 :=
   f.map_eq_zero_of_eq _ (by rw [Function.update_same, Function.update_noteq hij.symm]) hij
 #align alternating_map.map_update_self AlternatingMap.map_update_self
 
-theorem map_update_update {i j : ι} (hij : i ≠ j) (m : M) :
+theorem map_update_update [DecidableEq ι] {i j : ι} (hij : i ≠ j) (m : M) :
     f (Function.update (Function.update v i m) j m) = 0 :=
   f.map_eq_zero_of_eq _
     (by rw [Function.update_same, Function.update_noteq hij, Function.update_same]) hij
 #align alternating_map.map_update_update AlternatingMap.map_update_update
 
-theorem map_swap_add {i j : ι} (hij : i ≠ j) : f (v ∘ Equiv.swap i j) + f v = 0 :=
+theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equiv.swap i j) + f v = 0 :=
   by
   rw [Equiv.comp_swap_eq_update]
   convert f.map_update_update v hij (v i + v j)
@@ -614,17 +617,18 @@ theorem map_swap_add {i j : ι} (hij : i ≠ j) : f (v ∘ Equiv.swap i j) + f v
     Function.update_comm hij (v i + v j) (v _) v, Function.update_comm hij.symm (v i) (v i) v]
 #align alternating_map.map_swap_add AlternatingMap.map_swap_add
 
-theorem map_add_swap {i j : ι} (hij : i ≠ j) : f v + f (v ∘ Equiv.swap i j) = 0 :=
+theorem map_add_swap [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f v + f (v ∘ Equiv.swap i j) = 0 :=
   by
   rw [add_comm]
   exact f.map_swap_add v hij
 #align alternating_map.map_add_swap AlternatingMap.map_add_swap
 
-theorem map_swap {i j : ι} (hij : i ≠ j) : g (v ∘ Equiv.swap i j) = -g v :=
+theorem map_swap [DecidableEq ι] {i j : ι} (hij : i ≠ j) : g (v ∘ Equiv.swap i j) = -g v :=
   eq_neg_of_add_eq_zero_left <| g.map_swap_add v hij
 #align alternating_map.map_swap AlternatingMap.map_swap
 
-theorem map_perm [Fintype ι] (v : ι → M) (σ : Equiv.Perm ι) : g (v ∘ σ) = σ.sign • g v :=
+theorem map_perm [DecidableEq ι] [Fintype ι] (v : ι → M) (σ : Equiv.Perm ι) :
+    g (v ∘ σ) = σ.sign • g v :=
   by
   apply Equiv.Perm.swap_induction_on' σ
   · simp
@@ -632,7 +636,7 @@ theorem map_perm [Fintype ι] (v : ι → M) (σ : Equiv.Perm ι) : g (v ∘ σ)
     simpa [g.map_swap (v ∘ s) hxy, Equiv.Perm.sign_swap hxy] using hI
 #align alternating_map.map_perm AlternatingMap.map_perm
 
-theorem map_congr_perm [Fintype ι] (σ : Equiv.Perm ι) : g v = σ.sign • g (v ∘ σ) :=
+theorem map_congr_perm [DecidableEq ι] [Fintype ι] (σ : Equiv.Perm ι) : g v = σ.sign • g (v ∘ σ) :=
   by
   rw [g.map_perm, smul_smul]
   simp
@@ -704,7 +708,8 @@ theorem domDomCongr_eq_zero_iff (σ : ι ≃ ι') (f : AlternatingMap R M N ι)
   (domDomCongrEquiv σ : AlternatingMap R M N ι ≃+ AlternatingMap R M N ι').map_eq_zero_iff
 #align alternating_map.dom_dom_congr_eq_zero_iff AlternatingMap.domDomCongr_eq_zero_iff
 
-theorem domDomCongr_perm [Fintype ι] (σ : Equiv.Perm ι) : g.domDomCongr σ = σ.sign • g :=
+theorem domDomCongr_perm [Fintype ι] [DecidableEq ι] (σ : Equiv.Perm ι) :
+    g.domDomCongr σ = σ.sign • g :=
   AlternatingMap.ext fun v => g.map_perm v σ
 #align alternating_map.dom_dom_congr_perm AlternatingMap.domDomCongr_perm
 
@@ -722,6 +727,7 @@ theorem map_linear_dependent {K : Type _} [Ring K] {M : Type _} [AddCommGroup M]
     (v : ι → M) (h : ¬LinearIndependent K v) : f v = 0 :=
   by
   obtain ⟨s, g, h, i, hi, hz⟩ := not_linear_independent_iff.mp h
+  letI := Classical.decEq ι
   suffices f (update v i (g i • v i)) = 0
     by
     rw [f.map_smul, Function.update_eq_self, smul_eq_zero] at this
@@ -761,7 +767,7 @@ namespace MultilinearMap
 
 open Equiv
 
-variable [Fintype ι]
+variable [Fintype ι] [DecidableEq ι]
 
 private theorem alternization_map_eq_zero_of_eq_aux (m : MultilinearMap R (fun i : ι => M) N')
     (v : ι → M) (i j : ι) (i_ne_j : i ≠ j) (hv : v i = v j) :
@@ -819,7 +825,7 @@ namespace AlternatingMap
 
 /-- Alternatizing a multilinear map that is already alternating results in a scale factor of `n!`,
 where `n` is the number of inputs. -/
-theorem coe_alternatization [Fintype ι] (a : AlternatingMap R M N' ι) :
+theorem coe_alternatization [DecidableEq ι] [Fintype ι] (a : AlternatingMap R M N' ι) :
     (↑a : MultilinearMap R (fun ι => M) N').alternatization = Nat.factorial (Fintype.card ι) • a :=
   by
   apply AlternatingMap.coe_injective
@@ -832,7 +838,7 @@ end AlternatingMap
 
 namespace LinearMap
 
-variable {N'₂ : Type _} [AddCommGroup N'₂] [Module R N'₂] [Fintype ι]
+variable {N'₂ : Type _} [AddCommGroup N'₂] [Module R N'₂] [DecidableEq ι] [Fintype ι]
 
 /-- Composition with a linear map before and after alternatization are equivalent. -/
 theorem compMultilinearMap_alternatization (g : N' →ₗ[R] N'₂)
@@ -851,7 +857,7 @@ open BigOperators
 
 open TensorProduct
 
-variable {ιa ιb : Type _} [DecidableEq ιa] [DecidableEq ιb] [Fintype ιa] [Fintype ιb]
+variable {ιa ιb : Type _} [Fintype ιa] [Fintype ιb]
 
 variable {R' : Type _} {Mᵢ N₁ N₂ : Type _} [CommSemiring R'] [AddCommGroup N₁] [Module R' N₁]
   [AddCommGroup N₂] [Module R' N₂] [AddCommMonoid Mᵢ] [Module R' Mᵢ]
@@ -876,6 +882,8 @@ namespace AlternatingMap
 
 open Equiv
 
+variable [DecidableEq ιa] [DecidableEq ιb]
+
 /-- summand used in `alternating_map.dom_coprod` -/
 def DomCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
     (σ : Perm.ModSumCongr ιa ιb) : MultilinearMap R' (fun _ : Sum ιa ιb => Mᵢ) (N₁ ⊗[R'] N₂) :=
@@ -1039,8 +1047,8 @@ end AlternatingMap
 open Equiv
 
 /-- A helper lemma for `multilinear_map.dom_coprod_alternization`. -/
-theorem MultilinearMap.domCoprod_alternization_coe (a : MultilinearMap R' (fun _ : ιa => Mᵢ) N₁)
-    (b : MultilinearMap R' (fun _ : ιb => Mᵢ) N₂) :
+theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableEq ιb]
+    (a : MultilinearMap R' (fun _ : ιa => Mᵢ) N₁) (b : MultilinearMap R' (fun _ : ιb => Mᵢ) N₂) :
     MultilinearMap.domCoprod ↑a.alternatization ↑b.alternatization =
       ∑ (σa : Perm ιa) (σb : Perm ιb),
         σa.sign • σb.sign • MultilinearMap.domCoprod (a.domDomCongr σa) (b.domDomCongr σb) :=
@@ -1055,8 +1063,8 @@ open AlternatingMap
 /-- Computing the `multilinear_map.alternatization` of the `multilinear_map.dom_coprod` is the same
 as computing the `alternating_map.dom_coprod` of the `multilinear_map.alternatization`s.
 -/
-theorem MultilinearMap.domCoprod_alternization (a : MultilinearMap R' (fun _ : ιa => Mᵢ) N₁)
-    (b : MultilinearMap R' (fun _ : ιb => Mᵢ) N₂) :
+theorem MultilinearMap.domCoprod_alternization [DecidableEq ιa] [DecidableEq ιb]
+    (a : MultilinearMap R' (fun _ : ιa => Mᵢ) N₁) (b : MultilinearMap R' (fun _ : ιb => Mᵢ) N₂) :
     (MultilinearMap.domCoprod a b).alternatization =
       a.alternatization.domCoprod b.alternatization :=
   by
@@ -1094,8 +1102,8 @@ theorem MultilinearMap.domCoprod_alternization (a : MultilinearMap R' (fun _ : 
 /-- Taking the `multilinear_map.alternatization` of the `multilinear_map.dom_coprod` of two
 `alternating_map`s gives a scaled version of the `alternating_map.coprod` of those maps.
 -/
-theorem MultilinearMap.domCoprod_alternization_eq (a : AlternatingMap R' Mᵢ N₁ ιa)
-    (b : AlternatingMap R' Mᵢ N₂ ιb) :
+theorem MultilinearMap.domCoprod_alternization_eq [DecidableEq ιa] [DecidableEq ιb]
+    (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
     (MultilinearMap.domCoprod a b :
           MultilinearMap R' (fun _ : Sum ιa ιb => Mᵢ) (N₁ ⊗ N₂)).alternatization =
       ((Fintype.card ιa).factorial * (Fintype.card ιb).factorial) • a.domCoprod b :=
@@ -1125,12 +1133,13 @@ are distinct basis vectors. -/
 theorem Basis.ext_alternating {f g : AlternatingMap R' N₁ N₂ ι} (e : Basis ι₁ R' N₁)
     (h : ∀ v : ι → ι₁, Function.Injective v → (f fun i => e (v i)) = g fun i => e (v i)) : f = g :=
   by
-  refine' AlternatingMap.coe_multilinearMap_injective (Basis.ext_multilinear e fun v => _)
-  by_cases hi : Function.Injective v
-  · exact h v hi
-  · have : ¬Function.Injective fun i => e (v i) := hi.imp Function.Injective.of_comp
-    rw [coe_multilinear_map, coe_multilinear_map, f.map_eq_zero_of_not_injective _ this,
-      g.map_eq_zero_of_not_injective _ this]
+  classical
+    refine' AlternatingMap.coe_multilinearMap_injective (Basis.ext_multilinear e fun v => _)
+    by_cases hi : Function.Injective v
+    · exact h v hi
+    · have : ¬Function.Injective fun i => e (v i) := hi.imp Function.Injective.of_comp
+      rw [coe_multilinear_map, coe_multilinear_map, f.map_eq_zero_of_not_injective _ this,
+        g.map_eq_zero_of_not_injective _ this]
 #align basis.ext_alternating Basis.ext_alternating
 
 end Basis

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -21,7 +21,6 @@ suppress_compilation
 open BigOperators TensorProduct
 
 variable {ιa ιb : Type*} [Fintype ιa] [Fintype ιb]
-
 variable {R' : Type*} {Mᵢ N₁ N₂ : Type*} [CommSemiring R'] [AddCommGroup N₁] [Module R' N₁]
   [AddCommGroup N₂] [Module R' N₂] [AddCommMonoid Mᵢ] [Module R' Mᵢ]
 

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -45,19 +45,14 @@ using `map_swap` as a definition, and does not require `Neg N`.
 -- semiring / add_comm_monoid
 
 variable {R : Type*} [Semiring R]
-
 variable {M : Type*} [AddCommMonoid M] [Module R M]
-
 variable {N : Type*} [AddCommMonoid N] [Module R N]
-
 variable {P : Type*} [AddCommMonoid P] [Module R P]
 
 -- semiring / add_comm_group
 
 variable {M' : Type*} [AddCommGroup M'] [Module R M']
-
 variable {N' : Type*} [AddCommGroup N'] [Module R N']
-
 variable {ι ι' ι'' : Type*}
 
 section
@@ -82,11 +77,8 @@ add_decl_doc AlternatingMap.toMultilinearMap
 namespace AlternatingMap
 
 variable (f f' : M [⋀^ι]→ₗ[R] N)
-
 variable (g g₂ : M [⋀^ι]→ₗ[R] N')
-
 variable (g' : M' [⋀^ι]→ₗ[R] N')
-
 variable (v : ι → M) (v' : ι → M')
 
 open Function
@@ -535,7 +527,6 @@ end LinearMap
 namespace AlternatingMap
 
 variable {M₂ : Type*} [AddCommMonoid M₂] [Module R M₂]
-
 variable {M₃ : Type*} [AddCommMonoid M₃] [Module R M₃]
 
 /-- Composing an alternating map with the same linear map on each argument gives again an
@@ -965,9 +956,7 @@ section Basis
 open AlternatingMap
 
 variable {ι₁ : Type*} [Finite ι]
-
 variable {R' : Type*} {N₁ N₂ : Type*} [CommSemiring R'] [AddCommMonoid N₁] [AddCommMonoid N₂]
-
 variable [Module R' N₁] [Module R' N₂]
 
 /-- Two alternating maps indexed by a `Fintype` are equal if they are equal when all arguments

The file Mathlib.GroupTheory.Perm.Cycle.Basic was too big and this PR splits it in several components:

• Mathlib.GroupTheory.Perm.Cycle.Basic contains everything related to a permutation being a cycle,
• Mathlib.GroupTheory.Perm.Cycle.Factors is about the cycles of a permutation and the decomposition of a permutation into disjoint cycles
• Mathlib.GroupTheory.Perm.Closure contains generation results for the permutation groups
• Mathlib.GroupTheory.Perm.Finite contains general results specific to permutation of finite types

I moved some results to Mathlib.GroupTheory.Perm.Support

I also moved some results from Mathlib.GroupTheory.Perm.Sign to Mathlib.GroupTheory.Perm.Finite

Some imports could be reduced, and the shake linter required a few adjustments in some other.

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr>

@@ -5,7 +5,7 @@ Authors: Eric Wieser
 -/
 import Mathlib.LinearAlgebra.Alternating.Basic
 import Mathlib.LinearAlgebra.Multilinear.TensorProduct
-
+import Mathlib.GroupTheory.GroupAction.Quotient
 /-!
 # Exterior product of alternating maps
 

That is, \bigwedge, not \Lambda

Co-authored-by: Richard Copley <rcopley@gmail.com> Co-authored-by: Patrick Massot <patrickmassot@free.fr>

@@ -43,7 +43,7 @@ open Equiv
 variable [DecidableEq ιa] [DecidableEq ιb]
 
 /-- summand used in `AlternatingMap.domCoprod` -/
-def domCoprod.summand (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂)
+def domCoprod.summand (a : Mᵢ [⋀^ιa]→ₗ[R'] N₁) (b : Mᵢ [⋀^ιb]→ₗ[R'] N₂)
     (σ : Perm.ModSumCongr ιa ιb) : MultilinearMap R' (fun _ : Sum ιa ιb => Mᵢ) (N₁ ⊗[R'] N₂) :=
   Quotient.liftOn' σ
     (fun σ =>
@@ -66,7 +66,7 @@ def domCoprod.summand (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→
     erw [← a.map_congr_perm fun i => v (σ₁ _), ← b.map_congr_perm fun i => v (σ₁ _)]
 #align alternating_map.dom_coprod.summand AlternatingMap.domCoprod.summand
 
-theorem domCoprod.summand_mk'' (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂)
+theorem domCoprod.summand_mk'' (a : Mᵢ [⋀^ιa]→ₗ[R'] N₁) (b : Mᵢ [⋀^ιb]→ₗ[R'] N₂)
     (σ : Equiv.Perm (Sum ιa ιb)) :
     domCoprod.summand a b (Quotient.mk'' σ) =
       Equiv.Perm.sign σ •
@@ -76,8 +76,8 @@ theorem domCoprod.summand_mk'' (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^
 #align alternating_map.dom_coprod.summand_mk' AlternatingMap.domCoprod.summand_mk''
 
 /-- Swapping elements in `σ` with equal values in `v` results in an addition that cancels -/
-theorem domCoprod.summand_add_swap_smul_eq_zero (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁)
-    (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
+theorem domCoprod.summand_add_swap_smul_eq_zero (a : Mᵢ [⋀^ιa]→ₗ[R'] N₁)
+    (b : Mᵢ [⋀^ιb]→ₗ[R'] N₂) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
     {i j : Sum ιa ιb} (hv : v i = v j) (hij : i ≠ j) :
     domCoprod.summand a b σ v + domCoprod.summand a b (swap i j • σ) v = 0 := by
   refine Quotient.inductionOn' σ fun σ => ?_
@@ -94,8 +94,8 @@ theorem domCoprod.summand_add_swap_smul_eq_zero (a : Mᵢ [Λ^ιa]→ₗ[R'] N
 
 /-- Swapping elements in `σ` with equal values in `v` result in zero if the swap has no effect
 on the quotient. -/
-theorem domCoprod.summand_eq_zero_of_smul_invariant (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁)
-    (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
+theorem domCoprod.summand_eq_zero_of_smul_invariant (a : Mᵢ [⋀^ιa]→ₗ[R'] N₁)
+    (b : Mᵢ [⋀^ιb]→ₗ[R'] N₂) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
     {i j : Sum ιa ιb} (hv : v i = v j) (hij : i ≠ j) :
     swap i j • σ = σ → domCoprod.summand a b σ v = 0 := by
   refine Quotient.inductionOn' σ fun σ => ?_
@@ -154,8 +154,8 @@ The specialized version can be obtained by combining this definition with `finSu
 `LinearMap.mul'`.
 -/
 @[simps]
-def domCoprod (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂) :
-    Mᵢ [Λ^ιa ⊕ ιb]→ₗ[R'] (N₁ ⊗[R'] N₂) :=
+def domCoprod (a : Mᵢ [⋀^ιa]→ₗ[R'] N₁) (b : Mᵢ [⋀^ιb]→ₗ[R'] N₂) :
+    Mᵢ [⋀^ιa ⊕ ιb]→ₗ[R'] (N₁ ⊗[R'] N₂) :=
   { ∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ with
     toFun := fun v => (⇑(∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ)) v
     map_eq_zero_of_eq' := fun v i j hv hij => by
@@ -170,7 +170,7 @@ def domCoprod (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N
 #align alternating_map.dom_coprod AlternatingMap.domCoprod
 #align alternating_map.dom_coprod_apply AlternatingMap.domCoprod_apply
 
-theorem domCoprod_coe (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂) :
+theorem domCoprod_coe (a : Mᵢ [⋀^ιa]→ₗ[R'] N₁) (b : Mᵢ [⋀^ιb]→ₗ[R'] N₂) :
     (↑(a.domCoprod b) : MultilinearMap R' (fun _ => Mᵢ) _) =
       ∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ :=
   MultilinearMap.ext fun _ => rfl
@@ -179,8 +179,8 @@ theorem domCoprod_coe (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→
 /-- A more bundled version of `AlternatingMap.domCoprod` that maps
 `((ι₁ → N) → N₁) ⊗ ((ι₂ → N) → N₂)` to `(ι₁ ⊕ ι₂ → N) → N₁ ⊗ N₂`. -/
 def domCoprod' :
-    (Mᵢ [Λ^ιa]→ₗ[R'] N₁) ⊗[R'] (Mᵢ [Λ^ιb]→ₗ[R'] N₂) →ₗ[R']
-      (Mᵢ [Λ^ιa ⊕ ιb]→ₗ[R'] (N₁ ⊗[R'] N₂)) :=
+    (Mᵢ [⋀^ιa]→ₗ[R'] N₁) ⊗[R'] (Mᵢ [⋀^ιb]→ₗ[R'] N₂) →ₗ[R']
+      (Mᵢ [⋀^ιa ⊕ ιb]→ₗ[R'] (N₁ ⊗[R'] N₂)) :=
   TensorProduct.lift <| by
     refine'
       LinearMap.mk₂ R' domCoprod (fun m₁ m₂ n => _) (fun c m n => _) (fun m n₁ n₂ => _)
@@ -200,7 +200,7 @@ def domCoprod' :
 #align alternating_map.dom_coprod' AlternatingMap.domCoprod'
 
 @[simp]
-theorem domCoprod'_apply (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂) :
+theorem domCoprod'_apply (a : Mᵢ [⋀^ιa]→ₗ[R'] N₁) (b : Mᵢ [⋀^ιb]→ₗ[R'] N₂) :
     domCoprod' (a ⊗ₜ[R'] b) = domCoprod a b :=
   rfl
 #align alternating_map.dom_coprod'_apply AlternatingMap.domCoprod'_apply
@@ -271,7 +271,7 @@ theorem MultilinearMap.domCoprod_alternization [DecidableEq ιa] [DecidableEq ι
 `AlternatingMap`s gives a scaled version of the `AlternatingMap.coprod` of those maps.
 -/
 theorem MultilinearMap.domCoprod_alternization_eq [DecidableEq ιa] [DecidableEq ιb]
-    (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂) :
+    (a : Mᵢ [⋀^ιa]→ₗ[R'] N₁) (b : Mᵢ [⋀^ιb]→ₗ[R'] N₂) :
     MultilinearMap.alternatization
       (MultilinearMap.domCoprod a b : MultilinearMap R' (fun _ : Sum ιa ιb => Mᵢ) (N₁ ⊗ N₂)) =
       ((Fintype.card ιa).factorial * (Fintype.card ιb).factorial) • a.domCoprod b := by

That is, \bigwedge, not \Lambda

Co-authored-by: Richard Copley <rcopley@gmail.com> Co-authored-by: Patrick Massot <patrickmassot@free.fr>

@@ -64,15 +64,15 @@ section
 
 variable (R M N ι)
 
-/-- An alternating map is a multilinear map that vanishes when two of its arguments are equal.
--/
+/-- An alternating map from `ι → M` to `N`, denoted `M [⋀^ι]→ₗ[R] N`,
+is a multilinear map that vanishes when two of its arguments are equal. -/
 structure AlternatingMap extends MultilinearMap R (fun _ : ι => M) N where
   /-- The map is alternating: if `v` has two equal coordinates, then `f v = 0`. -/
   map_eq_zero_of_eq' : ∀ (v : ι → M) (i j : ι), v i = v j → i ≠ j → toFun v = 0
 #align alternating_map AlternatingMap
 
 @[inherit_doc]
-notation M " [Λ^" ι "]→ₗ[" R "] " N:100 => AlternatingMap R M N ι
+notation M " [⋀^" ι "]→ₗ[" R "] " N:100 => AlternatingMap R M N ι
 
 end
 
@@ -81,11 +81,11 @@ add_decl_doc AlternatingMap.toMultilinearMap
 
 namespace AlternatingMap
 
-variable (f f' : M [Λ^ι]→ₗ[R] N)
+variable (f f' : M [⋀^ι]→ₗ[R] N)
 
-variable (g g₂ : M [Λ^ι]→ₗ[R] N')
+variable (g g₂ : M [⋀^ι]→ₗ[R] N')
 
-variable (g' : M' [Λ^ι]→ₗ[R] N')
+variable (g' : M' [⋀^ι]→ₗ[R] N')
 
 variable (v : ι → M) (v' : ι → M')
 
@@ -96,7 +96,7 @@ open Function
 
 section Coercions
 
-instance instFunLike : FunLike (M [Λ^ι]→ₗ[R] N) (ι → M) N where
+instance instFunLike : FunLike (M [⋀^ι]→ₗ[R] N) (ι → M) N where
   coe f := f.toFun
   coe_injective' := fun f g h ↦ by
     rcases f with ⟨⟨_, _, _⟩, _⟩
@@ -105,7 +105,7 @@ instance instFunLike : FunLike (M [Λ^ι]→ₗ[R] N) (ι → M) N where
 #align alternating_map.fun_like AlternatingMap.instFunLike
 
 -- shortcut instance
-instance coeFun : CoeFun (M [Λ^ι]→ₗ[R] N) fun _ => (ι → M) → N :=
+instance coeFun : CoeFun (M [⋀^ι]→ₗ[R] N) fun _ => (ι → M) → N :=
   ⟨DFunLike.coe⟩
 #align alternating_map.has_coe_to_fun AlternatingMap.coeFun
 
@@ -119,39 +119,39 @@ theorem toFun_eq_coe : f.toFun = f :=
 -- Porting note: changed statement to reflect new `mk` signature
 @[simp]
 theorem coe_mk (f : MultilinearMap R (fun _ : ι => M) N) (h) :
-    ⇑(⟨f, h⟩ : M [Λ^ι]→ₗ[R] N) = f :=
+    ⇑(⟨f, h⟩ : M [⋀^ι]→ₗ[R] N) = f :=
   rfl
 #align alternating_map.coe_mk AlternatingMap.coe_mkₓ
 
-theorem congr_fun {f g : M [Λ^ι]→ₗ[R] N} (h : f = g) (x : ι → M) : f x = g x :=
-  congr_arg (fun h : M [Λ^ι]→ₗ[R] N => h x) h
+theorem congr_fun {f g : M [⋀^ι]→ₗ[R] N} (h : f = g) (x : ι → M) : f x = g x :=
+  congr_arg (fun h : M [⋀^ι]→ₗ[R] N => h x) h
 #align alternating_map.congr_fun AlternatingMap.congr_fun
 
-theorem congr_arg (f : M [Λ^ι]→ₗ[R] N) {x y : ι → M} (h : x = y) : f x = f y :=
+theorem congr_arg (f : M [⋀^ι]→ₗ[R] N) {x y : ι → M} (h : x = y) : f x = f y :=
   _root_.congr_arg (fun x : ι → M => f x) h
 #align alternating_map.congr_arg AlternatingMap.congr_arg
 
-theorem coe_injective : Injective ((↑) : M [Λ^ι]→ₗ[R] N → (ι → M) → N) :=
+theorem coe_injective : Injective ((↑) : M [⋀^ι]→ₗ[R] N → (ι → M) → N) :=
   DFunLike.coe_injective
 #align alternating_map.coe_injective AlternatingMap.coe_injective
 
 @[norm_cast] -- @[simp] -- Porting note (#10618): simp can prove this
-theorem coe_inj {f g : M [Λ^ι]→ₗ[R] N} : (f : (ι → M) → N) = g ↔ f = g :=
+theorem coe_inj {f g : M [⋀^ι]→ₗ[R] N} : (f : (ι → M) → N) = g ↔ f = g :=
   coe_injective.eq_iff
 #align alternating_map.coe_inj AlternatingMap.coe_inj
 
 @[ext]
-theorem ext {f f' : M [Λ^ι]→ₗ[R] N} (H : ∀ x, f x = f' x) : f = f' :=
+theorem ext {f f' : M [⋀^ι]→ₗ[R] N} (H : ∀ x, f x = f' x) : f = f' :=
   DFunLike.ext _ _ H
 #align alternating_map.ext AlternatingMap.ext
 
-theorem ext_iff {f g : M [Λ^ι]→ₗ[R] N} : f = g ↔ ∀ x, f x = g x :=
+theorem ext_iff {f g : M [⋀^ι]→ₗ[R] N} : f = g ↔ ∀ x, f x = g x :=
   ⟨fun h _ => h ▸ rfl, fun h => ext h⟩
 #align alternating_map.ext_iff AlternatingMap.ext_iff
 
 attribute [coe] AlternatingMap.toMultilinearMap
 
-instance coe : Coe (M [Λ^ι]→ₗ[R] N) (MultilinearMap R (fun _ : ι => M) N) :=
+instance coe : Coe (M [⋀^ι]→ₗ[R] N) (MultilinearMap R (fun _ : ι => M) N) :=
   ⟨fun x => x.toMultilinearMap⟩
 #align alternating_map.multilinear_map.has_coe AlternatingMap.coe
 
@@ -161,7 +161,7 @@ theorem coe_multilinearMap : ⇑(f : MultilinearMap R (fun _ : ι => M) N) = f :
 #align alternating_map.coe_multilinear_map AlternatingMap.coe_multilinearMap
 
 theorem coe_multilinearMap_injective :
-    Function.Injective ((↑) : M [Λ^ι]→ₗ[R] N → MultilinearMap R (fun _ : ι => M) N) :=
+    Function.Injective ((↑) : M [⋀^ι]→ₗ[R] N → MultilinearMap R (fun _ : ι => M) N) :=
   fun _ _ h => ext <| MultilinearMap.congr_fun h
 #align alternating_map.coe_multilinear_map_injective AlternatingMap.coe_multilinearMap_injective
 
@@ -171,7 +171,7 @@ theorem coe_multilinearMap_injective :
 -- Porting note: removed `simp`
 -- @[simp]
 theorem coe_multilinearMap_mk (f : (ι → M) → N) (h₁ h₂ h₃) :
-    ((⟨⟨f, h₁, h₂⟩, h₃⟩ : M [Λ^ι]→ₗ[R] N) : MultilinearMap R (fun _ : ι => M) N) =
+    ((⟨⟨f, h₁, h₂⟩, h₃⟩ : M [⋀^ι]→ₗ[R] N) : MultilinearMap R (fun _ : ι => M) N) =
       ⟨f, @h₁, @h₂⟩ :=
   by simp
 #align alternating_map.coe_multilinear_map_mk AlternatingMap.coe_multilinearMap_mk
@@ -246,7 +246,7 @@ section SMul
 
 variable {S : Type*} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
 
-instance smul : SMul S (M [Λ^ι]→ₗ[R] N) :=
+instance smul : SMul S (M [⋀^ι]→ₗ[R] N) :=
   ⟨fun c f =>
     { c • (f : MultilinearMap R (fun _ : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }⟩
@@ -262,12 +262,12 @@ theorem coe_smul (c : S) : ↑(c • f) = c • (f : MultilinearMap R (fun _ : 
   rfl
 #align alternating_map.coe_smul AlternatingMap.coe_smul
 
-theorem coeFn_smul (c : S) (f : M [Λ^ι]→ₗ[R] N) : ⇑(c • f) = c • ⇑f :=
+theorem coeFn_smul (c : S) (f : M [⋀^ι]→ₗ[R] N) : ⇑(c • f) = c • ⇑f :=
   rfl
 #align alternating_map.coe_fn_smul AlternatingMap.coeFn_smul
 
 instance isCentralScalar [DistribMulAction Sᵐᵒᵖ N] [IsCentralScalar S N] :
-    IsCentralScalar S (M [Λ^ι]→ₗ[R] N) :=
+    IsCentralScalar S (M [⋀^ι]→ₗ[R] N) :=
   ⟨fun _ _ => ext fun _ => op_smul_eq_smul _ _⟩
 #align alternating_map.is_central_scalar AlternatingMap.isCentralScalar
 
@@ -275,7 +275,7 @@ end SMul
 
 /-- The cartesian product of two alternating maps, as an alternating map. -/
 @[simps!]
-def prod (f : M [Λ^ι]→ₗ[R] N) (g : M [Λ^ι]→ₗ[R] P) : M [Λ^ι]→ₗ[R] (N × P) :=
+def prod (f : M [⋀^ι]→ₗ[R] N) (g : M [⋀^ι]→ₗ[R] P) : M [⋀^ι]→ₗ[R] (N × P) :=
   { f.toMultilinearMap.prod g.toMultilinearMap with
     map_eq_zero_of_eq' := fun _ _ _ h hne =>
       Prod.ext (f.map_eq_zero_of_eq _ h hne) (g.map_eq_zero_of_eq _ h hne) }
@@ -283,7 +283,7 @@ def prod (f : M [Λ^ι]→ₗ[R] N) (g : M [Λ^ι]→ₗ[R] P) : M [Λ^ι]→ₗ
 #align alternating_map.prod_apply AlternatingMap.prod_apply
 
 @[simp]
-theorem coe_prod (f : M [Λ^ι]→ₗ[R] N) (g : M [Λ^ι]→ₗ[R] P) :
+theorem coe_prod (f : M [⋀^ι]→ₗ[R] N) (g : M [⋀^ι]→ₗ[R] P) :
     (f.prod g : MultilinearMap R (fun _ : ι => M) (N × P)) = MultilinearMap.prod f g :=
   rfl
 #align alternating_map.coe_prod AlternatingMap.coe_prod
@@ -292,7 +292,7 @@ theorem coe_prod (f : M [Λ^ι]→ₗ[R] N) (g : M [Λ^ι]→ₗ[R] P) :
 alternating map taking values in the space of functions `Π i, N i`. -/
 @[simps!]
 def pi {ι' : Type*} {N : ι' → Type*} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
-    (f : ∀ i, M [Λ^ι]→ₗ[R] N i) : M [Λ^ι]→ₗ[R] (∀ i, N i) :=
+    (f : ∀ i, M [⋀^ι]→ₗ[R] N i) : M [⋀^ι]→ₗ[R] (∀ i, N i) :=
   { MultilinearMap.pi fun a => (f a).toMultilinearMap with
     map_eq_zero_of_eq' := fun _ _ _ h hne => funext fun a => (f a).map_eq_zero_of_eq _ h hne }
 #align alternating_map.pi AlternatingMap.pi
@@ -300,7 +300,7 @@ def pi {ι' : Type*} {N : ι' → Type*} [∀ i, AddCommMonoid (N i)] [∀ i, Mo
 
 @[simp]
 theorem coe_pi {ι' : Type*} {N : ι' → Type*} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
-    (f : ∀ i, M [Λ^ι]→ₗ[R] N i) :
+    (f : ∀ i, M [⋀^ι]→ₗ[R] N i) :
     (pi f : MultilinearMap R (fun _ : ι => M) (∀ i, N i)) = MultilinearMap.pi fun a => f a :=
   rfl
 #align alternating_map.coe_pi AlternatingMap.coe_pi
@@ -309,7 +309,7 @@ theorem coe_pi {ι' : Type*} {N : ι' → Type*} [∀ i, AddCommMonoid (N i)] [
 sending `m` to `f m • z`. -/
 @[simps!]
 def smulRight {R M₁ M₂ ι : Type*} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
-    [Module R M₁] [Module R M₂] (f : M₁ [Λ^ι]→ₗ[R] R) (z : M₂) : M₁ [Λ^ι]→ₗ[R] M₂ :=
+    [Module R M₁] [Module R M₂] (f : M₁ [⋀^ι]→ₗ[R] R) (z : M₂) : M₁ [⋀^ι]→ₗ[R] M₂ :=
   { f.toMultilinearMap.smulRight z with
     map_eq_zero_of_eq' := fun v i j h hne => by simp [f.map_eq_zero_of_eq v h hne] }
 #align alternating_map.smul_right AlternatingMap.smulRight
@@ -317,12 +317,12 @@ def smulRight {R M₁ M₂ ι : Type*} [CommSemiring R] [AddCommMonoid M₁] [Ad
 
 @[simp]
 theorem coe_smulRight {R M₁ M₂ ι : Type*} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
-    [Module R M₁] [Module R M₂] (f : M₁ [Λ^ι]→ₗ[R] R) (z : M₂) :
+    [Module R M₁] [Module R M₂] (f : M₁ [⋀^ι]→ₗ[R] R) (z : M₂) :
     (f.smulRight z : MultilinearMap R (fun _ : ι => M₁) M₂) = MultilinearMap.smulRight f z :=
   rfl
 #align alternating_map.coe_smul_right AlternatingMap.coe_smulRight
 
-instance add : Add (M [Λ^ι]→ₗ[R] N) :=
+instance add : Add (M [⋀^ι]→ₗ[R] N) :=
   ⟨fun a b =>
     { (a + b : MultilinearMap R (fun _ : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by
@@ -339,35 +339,35 @@ theorem coe_add : (↑(f + f') : MultilinearMap R (fun _ : ι => M) N) = f + f'
   rfl
 #align alternating_map.coe_add AlternatingMap.coe_add
 
-instance zero : Zero (M [Λ^ι]→ₗ[R] N) :=
+instance zero : Zero (M [⋀^ι]→ₗ[R] N) :=
   ⟨{ (0 : MultilinearMap R (fun _ : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j _ _ => by simp }⟩
 #align alternating_map.has_zero AlternatingMap.zero
 
 @[simp]
-theorem zero_apply : (0 : M [Λ^ι]→ₗ[R] N) v = 0 :=
+theorem zero_apply : (0 : M [⋀^ι]→ₗ[R] N) v = 0 :=
   rfl
 #align alternating_map.zero_apply AlternatingMap.zero_apply
 
 @[norm_cast]
-theorem coe_zero : ((0 : M [Λ^ι]→ₗ[R] N) : MultilinearMap R (fun _ : ι => M) N) = 0 :=
+theorem coe_zero : ((0 : M [⋀^ι]→ₗ[R] N) : MultilinearMap R (fun _ : ι => M) N) = 0 :=
   rfl
 #align alternating_map.coe_zero AlternatingMap.coe_zero
 
 @[simp]
 theorem mk_zero :
-    mk (0 : MultilinearMap R (fun _ : ι ↦ M) N) (0 : M [Λ^ι]→ₗ[R] N).2 = 0 :=
+    mk (0 : MultilinearMap R (fun _ : ι ↦ M) N) (0 : M [⋀^ι]→ₗ[R] N).2 = 0 :=
   rfl
 
-instance inhabited : Inhabited (M [Λ^ι]→ₗ[R] N) :=
+instance inhabited : Inhabited (M [⋀^ι]→ₗ[R] N) :=
   ⟨0⟩
 #align alternating_map.inhabited AlternatingMap.inhabited
 
-instance addCommMonoid : AddCommMonoid (M [Λ^ι]→ₗ[R] N) :=
+instance addCommMonoid : AddCommMonoid (M [⋀^ι]→ₗ[R] N) :=
   coe_injective.addCommMonoid _ rfl (fun _ _ => rfl) fun _ _ => coeFn_smul _ _
 #align alternating_map.add_comm_monoid AlternatingMap.addCommMonoid
 
-instance neg : Neg (M [Λ^ι]→ₗ[R] N') :=
+instance neg : Neg (M [⋀^ι]→ₗ[R] N') :=
   ⟨fun f =>
     { -(f : MultilinearMap R (fun _ : ι => M) N') with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }⟩
@@ -379,11 +379,11 @@ theorem neg_apply (m : ι → M) : (-g) m = -g m :=
 #align alternating_map.neg_apply AlternatingMap.neg_apply
 
 @[norm_cast]
-theorem coe_neg : ((-g : M [Λ^ι]→ₗ[R] N') : MultilinearMap R (fun _ : ι => M) N') = -g :=
+theorem coe_neg : ((-g : M [⋀^ι]→ₗ[R] N') : MultilinearMap R (fun _ : ι => M) N') = -g :=
   rfl
 #align alternating_map.coe_neg AlternatingMap.coe_neg
 
-instance sub : Sub (M [Λ^ι]→ₗ[R] N') :=
+instance sub : Sub (M [⋀^ι]→ₗ[R] N') :=
   ⟨fun f g =>
     { (f - g : MultilinearMap R (fun _ : ι => M) N') with
       map_eq_zero_of_eq' := fun v i j h hij => by
@@ -400,7 +400,7 @@ theorem coe_sub : (↑(g - g₂) : MultilinearMap R (fun _ : ι => M) N') = g -
   rfl
 #align alternating_map.coe_sub AlternatingMap.coe_sub
 
-instance addCommGroup : AddCommGroup (M [Λ^ι]→ₗ[R] N') :=
+instance addCommGroup : AddCommGroup (M [⋀^ι]→ₗ[R] N') :=
   coe_injective.addCommGroup _ rfl (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl)
     (fun _ _ => coeFn_smul _ _) fun _ _ => coeFn_smul _ _
 #align alternating_map.add_comm_group AlternatingMap.addCommGroup
@@ -408,7 +408,7 @@ section DistribMulAction
 
 variable {S : Type*} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
 
-instance distribMulAction : DistribMulAction S (M [Λ^ι]→ₗ[R] N) where
+instance distribMulAction : DistribMulAction S (M [⋀^ι]→ₗ[R] N) where
   one_smul _ := ext fun _ => one_smul _ _
   mul_smul _ _ _ := ext fun _ => mul_smul _ _ _
   smul_zero _ := ext fun _ => smul_zero _
@@ -423,13 +423,13 @@ variable {S : Type*} [Semiring S] [Module S N] [SMulCommClass R S N]
 
 /-- The space of multilinear maps over an algebra over `R` is a module over `R`, for the pointwise
 addition and scalar multiplication. -/
-instance module : Module S (M [Λ^ι]→ₗ[R] N) where
+instance module : Module S (M [⋀^ι]→ₗ[R] N) where
   add_smul _ _ _ := ext fun _ => add_smul _ _ _
   zero_smul _ := ext fun _ => zero_smul _ _
 #align alternating_map.module AlternatingMap.module
 
 instance noZeroSMulDivisors [NoZeroSMulDivisors S N] :
-    NoZeroSMulDivisors S (M [Λ^ι]→ₗ[R] N) :=
+    NoZeroSMulDivisors S (M [⋀^ι]→ₗ[R] N) :=
   coe_injective.noZeroSMulDivisors _ rfl coeFn_smul
 #align alternating_map.no_zero_smul_divisors AlternatingMap.noZeroSMulDivisors
 
@@ -442,7 +442,7 @@ variable (R M N)
 /-- The natural equivalence between linear maps from `M` to `N`
 and `1`-multilinear alternating maps from `M` to `N`. -/
 @[simps!]
-def ofSubsingleton [Subsingleton ι] (i : ι) : (M →ₗ[R] N) ≃ (M [Λ^ι]→ₗ[R] N) where
+def ofSubsingleton [Subsingleton ι] (i : ι) : (M →ₗ[R] N) ≃ (M [⋀^ι]→ₗ[R] N) where
   toFun f := ⟨MultilinearMap.ofSubsingleton R M N i f, fun _ _ _ _ ↦ absurd (Subsingleton.elim _ _)⟩
   invFun f := (MultilinearMap.ofSubsingleton R M N i).symm f
   left_inv _ := rfl
@@ -455,7 +455,7 @@ variable (ι) {N}
 
 /-- The constant map is alternating when `ι` is empty. -/
 @[simps (config := .asFn)]
-def constOfIsEmpty [IsEmpty ι] (m : N) : M [Λ^ι]→ₗ[R] N :=
+def constOfIsEmpty [IsEmpty ι] (m : N) : M [⋀^ι]→ₗ[R] N :=
   { MultilinearMap.constOfIsEmpty R _ m with
     toFun := Function.const _ m
     map_eq_zero_of_eq' := fun _ => isEmptyElim }
@@ -466,8 +466,8 @@ end
 
 /-- Restrict the codomain of an alternating map to a submodule. -/
 @[simps]
-def codRestrict (f : M [Λ^ι]→ₗ[R] N) (p : Submodule R N) (h : ∀ v, f v ∈ p) :
-    M [Λ^ι]→ₗ[R] p :=
+def codRestrict (f : M [⋀^ι]→ₗ[R] N) (p : Submodule R N) (h : ∀ v, f v ∈ p) :
+    M [⋀^ι]→ₗ[R] p :=
   { f.toMultilinearMap.codRestrict p h with
     toFun := fun v => ⟨f v, h v⟩
     map_eq_zero_of_eq' := fun _ _ _ hv hij => Subtype.ext <| map_eq_zero_of_eq _ _ hv hij }
@@ -486,7 +486,7 @@ namespace LinearMap
 variable {N₂ : Type*} [AddCommMonoid N₂] [Module R N₂]
 
 /-- Composing an alternating map with a linear map on the left gives again an alternating map. -/
-def compAlternatingMap (g : N →ₗ[R] N₂) : (M [Λ^ι]→ₗ[R] N) →+ (M [Λ^ι]→ₗ[R] N₂) where
+def compAlternatingMap (g : N →ₗ[R] N₂) : (M [⋀^ι]→ₗ[R] N) →+ (M [⋀^ι]→ₗ[R] N₂) where
   toFun f :=
     { g.compMultilinearMap (f : MultilinearMap R (fun _ : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }
@@ -499,31 +499,31 @@ def compAlternatingMap (g : N →ₗ[R] N₂) : (M [Λ^ι]→ₗ[R] N) →+ (M [
 #align linear_map.comp_alternating_map LinearMap.compAlternatingMap
 
 @[simp]
-theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : M [Λ^ι]→ₗ[R] N) :
+theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : M [⋀^ι]→ₗ[R] N) :
     ⇑(g.compAlternatingMap f) = g ∘ f :=
   rfl
 #align linear_map.coe_comp_alternating_map LinearMap.coe_compAlternatingMap
 
 @[simp]
-theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : M [Λ^ι]→ₗ[R] N) (m : ι → M) :
+theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : M [⋀^ι]→ₗ[R] N) (m : ι → M) :
     g.compAlternatingMap f m = g (f m) :=
   rfl
 #align linear_map.comp_alternating_map_apply LinearMap.compAlternatingMap_apply
 
 theorem smulRight_eq_comp {R M₁ M₂ ι : Type*} [CommSemiring R] [AddCommMonoid M₁]
-    [AddCommMonoid M₂] [Module R M₁] [Module R M₂] (f : M₁ [Λ^ι]→ₗ[R] R) (z : M₂) :
+    [AddCommMonoid M₂] [Module R M₁] [Module R M₂] (f : M₁ [⋀^ι]→ₗ[R] R) (z : M₂) :
     f.smulRight z = (LinearMap.id.smulRight z).compAlternatingMap f :=
   rfl
 #align linear_map.smul_right_eq_comp LinearMap.smulRight_eq_comp
 
 @[simp]
-theorem subtype_compAlternatingMap_codRestrict (f : M [Λ^ι]→ₗ[R] N) (p : Submodule R N)
+theorem subtype_compAlternatingMap_codRestrict (f : M [⋀^ι]→ₗ[R] N) (p : Submodule R N)
     (h) : p.subtype.compAlternatingMap (f.codRestrict p h) = f :=
   AlternatingMap.ext fun _ => rfl
 #align linear_map.subtype_comp_alternating_map_cod_restrict LinearMap.subtype_compAlternatingMap_codRestrict
 
 @[simp]
-theorem compAlternatingMap_codRestrict (g : N →ₗ[R] N₂) (f : M [Λ^ι]→ₗ[R] N)
+theorem compAlternatingMap_codRestrict (g : N →ₗ[R] N₂) (f : M [⋀^ι]→ₗ[R] N)
     (p : Submodule R N₂) (h) :
     (g.codRestrict p h).compAlternatingMap f =
       (g.compAlternatingMap f).codRestrict p fun v => h (f v) :=
@@ -540,44 +540,44 @@ variable {M₃ : Type*} [AddCommMonoid M₃] [Module R M₃]
 
 /-- Composing an alternating map with the same linear map on each argument gives again an
 alternating map. -/
-def compLinearMap (f : M [Λ^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) : M₂ [Λ^ι]→ₗ[R] N :=
+def compLinearMap (f : M [⋀^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) : M₂ [⋀^ι]→ₗ[R] N :=
   { (f : MultilinearMap R (fun _ : ι => M) N).compLinearMap fun _ => g with
     map_eq_zero_of_eq' := fun _ _ _ h hij => f.map_eq_zero_of_eq _ (LinearMap.congr_arg h) hij }
 #align alternating_map.comp_linear_map AlternatingMap.compLinearMap
 
-theorem coe_compLinearMap (f : M [Λ^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) :
+theorem coe_compLinearMap (f : M [⋀^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) :
     ⇑(f.compLinearMap g) = f ∘ (g ∘ ·) :=
   rfl
 #align alternating_map.coe_comp_linear_map AlternatingMap.coe_compLinearMap
 
 @[simp]
-theorem compLinearMap_apply (f : M [Λ^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) (v : ι → M₂) :
+theorem compLinearMap_apply (f : M [⋀^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) (v : ι → M₂) :
     f.compLinearMap g v = f fun i => g (v i) :=
   rfl
 #align alternating_map.comp_linear_map_apply AlternatingMap.compLinearMap_apply
 
 /-- Composing an alternating map twice with the same linear map in each argument is
 the same as composing with their composition. -/
-theorem compLinearMap_assoc (f : M [Λ^ι]→ₗ[R] N) (g₁ : M₂ →ₗ[R] M) (g₂ : M₃ →ₗ[R] M₂) :
+theorem compLinearMap_assoc (f : M [⋀^ι]→ₗ[R] N) (g₁ : M₂ →ₗ[R] M) (g₂ : M₃ →ₗ[R] M₂) :
     (f.compLinearMap g₁).compLinearMap g₂ = f.compLinearMap (g₁ ∘ₗ g₂) :=
   rfl
 #align alternating_map.comp_linear_map_assoc AlternatingMap.compLinearMap_assoc
 
 @[simp]
-theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : M [Λ^ι]→ₗ[R] N).compLinearMap g = 0 := by
+theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : M [⋀^ι]→ₗ[R] N).compLinearMap g = 0 := by
   ext
   simp only [compLinearMap_apply, zero_apply]
 #align alternating_map.zero_comp_linear_map AlternatingMap.zero_compLinearMap
 
 @[simp]
-theorem add_compLinearMap (f₁ f₂ : M [Λ^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) :
+theorem add_compLinearMap (f₁ f₂ : M [⋀^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) :
     (f₁ + f₂).compLinearMap g = f₁.compLinearMap g + f₂.compLinearMap g := by
   ext
   simp only [compLinearMap_apply, add_apply]
 #align alternating_map.add_comp_linear_map AlternatingMap.add_compLinearMap
 
 @[simp]
-theorem compLinearMap_zero [Nonempty ι] (f : M [Λ^ι]→ₗ[R] N) :
+theorem compLinearMap_zero [Nonempty ι] (f : M [⋀^ι]→ₗ[R] N) :
     f.compLinearMap (0 : M₂ →ₗ[R] M) = 0 := by
   ext
   -- Porting note: Was `simp_rw [.., ← Pi.zero_def, map_zero, zero_apply]`.
@@ -587,18 +587,18 @@ theorem compLinearMap_zero [Nonempty ι] (f : M [Λ^ι]→ₗ[R] N) :
 
 /-- Composing an alternating map with the identity linear map in each argument. -/
 @[simp]
-theorem compLinearMap_id (f : M [Λ^ι]→ₗ[R] N) : f.compLinearMap LinearMap.id = f :=
+theorem compLinearMap_id (f : M [⋀^ι]→ₗ[R] N) : f.compLinearMap LinearMap.id = f :=
   ext fun _ => rfl
 #align alternating_map.comp_linear_map_id AlternatingMap.compLinearMap_id
 
 /-- Composing with a surjective linear map is injective. -/
 theorem compLinearMap_injective (f : M₂ →ₗ[R] M) (hf : Function.Surjective f) :
-    Function.Injective fun g : M [Λ^ι]→ₗ[R] N => g.compLinearMap f := fun g₁ g₂ h =>
+    Function.Injective fun g : M [⋀^ι]→ₗ[R] N => g.compLinearMap f := fun g₁ g₂ h =>
   ext fun x => by simpa [Function.surjInv_eq hf] using ext_iff.mp h (Function.surjInv hf ∘ x)
 #align alternating_map.comp_linear_map_injective AlternatingMap.compLinearMap_injective
 
 theorem compLinearMap_inj (f : M₂ →ₗ[R] M) (hf : Function.Surjective f)
-    (g₁ g₂ : M [Λ^ι]→ₗ[R] N) : g₁.compLinearMap f = g₂.compLinearMap f ↔ g₁ = g₂ :=
+    (g₁ g₂ : M [⋀^ι]→ₗ[R] N) : g₁.compLinearMap f = g₂.compLinearMap f ↔ g₁ = g₂ :=
   (compLinearMap_injective _ hf).eq_iff
 #align alternating_map.comp_linear_map_inj AlternatingMap.compLinearMap_inj
 
@@ -609,7 +609,7 @@ variable (S : Type*) [Semiring S] [Module S N] [SMulCommClass R S N]
 
 /-- Construct a linear equivalence between maps from a linear equivalence between domains. -/
 @[simps apply]
-def domLCongr (e : M ≃ₗ[R] M₂) : M [Λ^ι]→ₗ[R] N ≃ₗ[S] (M₂ [Λ^ι]→ₗ[R] N) where
+def domLCongr (e : M ≃ₗ[R] M₂) : M [⋀^ι]→ₗ[R] N ≃ₗ[S] (M₂ [⋀^ι]→ₗ[R] N) where
   toFun f := f.compLinearMap e.symm
   invFun g := g.compLinearMap e
   map_add' _ _ := rfl
@@ -639,14 +639,14 @@ end DomLcongr
 /-- Composing an alternating map with the same linear equiv on each argument gives the zero map
 if and only if the alternating map is the zero map. -/
 @[simp]
-theorem compLinearEquiv_eq_zero_iff (f : M [Λ^ι]→ₗ[R] N) (g : M₂ ≃ₗ[R] M) :
+theorem compLinearEquiv_eq_zero_iff (f : M [⋀^ι]→ₗ[R] N) (g : M₂ ≃ₗ[R] M) :
     f.compLinearMap (g : M₂ →ₗ[R] M) = 0 ↔ f = 0 :=
   (domLCongr R N ι ℕ g.symm).map_eq_zero_iff
 #align alternating_map.comp_linear_equiv_eq_zero_iff AlternatingMap.compLinearEquiv_eq_zero_iff
 
-variable (f f' : M [Λ^ι]→ₗ[R] N)
-variable (g g₂ : M [Λ^ι]→ₗ[R] N')
-variable (g' : M' [Λ^ι]→ₗ[R] N')
+variable (f f' : M [⋀^ι]→ₗ[R] N)
+variable (g g₂ : M [⋀^ι]→ₗ[R] N')
+variable (g' : M' [⋀^ι]→ₗ[R] N')
 variable (v : ι → M) (v' : ι → M')
 
 open Function
@@ -726,7 +726,7 @@ section DomDomCongr
 
 This is the alternating version of `MultilinearMap.domDomCongr`. -/
 @[simps]
-def domDomCongr (σ : ι ≃ ι') (f : M [Λ^ι]→ₗ[R] N) : M [Λ^ι']→ₗ[R] N :=
+def domDomCongr (σ : ι ≃ ι') (f : M [⋀^ι]→ₗ[R] N) : M [⋀^ι']→ₗ[R] N :=
   { f.toMultilinearMap.domDomCongr σ with
     toFun := fun v => f (v ∘ σ)
     map_eq_zero_of_eq' := fun v i j hv hij =>
@@ -736,28 +736,28 @@ def domDomCongr (σ : ι ≃ ι') (f : M [Λ^ι]→ₗ[R] N) : M [Λ^ι']→ₗ[
 #align alternating_map.dom_dom_congr_apply AlternatingMap.domDomCongr_apply
 
 @[simp]
-theorem domDomCongr_refl (f : M [Λ^ι]→ₗ[R] N) : f.domDomCongr (Equiv.refl ι) = f := rfl
+theorem domDomCongr_refl (f : M [⋀^ι]→ₗ[R] N) : f.domDomCongr (Equiv.refl ι) = f := rfl
 #align alternating_map.dom_dom_congr_refl AlternatingMap.domDomCongr_refl
 
-theorem domDomCongr_trans (σ₁ : ι ≃ ι') (σ₂ : ι' ≃ ι'') (f : M [Λ^ι]→ₗ[R] N) :
+theorem domDomCongr_trans (σ₁ : ι ≃ ι') (σ₂ : ι' ≃ ι'') (f : M [⋀^ι]→ₗ[R] N) :
     f.domDomCongr (σ₁.trans σ₂) = (f.domDomCongr σ₁).domDomCongr σ₂ :=
   rfl
 #align alternating_map.dom_dom_congr_trans AlternatingMap.domDomCongr_trans
 
 @[simp]
-theorem domDomCongr_zero (σ : ι ≃ ι') : (0 : M [Λ^ι]→ₗ[R] N).domDomCongr σ = 0 :=
+theorem domDomCongr_zero (σ : ι ≃ ι') : (0 : M [⋀^ι]→ₗ[R] N).domDomCongr σ = 0 :=
   rfl
 #align alternating_map.dom_dom_congr_zero AlternatingMap.domDomCongr_zero
 
 @[simp]
-theorem domDomCongr_add (σ : ι ≃ ι') (f g : M [Λ^ι]→ₗ[R] N) :
+theorem domDomCongr_add (σ : ι ≃ ι') (f g : M [⋀^ι]→ₗ[R] N) :
     (f + g).domDomCongr σ = f.domDomCongr σ + g.domDomCongr σ :=
   rfl
 #align alternating_map.dom_dom_congr_add AlternatingMap.domDomCongr_add
 
 @[simp]
 theorem domDomCongr_smul {S : Type*} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
-    (σ : ι ≃ ι') (c : S) (f : M [Λ^ι]→ₗ[R] N) :
+    (σ : ι ≃ ι') (c : S) (f : M [⋀^ι]→ₗ[R] N) :
     (c • f).domDomCongr σ = c • f.domDomCongr σ :=
   rfl
 #align alternating_map.dom_dom_congr_smul AlternatingMap.domDomCongr_smul
@@ -766,7 +766,7 @@ theorem domDomCongr_smul {S : Type*} [Monoid S] [DistribMulAction S N] [SMulComm
 
 This is declared separately because it does not work with dot notation. -/
 @[simps apply symm_apply]
-def domDomCongrEquiv (σ : ι ≃ ι') : M [Λ^ι]→ₗ[R] N ≃+ M [Λ^ι']→ₗ[R] N where
+def domDomCongrEquiv (σ : ι ≃ ι') : M [⋀^ι]→ₗ[R] N ≃+ M [⋀^ι']→ₗ[R] N where
   toFun := domDomCongr σ
   invFun := domDomCongr σ.symm
   left_inv f := by
@@ -786,7 +786,7 @@ variable (S : Type*) [Semiring S] [Module S N] [SMulCommClass R S N]
 
 /-- `AlternatingMap.domDomCongr` as a linear equivalence. -/
 @[simps apply symm_apply]
-def domDomCongrₗ (σ : ι ≃ ι') : M [Λ^ι]→ₗ[R] N ≃ₗ[S] M [Λ^ι']→ₗ[R] N where
+def domDomCongrₗ (σ : ι ≃ ι') : M [⋀^ι]→ₗ[R] N ≃ₗ[S] M [⋀^ι']→ₗ[R] N where
   toFun := domDomCongr σ
   invFun := domDomCongr σ.symm
   left_inv f := by ext; simp [Function.comp]
@@ -797,14 +797,14 @@ def domDomCongrₗ (σ : ι ≃ ι') : M [Λ^ι]→ₗ[R] N ≃ₗ[S] M [Λ^ι']
 
 @[simp]
 theorem domDomCongrₗ_refl :
-    (domDomCongrₗ S (Equiv.refl ι) : M [Λ^ι]→ₗ[R] N ≃ₗ[S] M [Λ^ι]→ₗ[R] N) =
+    (domDomCongrₗ S (Equiv.refl ι) : M [⋀^ι]→ₗ[R] N ≃ₗ[S] M [⋀^ι]→ₗ[R] N) =
       LinearEquiv.refl _ _ :=
   rfl
 #align alternating_map.dom_dom_lcongr_refl AlternatingMap.domDomCongrₗ_refl
 
 @[simp]
 theorem domDomCongrₗ_toAddEquiv (σ : ι ≃ ι') :
-    (↑(domDomCongrₗ S σ : M [Λ^ι]→ₗ[R] N ≃ₗ[S] _) : M [Λ^ι]→ₗ[R] N ≃+ _) =
+    (↑(domDomCongrₗ S σ : M [⋀^ι]→ₗ[R] N ≃ₗ[S] _) : M [⋀^ι]→ₗ[R] N ≃+ _) =
       domDomCongrEquiv σ :=
   rfl
 #align alternating_map.dom_dom_lcongr_to_add_equiv AlternatingMap.domDomCongrₗ_toAddEquiv
@@ -813,15 +813,15 @@ end DomDomLcongr
 
 /-- The results of applying `domDomCongr` to two maps are equal if and only if those maps are. -/
 @[simp]
-theorem domDomCongr_eq_iff (σ : ι ≃ ι') (f g : M [Λ^ι]→ₗ[R] N) :
+theorem domDomCongr_eq_iff (σ : ι ≃ ι') (f g : M [⋀^ι]→ₗ[R] N) :
     f.domDomCongr σ = g.domDomCongr σ ↔ f = g :=
-  (domDomCongrEquiv σ : _ ≃+ M [Λ^ι']→ₗ[R] N).apply_eq_iff_eq
+  (domDomCongrEquiv σ : _ ≃+ M [⋀^ι']→ₗ[R] N).apply_eq_iff_eq
 #align alternating_map.dom_dom_congr_eq_iff AlternatingMap.domDomCongr_eq_iff
 
 @[simp]
-theorem domDomCongr_eq_zero_iff (σ : ι ≃ ι') (f : M [Λ^ι]→ₗ[R] N) :
+theorem domDomCongr_eq_zero_iff (σ : ι ≃ ι') (f : M [⋀^ι]→ₗ[R] N) :
     f.domDomCongr σ = 0 ↔ f = 0 :=
-  (domDomCongrEquiv σ : M [Λ^ι]→ₗ[R] N ≃+ M [Λ^ι']→ₗ[R] N).map_eq_zero_iff
+  (domDomCongrEquiv σ : M [⋀^ι]→ₗ[R] N ≃+ M [⋀^ι']→ₗ[R] N).map_eq_zero_iff
 #align alternating_map.dom_dom_congr_eq_zero_iff AlternatingMap.domDomCongr_eq_zero_iff
 
 theorem domDomCongr_perm [Fintype ι] [DecidableEq ι] (σ : Equiv.Perm ι) :
@@ -839,7 +839,7 @@ end DomDomCongr
 
 /-- If the arguments are linearly dependent then the result is `0`. -/
 theorem map_linearDependent {K : Type*} [Ring K] {M : Type*} [AddCommGroup M] [Module K M]
-    {N : Type*} [AddCommGroup N] [Module K N] [NoZeroSMulDivisors K N] (f : M [Λ^ι]→ₗ[K] N)
+    {N : Type*} [AddCommGroup N] [Module K N] [NoZeroSMulDivisors K N] (f : M [⋀^ι]→ₗ[K] N)
     (v : ι → M) (h : ¬LinearIndependent K v) : f v = 0 := by
   obtain ⟨s, g, h, i, hi, hz⟩ := not_linearIndependent_iff.mp h
   letI := Classical.decEq ι
@@ -861,13 +861,13 @@ section Fin
 open Fin
 
 /-- A version of `MultilinearMap.cons_add` for `AlternatingMap`. -/
-theorem map_vecCons_add {n : ℕ} (f : M [Λ^Fin n.succ]→ₗ[R] N) (m : Fin n → M) (x y : M) :
+theorem map_vecCons_add {n : ℕ} (f : M [⋀^Fin n.succ]→ₗ[R] N) (m : Fin n → M) (x y : M) :
     f (Matrix.vecCons (x + y) m) = f (Matrix.vecCons x m) + f (Matrix.vecCons y m) :=
   f.toMultilinearMap.cons_add _ _ _
 #align alternating_map.map_vec_cons_add AlternatingMap.map_vecCons_add
 
 /-- A version of `MultilinearMap.cons_smul` for `AlternatingMap`. -/
-theorem map_vecCons_smul {n : ℕ} (f : M [Λ^Fin n.succ]→ₗ[R] N) (m : Fin n → M) (c : R)
+theorem map_vecCons_smul {n : ℕ} (f : M [⋀^Fin n.succ]→ₗ[R] N) (m : Fin n → M) (c : R)
     (x : M) : f (Matrix.vecCons (c • x) m) = c • f (Matrix.vecCons x m) :=
   f.toMultilinearMap.cons_smul _ _ _
 #align alternating_map.map_vec_cons_smul AlternatingMap.map_vecCons_smul
@@ -897,7 +897,7 @@ private theorem alternization_map_eq_zero_of_eq_aux (m : MultilinearMap R (fun _
 
 /-- Produce an `AlternatingMap` out of a `MultilinearMap`, by summing over all argument
 permutations. -/
-def alternatization : MultilinearMap R (fun _ : ι => M) N' →+ M [Λ^ι]→ₗ[R] N' where
+def alternatization : MultilinearMap R (fun _ : ι => M) N' →+ M [⋀^ι]→ₗ[R] N' where
   toFun m :=
     { ∑ σ : Perm ι, Equiv.Perm.sign σ • m.domDomCongr σ with
       toFun := ⇑(∑ σ : Perm ι, Equiv.Perm.sign σ • m.domDomCongr σ)
@@ -934,7 +934,7 @@ namespace AlternatingMap
 
 /-- Alternatizing a multilinear map that is already alternating results in a scale factor of `n!`,
 where `n` is the number of inputs. -/
-theorem coe_alternatization [DecidableEq ι] [Fintype ι] (a : M [Λ^ι]→ₗ[R] N') :
+theorem coe_alternatization [DecidableEq ι] [Fintype ι] (a : M [⋀^ι]→ₗ[R] N') :
     MultilinearMap.alternatization (a : MultilinearMap R (fun _ => M) N')
     = Nat.factorial (Fintype.card ι) • a := by
   apply AlternatingMap.coe_injective
@@ -972,7 +972,7 @@ variable [Module R' N₁] [Module R' N₂]
 
 /-- Two alternating maps indexed by a `Fintype` are equal if they are equal when all arguments
 are distinct basis vectors. -/
-theorem Basis.ext_alternating {f g : N₁ [Λ^ι]→ₗ[R'] N₂} (e : Basis ι₁ R' N₁)
+theorem Basis.ext_alternating {f g : N₁ [⋀^ι]→ₗ[R'] N₂} (e : Basis ι₁ R' N₁)
     (h : ∀ v : ι → ι₁, Function.Injective v → (f fun i => e (v i)) = g fun i => e (v i)) :
     f = g := by
   classical
@@ -1004,8 +1004,8 @@ It can be thought of as a map $Hom(\bigwedge^{n+1} M, N) \to Hom(M, Hom(\bigwedg
 This is `MultilinearMap.curryLeft` for `AlternatingMap`. See also
 `AlternatingMap.curryLeftLinearMap`. -/
 @[simps]
-def curryLeft {n : ℕ} (f : M'' [Λ^Fin n.succ]→ₗ[R'] N'') :
-    M'' →ₗ[R'] M'' [Λ^Fin n]→ₗ[R'] N'' where
+def curryLeft {n : ℕ} (f : M'' [⋀^Fin n.succ]→ₗ[R'] N'') :
+    M'' →ₗ[R'] M'' [⋀^Fin n]→ₗ[R'] N'' where
   toFun m :=
     { f.toMultilinearMap.curryLeft m with
       toFun := fun v => f (Matrix.vecCons m v)
@@ -1018,18 +1018,18 @@ def curryLeft {n : ℕ} (f : M'' [Λ^Fin n.succ]→ₗ[R'] N'') :
 #align alternating_map.curry_left_apply_apply AlternatingMap.curryLeft_apply_apply
 
 @[simp]
-theorem curryLeft_zero {n : ℕ} : curryLeft (0 : M'' [Λ^Fin n.succ]→ₗ[R'] N'') = 0 :=
+theorem curryLeft_zero {n : ℕ} : curryLeft (0 : M'' [⋀^Fin n.succ]→ₗ[R'] N'') = 0 :=
   rfl
 #align alternating_map.curry_left_zero AlternatingMap.curryLeft_zero
 
 @[simp]
-theorem curryLeft_add {n : ℕ} (f g : M'' [Λ^Fin n.succ]→ₗ[R'] N'') :
+theorem curryLeft_add {n : ℕ} (f g : M'' [⋀^Fin n.succ]→ₗ[R'] N'') :
     curryLeft (f + g) = curryLeft f + curryLeft g :=
   rfl
 #align alternating_map.curry_left_add AlternatingMap.curryLeft_add
 
 @[simp]
-theorem curryLeft_smul {n : ℕ} (r : R') (f : M'' [Λ^Fin n.succ]→ₗ[R'] N'') :
+theorem curryLeft_smul {n : ℕ} (r : R') (f : M'' [⋀^Fin n.succ]→ₗ[R'] N'') :
     curryLeft (r • f) = r • curryLeft f :=
   rfl
 #align alternating_map.curry_left_smul AlternatingMap.curryLeft_smul
@@ -1038,7 +1038,7 @@ theorem curryLeft_smul {n : ℕ} (r : R') (f : M'' [Λ^Fin n.succ]→ₗ[R'] N''
 does not work for this version. -/
 @[simps]
 def curryLeftLinearMap {n : ℕ} :
-    (M'' [Λ^Fin n.succ]→ₗ[R'] N'') →ₗ[R'] M'' →ₗ[R'] M'' [Λ^Fin n]→ₗ[R'] N'' where
+    (M'' [⋀^Fin n.succ]→ₗ[R'] N'') →ₗ[R'] M'' →ₗ[R'] M'' [⋀^Fin n]→ₗ[R'] N'' where
   toFun f := f.curryLeft
   map_add' := curryLeft_add
   map_smul' := curryLeft_smul
@@ -1047,21 +1047,21 @@ def curryLeftLinearMap {n : ℕ} :
 
 /-- Currying with the same element twice gives the zero map. -/
 @[simp]
-theorem curryLeft_same {n : ℕ} (f : M'' [Λ^Fin n.succ.succ]→ₗ[R'] N'') (m : M'') :
+theorem curryLeft_same {n : ℕ} (f : M'' [⋀^Fin n.succ.succ]→ₗ[R'] N'') (m : M'') :
     (f.curryLeft m).curryLeft m = 0 :=
   ext fun x => f.map_eq_zero_of_eq _ (by simp) Fin.zero_ne_one
 #align alternating_map.curry_left_same AlternatingMap.curryLeft_same
 
 @[simp]
 theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
-    (f : M'' [Λ^Fin n.succ]→ₗ[R'] N'') (m : M'') :
+    (f : M'' [⋀^Fin n.succ]→ₗ[R'] N'') (m : M'') :
     (g.compAlternatingMap f).curryLeft m = g.compAlternatingMap (f.curryLeft m) :=
   rfl
 #align alternating_map.curry_left_comp_alternating_map AlternatingMap.curryLeft_compAlternatingMap
 
 @[simp]
 theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')
-    (f : M'' [Λ^Fin n.succ]→ₗ[R'] N'') (m : M₂'') :
+    (f : M'' [⋀^Fin n.succ]→ₗ[R'] N'') (m : M₂'') :
     (f.compLinearMap g).curryLeft m = (f.curryLeft (g m)).compLinearMap g :=
   ext fun v => congr_arg f <| funext <| by
     refine' Fin.cases _ _
@@ -1072,7 +1072,7 @@ theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')
 /-- The space of constant maps is equivalent to the space of maps that are alternating with respect
 to an empty family. -/
 @[simps]
-def constLinearEquivOfIsEmpty [IsEmpty ι] : N'' ≃ₗ[R'] (M'' [Λ^ι]→ₗ[R'] N'') where
+def constLinearEquivOfIsEmpty [IsEmpty ι] : N'' ≃ₗ[R'] (M'' [⋀^ι]→ₗ[R'] N'') where
   toFun := AlternatingMap.constOfIsEmpty R' M'' ι
   map_add' _ _ := rfl
   map_smul' _ _ := rfl

Classifies by adding issue number (#10691) to porting notes claiming was rw.

@@ -62,7 +62,7 @@ def domCoprod.summand (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→
       TensorProduct.smul_tmul']
     simp only [Sum.map_inr, Perm.sumCongrHom_apply, Perm.sumCongr_apply, Sum.map_inl,
       Function.comp_apply, Perm.coe_mul]
-    -- Porting note: Was `rw`.
+    -- Porting note (#10691): was `rw`.
     erw [← a.map_congr_perm fun i => v (σ₁ _), ← b.map_congr_perm fun i => v (σ₁ _)]
 #align alternating_map.dom_coprod.summand AlternatingMap.domCoprod.summand
 

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -135,7 +135,7 @@ theorem coe_injective : Injective ((↑) : M [Λ^ι]→ₗ[R] N → (ι → M) 
   DFunLike.coe_injective
 #align alternating_map.coe_injective AlternatingMap.coe_injective
 
-@[norm_cast] -- @[simp] -- Porting note: simp can prove this
+@[norm_cast] -- @[simp] -- Porting note (#10618): simp can prove this
 theorem coe_inj {f g : M [Λ^ι]→ₗ[R] N} : (f : (ι → M) → N) = g ↔ f = g :=
   coe_injective.eq_iff
 #align alternating_map.coe_inj AlternatingMap.coe_inj

Fixed minor typo.

@@ -22,7 +22,7 @@ arguments of the same type.
 * `f.map_perm` expresses how `f` varies by a sign change under a permutation of its inputs.
 * An `AddCommMonoid`, `AddCommGroup`, and `Module` structure over `AlternatingMap`s that
   matches the definitions over `MultilinearMap`s.
-* `MultilinearMap.domDomCongr`, for permutating the elements within a family.
+* `MultilinearMap.domDomCongr`, for permuting the elements within a family.
 * `MultilinearMap.alternatization`, which makes an alternating map out of a non-alternating one.
 * `AlternatingMap.curryLeft`, for binding the leftmost argument of an alternating map indexed
   by `Fin n.succ`.

This follows up from #9785, which renamed FunLike to DFunLike, by introducing a new abbreviation FunLike F α β := DFunLike F α (fun _ => β), to make the non-dependent use of FunLike easier.

I searched for the pattern DFunLike.*fun and DFunLike.*λ in all files to replace expressions of the form DFunLike F α (fun _ => β) with FunLike F α β. I did this everywhere except for extends clauses for two reasons: it would conflict with #8386, and more importantly extends must directly refer to a structure with no unfolding of defs or abbrevs.

@@ -96,13 +96,13 @@ open Function
 
 section Coercions
 
-instance instDFunLike : DFunLike (M [Λ^ι]→ₗ[R] N) (ι → M) (fun _ => N) where
+instance instFunLike : FunLike (M [Λ^ι]→ₗ[R] N) (ι → M) N where
   coe f := f.toFun
   coe_injective' := fun f g h ↦ by
     rcases f with ⟨⟨_, _, _⟩, _⟩
     rcases g with ⟨⟨_, _, _⟩, _⟩
     congr
-#align alternating_map.fun_like AlternatingMap.instDFunLike
+#align alternating_map.fun_like AlternatingMap.instFunLike
 
 -- shortcut instance
 instance coeFun : CoeFun (M [Λ^ι]→ₗ[R] N) fun _ => (ι → M) → N :=

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>

@@ -96,17 +96,17 @@ open Function
 
 section Coercions
 
-instance funLike : FunLike (M [Λ^ι]→ₗ[R] N) (ι → M) (fun _ => N) where
+instance instDFunLike : DFunLike (M [Λ^ι]→ₗ[R] N) (ι → M) (fun _ => N) where
   coe f := f.toFun
   coe_injective' := fun f g h ↦ by
     rcases f with ⟨⟨_, _, _⟩, _⟩
     rcases g with ⟨⟨_, _, _⟩, _⟩
     congr
-#align alternating_map.fun_like AlternatingMap.funLike
+#align alternating_map.fun_like AlternatingMap.instDFunLike
 
 -- shortcut instance
 instance coeFun : CoeFun (M [Λ^ι]→ₗ[R] N) fun _ => (ι → M) → N :=
-  ⟨FunLike.coe⟩
+  ⟨DFunLike.coe⟩
 #align alternating_map.has_coe_to_fun AlternatingMap.coeFun
 
 initialize_simps_projections AlternatingMap (toFun → apply)
@@ -132,7 +132,7 @@ theorem congr_arg (f : M [Λ^ι]→ₗ[R] N) {x y : ι → M} (h : x = y) : f x
 #align alternating_map.congr_arg AlternatingMap.congr_arg
 
 theorem coe_injective : Injective ((↑) : M [Λ^ι]→ₗ[R] N → (ι → M) → N) :=
-  FunLike.coe_injective
+  DFunLike.coe_injective
 #align alternating_map.coe_injective AlternatingMap.coe_injective
 
 @[norm_cast] -- @[simp] -- Porting note: simp can prove this
@@ -142,7 +142,7 @@ theorem coe_inj {f g : M [Λ^ι]→ₗ[R] N} : (f : (ι → M) → N) = g ↔ f
 
 @[ext]
 theorem ext {f f' : M [Λ^ι]→ₗ[R] N} (H : ∀ x, f x = f' x) : f = f' :=
-  FunLike.ext _ _ H
+  DFunLike.ext _ _ H
 #align alternating_map.ext AlternatingMap.ext
 
 theorem ext_iff {f g : M [Λ^ι]→ₗ[R] N} : f = g ↔ ∀ x, f x = g x :=

Generalize Equiv.Perm.ModSumCongr.swap_smul_involutive to any action of Equiv.Perm _, move it to Perm/Basic.

@@ -32,12 +32,7 @@ abbrev ModSumCongr (α β : Type*) :=
   _ ⧸ (Equiv.Perm.sumCongrHom α β).range
 #align equiv.perm.mod_sum_congr Equiv.Perm.ModSumCongr
 
-theorem ModSumCongr.swap_smul_involutive {α β : Type*} [DecidableEq (Sum α β)] (i j : Sum α β) :
-    Function.Involutive (SMul.smul (Equiv.swap i j) : ModSumCongr α β → ModSumCongr α β) :=
-  fun σ => by
-    refine Quotient.inductionOn' σ fun σ => ?_
-    exact _root_.congr_arg Quotient.mk'' (Equiv.swap_mul_involutive i j σ)
-#align equiv.perm.mod_sum_congr.swap_smul_involutive Equiv.Perm.ModSumCongr.swap_smul_involutive
+#align equiv.perm.mod_sum_congr.swap_smul_involutive Equiv.swap_smul_involutive
 
 end Equiv.Perm
 
@@ -171,7 +166,7 @@ def domCoprod (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N
           (fun σ _ => domCoprod.summand_add_swap_smul_eq_zero a b σ hv hij)
           (fun σ _ => mt <| domCoprod.summand_eq_zero_of_smul_invariant a b σ hv hij)
           (fun σ _ => Finset.mem_univ _) fun σ _ =>
-          Equiv.Perm.ModSumCongr.swap_smul_involutive i j σ }
+          Equiv.swap_smul_involutive i j σ }
 #align alternating_map.dom_coprod AlternatingMap.domCoprod
 #align alternating_map.dom_coprod_apply AlternatingMap.domCoprod_apply
 

I used the regex \(\(· (.) ·\) (.)\), replacing with ($2 $1 ·).

@@ -546,7 +546,7 @@ def compLinearMap (f : M [Λ^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) : M₂ [Λ^
 #align alternating_map.comp_linear_map AlternatingMap.compLinearMap
 
 theorem coe_compLinearMap (f : M [Λ^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) :
-    ⇑(f.compLinearMap g) = f ∘ (· ∘ ·) g :=
+    ⇑(f.compLinearMap g) = f ∘ (g ∘ ·) :=
   rfl
 #align alternating_map.coe_comp_linear_map AlternatingMap.coe_compLinearMap
 

Use M [Λ^ι]→ₗ[R] N for AlternatingMap R M N ι, similarly to the existing notation M [Λ^ι]→L[R] N for ContinuousAlternatingMap R M N ι.

@@ -48,7 +48,7 @@ open Equiv
 variable [DecidableEq ιa] [DecidableEq ιb]
 
 /-- summand used in `AlternatingMap.domCoprod` -/
-def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
+def domCoprod.summand (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂)
     (σ : Perm.ModSumCongr ιa ιb) : MultilinearMap R' (fun _ : Sum ιa ιb => Mᵢ) (N₁ ⊗[R'] N₂) :=
   Quotient.liftOn' σ
     (fun σ =>
@@ -71,7 +71,7 @@ def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap
     erw [← a.map_congr_perm fun i => v (σ₁ _), ← b.map_congr_perm fun i => v (σ₁ _)]
 #align alternating_map.dom_coprod.summand AlternatingMap.domCoprod.summand
 
-theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
+theorem domCoprod.summand_mk'' (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂)
     (σ : Equiv.Perm (Sum ιa ιb)) :
     domCoprod.summand a b (Quotient.mk'' σ) =
       Equiv.Perm.sign σ •
@@ -81,8 +81,8 @@ theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : Altern
 #align alternating_map.dom_coprod.summand_mk' AlternatingMap.domCoprod.summand_mk''
 
 /-- Swapping elements in `σ` with equal values in `v` results in an addition that cancels -/
-theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁ ιa)
-    (b : AlternatingMap R' Mᵢ N₂ ιb) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
+theorem domCoprod.summand_add_swap_smul_eq_zero (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁)
+    (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
     {i j : Sum ιa ιb} (hv : v i = v j) (hij : i ≠ j) :
     domCoprod.summand a b σ v + domCoprod.summand a b (swap i j • σ) v = 0 := by
   refine Quotient.inductionOn' σ fun σ => ?_
@@ -99,8 +99,8 @@ theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁
 
 /-- Swapping elements in `σ` with equal values in `v` result in zero if the swap has no effect
 on the quotient. -/
-theorem domCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ N₁ ιa)
-    (b : AlternatingMap R' Mᵢ N₂ ιb) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
+theorem domCoprod.summand_eq_zero_of_smul_invariant (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁)
+    (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
     {i j : Sum ιa ιb} (hv : v i = v j) (hij : i ≠ j) :
     swap i j • σ = σ → domCoprod.summand a b σ v = 0 := by
   refine Quotient.inductionOn' σ fun σ => ?_
@@ -159,8 +159,8 @@ The specialized version can be obtained by combining this definition with `finSu
 `LinearMap.mul'`.
 -/
 @[simps]
-def domCoprod (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
-    AlternatingMap R' Mᵢ (N₁ ⊗[R'] N₂) (Sum ιa ιb) :=
+def domCoprod (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂) :
+    Mᵢ [Λ^ιa ⊕ ιb]→ₗ[R'] (N₁ ⊗[R'] N₂) :=
   { ∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ with
     toFun := fun v => (⇑(∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ)) v
     map_eq_zero_of_eq' := fun v i j hv hij => by
@@ -175,7 +175,7 @@ def domCoprod (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ
 #align alternating_map.dom_coprod AlternatingMap.domCoprod
 #align alternating_map.dom_coprod_apply AlternatingMap.domCoprod_apply
 
-theorem domCoprod_coe (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
+theorem domCoprod_coe (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂) :
     (↑(a.domCoprod b) : MultilinearMap R' (fun _ => Mᵢ) _) =
       ∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ :=
   MultilinearMap.ext fun _ => rfl
@@ -184,8 +184,8 @@ theorem domCoprod_coe (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap
 /-- A more bundled version of `AlternatingMap.domCoprod` that maps
 `((ι₁ → N) → N₁) ⊗ ((ι₂ → N) → N₂)` to `(ι₁ ⊕ ι₂ → N) → N₁ ⊗ N₂`. -/
 def domCoprod' :
-    AlternatingMap R' Mᵢ N₁ ιa ⊗[R'] AlternatingMap R' Mᵢ N₂ ιb →ₗ[R']
-      AlternatingMap R' Mᵢ (N₁ ⊗[R'] N₂) (Sum ιa ιb) :=
+    (Mᵢ [Λ^ιa]→ₗ[R'] N₁) ⊗[R'] (Mᵢ [Λ^ιb]→ₗ[R'] N₂) →ₗ[R']
+      (Mᵢ [Λ^ιa ⊕ ιb]→ₗ[R'] (N₁ ⊗[R'] N₂)) :=
   TensorProduct.lift <| by
     refine'
       LinearMap.mk₂ R' domCoprod (fun m₁ m₂ n => _) (fun c m n => _) (fun m n₁ n₂ => _)
@@ -205,7 +205,7 @@ def domCoprod' :
 #align alternating_map.dom_coprod' AlternatingMap.domCoprod'
 
 @[simp]
-theorem domCoprod'_apply (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
+theorem domCoprod'_apply (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂) :
     domCoprod' (a ⊗ₜ[R'] b) = domCoprod a b :=
   rfl
 #align alternating_map.dom_coprod'_apply AlternatingMap.domCoprod'_apply
@@ -276,7 +276,7 @@ theorem MultilinearMap.domCoprod_alternization [DecidableEq ιa] [DecidableEq ι
 `AlternatingMap`s gives a scaled version of the `AlternatingMap.coprod` of those maps.
 -/
 theorem MultilinearMap.domCoprod_alternization_eq [DecidableEq ιa] [DecidableEq ιb]
-    (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
+    (a : Mᵢ [Λ^ιa]→ₗ[R'] N₁) (b : Mᵢ [Λ^ιb]→ₗ[R'] N₂) :
     MultilinearMap.alternatization
       (MultilinearMap.domCoprod a b : MultilinearMap R' (fun _ : Sum ιa ιb => Mᵢ) (N₁ ⊗ N₂)) =
       ((Fintype.card ιa).factorial * (Fintype.card ιb).factorial) • a.domCoprod b := by

Use M [Λ^ι]→ₗ[R] N for AlternatingMap R M N ι, similarly to the existing notation M [Λ^ι]→L[R] N for ContinuousAlternatingMap R M N ι.

@@ -71,6 +71,9 @@ structure AlternatingMap extends MultilinearMap R (fun _ : ι => M) N where
   map_eq_zero_of_eq' : ∀ (v : ι → M) (i j : ι), v i = v j → i ≠ j → toFun v = 0
 #align alternating_map AlternatingMap
 
+@[inherit_doc]
+notation M " [Λ^" ι "]→ₗ[" R "] " N:100 => AlternatingMap R M N ι
+
 end
 
 /-- The multilinear map associated to an alternating map -/
@@ -78,11 +81,11 @@ add_decl_doc AlternatingMap.toMultilinearMap
 
 namespace AlternatingMap
 
-variable (f f' : AlternatingMap R M N ι)
+variable (f f' : M [Λ^ι]→ₗ[R] N)
 
-variable (g g₂ : AlternatingMap R M N' ι)
+variable (g g₂ : M [Λ^ι]→ₗ[R] N')
 
-variable (g' : AlternatingMap R M' N' ι)
+variable (g' : M' [Λ^ι]→ₗ[R] N')
 
 variable (v : ι → M) (v' : ι → M')
 
@@ -93,7 +96,7 @@ open Function
 
 section Coercions
 
-instance funLike : FunLike (AlternatingMap R M N ι) (ι → M) (fun _ => N) where
+instance funLike : FunLike (M [Λ^ι]→ₗ[R] N) (ι → M) (fun _ => N) where
   coe f := f.toFun
   coe_injective' := fun f g h ↦ by
     rcases f with ⟨⟨_, _, _⟩, _⟩
@@ -102,7 +105,7 @@ instance funLike : FunLike (AlternatingMap R M N ι) (ι → M) (fun _ => N) whe
 #align alternating_map.fun_like AlternatingMap.funLike
 
 -- shortcut instance
-instance coeFun : CoeFun (AlternatingMap R M N ι) fun _ => (ι → M) → N :=
+instance coeFun : CoeFun (M [Λ^ι]→ₗ[R] N) fun _ => (ι → M) → N :=
   ⟨FunLike.coe⟩
 #align alternating_map.has_coe_to_fun AlternatingMap.coeFun
 
@@ -116,39 +119,39 @@ theorem toFun_eq_coe : f.toFun = f :=
 -- Porting note: changed statement to reflect new `mk` signature
 @[simp]
 theorem coe_mk (f : MultilinearMap R (fun _ : ι => M) N) (h) :
-    ⇑(⟨f, h⟩ : AlternatingMap R M N ι) = f :=
+    ⇑(⟨f, h⟩ : M [Λ^ι]→ₗ[R] N) = f :=
   rfl
 #align alternating_map.coe_mk AlternatingMap.coe_mkₓ
 
-theorem congr_fun {f g : AlternatingMap R M N ι} (h : f = g) (x : ι → M) : f x = g x :=
-  congr_arg (fun h : AlternatingMap R M N ι => h x) h
+theorem congr_fun {f g : M [Λ^ι]→ₗ[R] N} (h : f = g) (x : ι → M) : f x = g x :=
+  congr_arg (fun h : M [Λ^ι]→ₗ[R] N => h x) h
 #align alternating_map.congr_fun AlternatingMap.congr_fun
 
-theorem congr_arg (f : AlternatingMap R M N ι) {x y : ι → M} (h : x = y) : f x = f y :=
+theorem congr_arg (f : M [Λ^ι]→ₗ[R] N) {x y : ι → M} (h : x = y) : f x = f y :=
   _root_.congr_arg (fun x : ι → M => f x) h
 #align alternating_map.congr_arg AlternatingMap.congr_arg
 
-theorem coe_injective : Injective ((↑) : AlternatingMap R M N ι → (ι → M) → N) :=
+theorem coe_injective : Injective ((↑) : M [Λ^ι]→ₗ[R] N → (ι → M) → N) :=
   FunLike.coe_injective
 #align alternating_map.coe_injective AlternatingMap.coe_injective
 
 @[norm_cast] -- @[simp] -- Porting note: simp can prove this
-theorem coe_inj {f g : AlternatingMap R M N ι} : (f : (ι → M) → N) = g ↔ f = g :=
+theorem coe_inj {f g : M [Λ^ι]→ₗ[R] N} : (f : (ι → M) → N) = g ↔ f = g :=
   coe_injective.eq_iff
 #align alternating_map.coe_inj AlternatingMap.coe_inj
 
 @[ext]
-theorem ext {f f' : AlternatingMap R M N ι} (H : ∀ x, f x = f' x) : f = f' :=
+theorem ext {f f' : M [Λ^ι]→ₗ[R] N} (H : ∀ x, f x = f' x) : f = f' :=
   FunLike.ext _ _ H
 #align alternating_map.ext AlternatingMap.ext
 
-theorem ext_iff {f g : AlternatingMap R M N ι} : f = g ↔ ∀ x, f x = g x :=
+theorem ext_iff {f g : M [Λ^ι]→ₗ[R] N} : f = g ↔ ∀ x, f x = g x :=
   ⟨fun h _ => h ▸ rfl, fun h => ext h⟩
 #align alternating_map.ext_iff AlternatingMap.ext_iff
 
 attribute [coe] AlternatingMap.toMultilinearMap
 
-instance coe : Coe (AlternatingMap R M N ι) (MultilinearMap R (fun _ : ι => M) N) :=
+instance coe : Coe (M [Λ^ι]→ₗ[R] N) (MultilinearMap R (fun _ : ι => M) N) :=
   ⟨fun x => x.toMultilinearMap⟩
 #align alternating_map.multilinear_map.has_coe AlternatingMap.coe
 
@@ -158,7 +161,7 @@ theorem coe_multilinearMap : ⇑(f : MultilinearMap R (fun _ : ι => M) N) = f :
 #align alternating_map.coe_multilinear_map AlternatingMap.coe_multilinearMap
 
 theorem coe_multilinearMap_injective :
-    Function.Injective ((↑) : AlternatingMap R M N ι → MultilinearMap R (fun _ : ι => M) N) :=
+    Function.Injective ((↑) : M [Λ^ι]→ₗ[R] N → MultilinearMap R (fun _ : ι => M) N) :=
   fun _ _ h => ext <| MultilinearMap.congr_fun h
 #align alternating_map.coe_multilinear_map_injective AlternatingMap.coe_multilinearMap_injective
 
@@ -168,7 +171,7 @@ theorem coe_multilinearMap_injective :
 -- Porting note: removed `simp`
 -- @[simp]
 theorem coe_multilinearMap_mk (f : (ι → M) → N) (h₁ h₂ h₃) :
-    ((⟨⟨f, h₁, h₂⟩, h₃⟩ : AlternatingMap R M N ι) : MultilinearMap R (fun _ : ι => M) N) =
+    ((⟨⟨f, h₁, h₂⟩, h₃⟩ : M [Λ^ι]→ₗ[R] N) : MultilinearMap R (fun _ : ι => M) N) =
       ⟨f, @h₁, @h₂⟩ :=
   by simp
 #align alternating_map.coe_multilinear_map_mk AlternatingMap.coe_multilinearMap_mk
@@ -243,7 +246,7 @@ section SMul
 
 variable {S : Type*} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
 
-instance smul : SMul S (AlternatingMap R M N ι) :=
+instance smul : SMul S (M [Λ^ι]→ₗ[R] N) :=
   ⟨fun c f =>
     { c • (f : MultilinearMap R (fun _ : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }⟩
@@ -259,12 +262,12 @@ theorem coe_smul (c : S) : ↑(c • f) = c • (f : MultilinearMap R (fun _ : 
   rfl
 #align alternating_map.coe_smul AlternatingMap.coe_smul
 
-theorem coeFn_smul (c : S) (f : AlternatingMap R M N ι) : ⇑(c • f) = c • ⇑f :=
+theorem coeFn_smul (c : S) (f : M [Λ^ι]→ₗ[R] N) : ⇑(c • f) = c • ⇑f :=
   rfl
 #align alternating_map.coe_fn_smul AlternatingMap.coeFn_smul
 
 instance isCentralScalar [DistribMulAction Sᵐᵒᵖ N] [IsCentralScalar S N] :
-    IsCentralScalar S (AlternatingMap R M N ι) :=
+    IsCentralScalar S (M [Λ^ι]→ₗ[R] N) :=
   ⟨fun _ _ => ext fun _ => op_smul_eq_smul _ _⟩
 #align alternating_map.is_central_scalar AlternatingMap.isCentralScalar
 
@@ -272,7 +275,7 @@ end SMul
 
 /-- The cartesian product of two alternating maps, as an alternating map. -/
 @[simps!]
-def prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) : AlternatingMap R M (N × P) ι :=
+def prod (f : M [Λ^ι]→ₗ[R] N) (g : M [Λ^ι]→ₗ[R] P) : M [Λ^ι]→ₗ[R] (N × P) :=
   { f.toMultilinearMap.prod g.toMultilinearMap with
     map_eq_zero_of_eq' := fun _ _ _ h hne =>
       Prod.ext (f.map_eq_zero_of_eq _ h hne) (g.map_eq_zero_of_eq _ h hne) }
@@ -280,7 +283,7 @@ def prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) : Alternati
 #align alternating_map.prod_apply AlternatingMap.prod_apply
 
 @[simp]
-theorem coe_prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) :
+theorem coe_prod (f : M [Λ^ι]→ₗ[R] N) (g : M [Λ^ι]→ₗ[R] P) :
     (f.prod g : MultilinearMap R (fun _ : ι => M) (N × P)) = MultilinearMap.prod f g :=
   rfl
 #align alternating_map.coe_prod AlternatingMap.coe_prod
@@ -289,7 +292,7 @@ theorem coe_prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) :
 alternating map taking values in the space of functions `Π i, N i`. -/
 @[simps!]
 def pi {ι' : Type*} {N : ι' → Type*} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
-    (f : ∀ i, AlternatingMap R M (N i) ι) : AlternatingMap R M (∀ i, N i) ι :=
+    (f : ∀ i, M [Λ^ι]→ₗ[R] N i) : M [Λ^ι]→ₗ[R] (∀ i, N i) :=
   { MultilinearMap.pi fun a => (f a).toMultilinearMap with
     map_eq_zero_of_eq' := fun _ _ _ h hne => funext fun a => (f a).map_eq_zero_of_eq _ h hne }
 #align alternating_map.pi AlternatingMap.pi
@@ -297,7 +300,7 @@ def pi {ι' : Type*} {N : ι' → Type*} [∀ i, AddCommMonoid (N i)] [∀ i, Mo
 
 @[simp]
 theorem coe_pi {ι' : Type*} {N : ι' → Type*} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
-    (f : ∀ i, AlternatingMap R M (N i) ι) :
+    (f : ∀ i, M [Λ^ι]→ₗ[R] N i) :
     (pi f : MultilinearMap R (fun _ : ι => M) (∀ i, N i)) = MultilinearMap.pi fun a => f a :=
   rfl
 #align alternating_map.coe_pi AlternatingMap.coe_pi
@@ -306,7 +309,7 @@ theorem coe_pi {ι' : Type*} {N : ι' → Type*} [∀ i, AddCommMonoid (N i)] [
 sending `m` to `f m • z`. -/
 @[simps!]
 def smulRight {R M₁ M₂ ι : Type*} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
-    [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) : AlternatingMap R M₁ M₂ ι :=
+    [Module R M₁] [Module R M₂] (f : M₁ [Λ^ι]→ₗ[R] R) (z : M₂) : M₁ [Λ^ι]→ₗ[R] M₂ :=
   { f.toMultilinearMap.smulRight z with
     map_eq_zero_of_eq' := fun v i j h hne => by simp [f.map_eq_zero_of_eq v h hne] }
 #align alternating_map.smul_right AlternatingMap.smulRight
@@ -314,12 +317,12 @@ def smulRight {R M₁ M₂ ι : Type*} [CommSemiring R] [AddCommMonoid M₁] [Ad
 
 @[simp]
 theorem coe_smulRight {R M₁ M₂ ι : Type*} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
-    [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) :
+    [Module R M₁] [Module R M₂] (f : M₁ [Λ^ι]→ₗ[R] R) (z : M₂) :
     (f.smulRight z : MultilinearMap R (fun _ : ι => M₁) M₂) = MultilinearMap.smulRight f z :=
   rfl
 #align alternating_map.coe_smul_right AlternatingMap.coe_smulRight
 
-instance add : Add (AlternatingMap R M N ι) :=
+instance add : Add (M [Λ^ι]→ₗ[R] N) :=
   ⟨fun a b =>
     { (a + b : MultilinearMap R (fun _ : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by
@@ -336,35 +339,35 @@ theorem coe_add : (↑(f + f') : MultilinearMap R (fun _ : ι => M) N) = f + f'
   rfl
 #align alternating_map.coe_add AlternatingMap.coe_add
 
-instance zero : Zero (AlternatingMap R M N ι) :=
+instance zero : Zero (M [Λ^ι]→ₗ[R] N) :=
   ⟨{ (0 : MultilinearMap R (fun _ : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j _ _ => by simp }⟩
 #align alternating_map.has_zero AlternatingMap.zero
 
 @[simp]
-theorem zero_apply : (0 : AlternatingMap R M N ι) v = 0 :=
+theorem zero_apply : (0 : M [Λ^ι]→ₗ[R] N) v = 0 :=
   rfl
 #align alternating_map.zero_apply AlternatingMap.zero_apply
 
 @[norm_cast]
-theorem coe_zero : ((0 : AlternatingMap R M N ι) : MultilinearMap R (fun _ : ι => M) N) = 0 :=
+theorem coe_zero : ((0 : M [Λ^ι]→ₗ[R] N) : MultilinearMap R (fun _ : ι => M) N) = 0 :=
   rfl
 #align alternating_map.coe_zero AlternatingMap.coe_zero
 
 @[simp]
 theorem mk_zero :
-    mk (0 : MultilinearMap R (fun _ : ι ↦ M) N) (0 : AlternatingMap R M N ι).2 = 0 :=
+    mk (0 : MultilinearMap R (fun _ : ι ↦ M) N) (0 : M [Λ^ι]→ₗ[R] N).2 = 0 :=
   rfl
 
-instance inhabited : Inhabited (AlternatingMap R M N ι) :=
+instance inhabited : Inhabited (M [Λ^ι]→ₗ[R] N) :=
   ⟨0⟩
 #align alternating_map.inhabited AlternatingMap.inhabited
 
-instance addCommMonoid : AddCommMonoid (AlternatingMap R M N ι) :=
+instance addCommMonoid : AddCommMonoid (M [Λ^ι]→ₗ[R] N) :=
   coe_injective.addCommMonoid _ rfl (fun _ _ => rfl) fun _ _ => coeFn_smul _ _
 #align alternating_map.add_comm_monoid AlternatingMap.addCommMonoid
 
-instance neg : Neg (AlternatingMap R M N' ι) :=
+instance neg : Neg (M [Λ^ι]→ₗ[R] N') :=
   ⟨fun f =>
     { -(f : MultilinearMap R (fun _ : ι => M) N') with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }⟩
@@ -376,11 +379,11 @@ theorem neg_apply (m : ι → M) : (-g) m = -g m :=
 #align alternating_map.neg_apply AlternatingMap.neg_apply
 
 @[norm_cast]
-theorem coe_neg : ((-g : AlternatingMap R M N' ι) : MultilinearMap R (fun _ : ι => M) N') = -g :=
+theorem coe_neg : ((-g : M [Λ^ι]→ₗ[R] N') : MultilinearMap R (fun _ : ι => M) N') = -g :=
   rfl
 #align alternating_map.coe_neg AlternatingMap.coe_neg
 
-instance sub : Sub (AlternatingMap R M N' ι) :=
+instance sub : Sub (M [Λ^ι]→ₗ[R] N') :=
   ⟨fun f g =>
     { (f - g : MultilinearMap R (fun _ : ι => M) N') with
       map_eq_zero_of_eq' := fun v i j h hij => by
@@ -397,7 +400,7 @@ theorem coe_sub : (↑(g - g₂) : MultilinearMap R (fun _ : ι => M) N') = g -
   rfl
 #align alternating_map.coe_sub AlternatingMap.coe_sub
 
-instance addCommGroup : AddCommGroup (AlternatingMap R M N' ι) :=
+instance addCommGroup : AddCommGroup (M [Λ^ι]→ₗ[R] N') :=
   coe_injective.addCommGroup _ rfl (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl)
     (fun _ _ => coeFn_smul _ _) fun _ _ => coeFn_smul _ _
 #align alternating_map.add_comm_group AlternatingMap.addCommGroup
@@ -405,7 +408,7 @@ section DistribMulAction
 
 variable {S : Type*} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
 
-instance distribMulAction : DistribMulAction S (AlternatingMap R M N ι) where
+instance distribMulAction : DistribMulAction S (M [Λ^ι]→ₗ[R] N) where
   one_smul _ := ext fun _ => one_smul _ _
   mul_smul _ _ _ := ext fun _ => mul_smul _ _ _
   smul_zero _ := ext fun _ => smul_zero _
@@ -420,13 +423,13 @@ variable {S : Type*} [Semiring S] [Module S N] [SMulCommClass R S N]
 
 /-- The space of multilinear maps over an algebra over `R` is a module over `R`, for the pointwise
 addition and scalar multiplication. -/
-instance module : Module S (AlternatingMap R M N ι) where
+instance module : Module S (M [Λ^ι]→ₗ[R] N) where
   add_smul _ _ _ := ext fun _ => add_smul _ _ _
   zero_smul _ := ext fun _ => zero_smul _ _
 #align alternating_map.module AlternatingMap.module
 
 instance noZeroSMulDivisors [NoZeroSMulDivisors S N] :
-    NoZeroSMulDivisors S (AlternatingMap R M N ι) :=
+    NoZeroSMulDivisors S (M [Λ^ι]→ₗ[R] N) :=
   coe_injective.noZeroSMulDivisors _ rfl coeFn_smul
 #align alternating_map.no_zero_smul_divisors AlternatingMap.noZeroSMulDivisors
 
@@ -439,7 +442,7 @@ variable (R M N)
 /-- The natural equivalence between linear maps from `M` to `N`
 and `1`-multilinear alternating maps from `M` to `N`. -/
 @[simps!]
-def ofSubsingleton [Subsingleton ι] (i : ι) : (M →ₗ[R] N) ≃ AlternatingMap R M N ι where
+def ofSubsingleton [Subsingleton ι] (i : ι) : (M →ₗ[R] N) ≃ (M [Λ^ι]→ₗ[R] N) where
   toFun f := ⟨MultilinearMap.ofSubsingleton R M N i f, fun _ _ _ _ ↦ absurd (Subsingleton.elim _ _)⟩
   invFun f := (MultilinearMap.ofSubsingleton R M N i).symm f
   left_inv _ := rfl
@@ -452,7 +455,7 @@ variable (ι) {N}
 
 /-- The constant map is alternating when `ι` is empty. -/
 @[simps (config := .asFn)]
-def constOfIsEmpty [IsEmpty ι] (m : N) : AlternatingMap R M N ι :=
+def constOfIsEmpty [IsEmpty ι] (m : N) : M [Λ^ι]→ₗ[R] N :=
   { MultilinearMap.constOfIsEmpty R _ m with
     toFun := Function.const _ m
     map_eq_zero_of_eq' := fun _ => isEmptyElim }
@@ -463,8 +466,8 @@ end
 
 /-- Restrict the codomain of an alternating map to a submodule. -/
 @[simps]
-def codRestrict (f : AlternatingMap R M N ι) (p : Submodule R N) (h : ∀ v, f v ∈ p) :
-    AlternatingMap R M p ι :=
+def codRestrict (f : M [Λ^ι]→ₗ[R] N) (p : Submodule R N) (h : ∀ v, f v ∈ p) :
+    M [Λ^ι]→ₗ[R] p :=
   { f.toMultilinearMap.codRestrict p h with
     toFun := fun v => ⟨f v, h v⟩
     map_eq_zero_of_eq' := fun _ _ _ hv hij => Subtype.ext <| map_eq_zero_of_eq _ _ hv hij }
@@ -483,7 +486,7 @@ namespace LinearMap
 variable {N₂ : Type*} [AddCommMonoid N₂] [Module R N₂]
 
 /-- Composing an alternating map with a linear map on the left gives again an alternating map. -/
-def compAlternatingMap (g : N →ₗ[R] N₂) : AlternatingMap R M N ι →+ AlternatingMap R M N₂ ι where
+def compAlternatingMap (g : N →ₗ[R] N₂) : (M [Λ^ι]→ₗ[R] N) →+ (M [Λ^ι]→ₗ[R] N₂) where
   toFun f :=
     { g.compMultilinearMap (f : MultilinearMap R (fun _ : ι => M) N) with
       map_eq_zero_of_eq' := fun v i j h hij => by simp [f.map_eq_zero_of_eq v h hij] }
@@ -496,31 +499,31 @@ def compAlternatingMap (g : N →ₗ[R] N₂) : AlternatingMap R M N ι →+ Alt
 #align linear_map.comp_alternating_map LinearMap.compAlternatingMap
 
 @[simp]
-theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) :
+theorem coe_compAlternatingMap (g : N →ₗ[R] N₂) (f : M [Λ^ι]→ₗ[R] N) :
     ⇑(g.compAlternatingMap f) = g ∘ f :=
   rfl
 #align linear_map.coe_comp_alternating_map LinearMap.coe_compAlternatingMap
 
 @[simp]
-theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι) (m : ι → M) :
+theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : M [Λ^ι]→ₗ[R] N) (m : ι → M) :
     g.compAlternatingMap f m = g (f m) :=
   rfl
 #align linear_map.comp_alternating_map_apply LinearMap.compAlternatingMap_apply
 
 theorem smulRight_eq_comp {R M₁ M₂ ι : Type*} [CommSemiring R] [AddCommMonoid M₁]
-    [AddCommMonoid M₂] [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) :
+    [AddCommMonoid M₂] [Module R M₁] [Module R M₂] (f : M₁ [Λ^ι]→ₗ[R] R) (z : M₂) :
     f.smulRight z = (LinearMap.id.smulRight z).compAlternatingMap f :=
   rfl
 #align linear_map.smul_right_eq_comp LinearMap.smulRight_eq_comp
 
 @[simp]
-theorem subtype_compAlternatingMap_codRestrict (f : AlternatingMap R M N ι) (p : Submodule R N)
+theorem subtype_compAlternatingMap_codRestrict (f : M [Λ^ι]→ₗ[R] N) (p : Submodule R N)
     (h) : p.subtype.compAlternatingMap (f.codRestrict p h) = f :=
   AlternatingMap.ext fun _ => rfl
 #align linear_map.subtype_comp_alternating_map_cod_restrict LinearMap.subtype_compAlternatingMap_codRestrict
 
 @[simp]
-theorem compAlternatingMap_codRestrict (g : N →ₗ[R] N₂) (f : AlternatingMap R M N ι)
+theorem compAlternatingMap_codRestrict (g : N →ₗ[R] N₂) (f : M [Λ^ι]→ₗ[R] N)
     (p : Submodule R N₂) (h) :
     (g.codRestrict p h).compAlternatingMap f =
       (g.compAlternatingMap f).codRestrict p fun v => h (f v) :=
@@ -537,44 +540,44 @@ variable {M₃ : Type*} [AddCommMonoid M₃] [Module R M₃]
 
 /-- Composing an alternating map with the same linear map on each argument gives again an
 alternating map. -/
-def compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) : AlternatingMap R M₂ N ι :=
+def compLinearMap (f : M [Λ^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) : M₂ [Λ^ι]→ₗ[R] N :=
   { (f : MultilinearMap R (fun _ : ι => M) N).compLinearMap fun _ => g with
     map_eq_zero_of_eq' := fun _ _ _ h hij => f.map_eq_zero_of_eq _ (LinearMap.congr_arg h) hij }
 #align alternating_map.comp_linear_map AlternatingMap.compLinearMap
 
-theorem coe_compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
+theorem coe_compLinearMap (f : M [Λ^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) :
     ⇑(f.compLinearMap g) = f ∘ (· ∘ ·) g :=
   rfl
 #align alternating_map.coe_comp_linear_map AlternatingMap.coe_compLinearMap
 
 @[simp]
-theorem compLinearMap_apply (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) (v : ι → M₂) :
+theorem compLinearMap_apply (f : M [Λ^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) (v : ι → M₂) :
     f.compLinearMap g v = f fun i => g (v i) :=
   rfl
 #align alternating_map.comp_linear_map_apply AlternatingMap.compLinearMap_apply
 
 /-- Composing an alternating map twice with the same linear map in each argument is
 the same as composing with their composition. -/
-theorem compLinearMap_assoc (f : AlternatingMap R M N ι) (g₁ : M₂ →ₗ[R] M) (g₂ : M₃ →ₗ[R] M₂) :
+theorem compLinearMap_assoc (f : M [Λ^ι]→ₗ[R] N) (g₁ : M₂ →ₗ[R] M) (g₂ : M₃ →ₗ[R] M₂) :
     (f.compLinearMap g₁).compLinearMap g₂ = f.compLinearMap (g₁ ∘ₗ g₂) :=
   rfl
 #align alternating_map.comp_linear_map_assoc AlternatingMap.compLinearMap_assoc
 
 @[simp]
-theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : AlternatingMap R M N ι).compLinearMap g = 0 := by
+theorem zero_compLinearMap (g : M₂ →ₗ[R] M) : (0 : M [Λ^ι]→ₗ[R] N).compLinearMap g = 0 := by
   ext
   simp only [compLinearMap_apply, zero_apply]
 #align alternating_map.zero_comp_linear_map AlternatingMap.zero_compLinearMap
 
 @[simp]
-theorem add_compLinearMap (f₁ f₂ : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) :
+theorem add_compLinearMap (f₁ f₂ : M [Λ^ι]→ₗ[R] N) (g : M₂ →ₗ[R] M) :
     (f₁ + f₂).compLinearMap g = f₁.compLinearMap g + f₂.compLinearMap g := by
   ext
   simp only [compLinearMap_apply, add_apply]
 #align alternating_map.add_comp_linear_map AlternatingMap.add_compLinearMap
 
 @[simp]
-theorem compLinearMap_zero [Nonempty ι] (f : AlternatingMap R M N ι) :
+theorem compLinearMap_zero [Nonempty ι] (f : M [Λ^ι]→ₗ[R] N) :
     f.compLinearMap (0 : M₂ →ₗ[R] M) = 0 := by
   ext
   -- Porting note: Was `simp_rw [.., ← Pi.zero_def, map_zero, zero_apply]`.
@@ -584,18 +587,18 @@ theorem compLinearMap_zero [Nonempty ι] (f : AlternatingMap R M N ι) :
 
 /-- Composing an alternating map with the identity linear map in each argument. -/
 @[simp]
-theorem compLinearMap_id (f : AlternatingMap R M N ι) : f.compLinearMap LinearMap.id = f :=
+theorem compLinearMap_id (f : M [Λ^ι]→ₗ[R] N) : f.compLinearMap LinearMap.id = f :=
   ext fun _ => rfl
 #align alternating_map.comp_linear_map_id AlternatingMap.compLinearMap_id
 
 /-- Composing with a surjective linear map is injective. -/
 theorem compLinearMap_injective (f : M₂ →ₗ[R] M) (hf : Function.Surjective f) :
-    Function.Injective fun g : AlternatingMap R M N ι => g.compLinearMap f := fun g₁ g₂ h =>
+    Function.Injective fun g : M [Λ^ι]→ₗ[R] N => g.compLinearMap f := fun g₁ g₂ h =>
   ext fun x => by simpa [Function.surjInv_eq hf] using ext_iff.mp h (Function.surjInv hf ∘ x)
 #align alternating_map.comp_linear_map_injective AlternatingMap.compLinearMap_injective
 
 theorem compLinearMap_inj (f : M₂ →ₗ[R] M) (hf : Function.Surjective f)
-    (g₁ g₂ : AlternatingMap R M N ι) : g₁.compLinearMap f = g₂.compLinearMap f ↔ g₁ = g₂ :=
+    (g₁ g₂ : M [Λ^ι]→ₗ[R] N) : g₁.compLinearMap f = g₂.compLinearMap f ↔ g₁ = g₂ :=
   (compLinearMap_injective _ hf).eq_iff
 #align alternating_map.comp_linear_map_inj AlternatingMap.compLinearMap_inj
 
@@ -606,7 +609,7 @@ variable (S : Type*) [Semiring S] [Module S N] [SMulCommClass R S N]
 
 /-- Construct a linear equivalence between maps from a linear equivalence between domains. -/
 @[simps apply]
-def domLCongr (e : M ≃ₗ[R] M₂) : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M₂ N ι where
+def domLCongr (e : M ≃ₗ[R] M₂) : M [Λ^ι]→ₗ[R] N ≃ₗ[S] (M₂ [Λ^ι]→ₗ[R] N) where
   toFun f := f.compLinearMap e.symm
   invFun g := g.compLinearMap e
   map_add' _ _ := rfl
@@ -636,17 +639,14 @@ end DomLcongr
 /-- Composing an alternating map with the same linear equiv on each argument gives the zero map
 if and only if the alternating map is the zero map. -/
 @[simp]
-theorem compLinearEquiv_eq_zero_iff (f : AlternatingMap R M N ι) (g : M₂ ≃ₗ[R] M) :
+theorem compLinearEquiv_eq_zero_iff (f : M [Λ^ι]→ₗ[R] N) (g : M₂ ≃ₗ[R] M) :
     f.compLinearMap (g : M₂ →ₗ[R] M) = 0 ↔ f = 0 :=
   (domLCongr R N ι ℕ g.symm).map_eq_zero_iff
 #align alternating_map.comp_linear_equiv_eq_zero_iff AlternatingMap.compLinearEquiv_eq_zero_iff
 
-variable (f f' : AlternatingMap R M N ι)
-
-variable (g g₂ : AlternatingMap R M N' ι)
-
-variable (g' : AlternatingMap R M' N' ι)
-
+variable (f f' : M [Λ^ι]→ₗ[R] N)
+variable (g g₂ : M [Λ^ι]→ₗ[R] N')
+variable (g' : M' [Λ^ι]→ₗ[R] N')
 variable (v : ι → M) (v' : ι → M')
 
 open Function
@@ -726,7 +726,7 @@ section DomDomCongr
 
 This is the alternating version of `MultilinearMap.domDomCongr`. -/
 @[simps]
-def domDomCongr (σ : ι ≃ ι') (f : AlternatingMap R M N ι) : AlternatingMap R M N ι' :=
+def domDomCongr (σ : ι ≃ ι') (f : M [Λ^ι]→ₗ[R] N) : M [Λ^ι']→ₗ[R] N :=
   { f.toMultilinearMap.domDomCongr σ with
     toFun := fun v => f (v ∘ σ)
     map_eq_zero_of_eq' := fun v i j hv hij =>
@@ -736,28 +736,28 @@ def domDomCongr (σ : ι ≃ ι') (f : AlternatingMap R M N ι) : AlternatingMap
 #align alternating_map.dom_dom_congr_apply AlternatingMap.domDomCongr_apply
 
 @[simp]
-theorem domDomCongr_refl (f : AlternatingMap R M N ι) : f.domDomCongr (Equiv.refl ι) = f := rfl
+theorem domDomCongr_refl (f : M [Λ^ι]→ₗ[R] N) : f.domDomCongr (Equiv.refl ι) = f := rfl
 #align alternating_map.dom_dom_congr_refl AlternatingMap.domDomCongr_refl
 
-theorem domDomCongr_trans (σ₁ : ι ≃ ι') (σ₂ : ι' ≃ ι'') (f : AlternatingMap R M N ι) :
+theorem domDomCongr_trans (σ₁ : ι ≃ ι') (σ₂ : ι' ≃ ι'') (f : M [Λ^ι]→ₗ[R] N) :
     f.domDomCongr (σ₁.trans σ₂) = (f.domDomCongr σ₁).domDomCongr σ₂ :=
   rfl
 #align alternating_map.dom_dom_congr_trans AlternatingMap.domDomCongr_trans
 
 @[simp]
-theorem domDomCongr_zero (σ : ι ≃ ι') : (0 : AlternatingMap R M N ι).domDomCongr σ = 0 :=
+theorem domDomCongr_zero (σ : ι ≃ ι') : (0 : M [Λ^ι]→ₗ[R] N).domDomCongr σ = 0 :=
   rfl
 #align alternating_map.dom_dom_congr_zero AlternatingMap.domDomCongr_zero
 
 @[simp]
-theorem domDomCongr_add (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
+theorem domDomCongr_add (σ : ι ≃ ι') (f g : M [Λ^ι]→ₗ[R] N) :
     (f + g).domDomCongr σ = f.domDomCongr σ + g.domDomCongr σ :=
   rfl
 #align alternating_map.dom_dom_congr_add AlternatingMap.domDomCongr_add
 
 @[simp]
 theorem domDomCongr_smul {S : Type*} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
-    (σ : ι ≃ ι') (c : S) (f : AlternatingMap R M N ι) :
+    (σ : ι ≃ ι') (c : S) (f : M [Λ^ι]→ₗ[R] N) :
     (c • f).domDomCongr σ = c • f.domDomCongr σ :=
   rfl
 #align alternating_map.dom_dom_congr_smul AlternatingMap.domDomCongr_smul
@@ -766,7 +766,7 @@ theorem domDomCongr_smul {S : Type*} [Monoid S] [DistribMulAction S N] [SMulComm
 
 This is declared separately because it does not work with dot notation. -/
 @[simps apply symm_apply]
-def domDomCongrEquiv (σ : ι ≃ ι') : AlternatingMap R M N ι ≃+ AlternatingMap R M N ι' where
+def domDomCongrEquiv (σ : ι ≃ ι') : M [Λ^ι]→ₗ[R] N ≃+ M [Λ^ι']→ₗ[R] N where
   toFun := domDomCongr σ
   invFun := domDomCongr σ.symm
   left_inv f := by
@@ -786,42 +786,42 @@ variable (S : Type*) [Semiring S] [Module S N] [SMulCommClass R S N]
 
 /-- `AlternatingMap.domDomCongr` as a linear equivalence. -/
 @[simps apply symm_apply]
-def domDomLcongr (σ : ι ≃ ι') : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι' where
+def domDomCongrₗ (σ : ι ≃ ι') : M [Λ^ι]→ₗ[R] N ≃ₗ[S] M [Λ^ι']→ₗ[R] N where
   toFun := domDomCongr σ
   invFun := domDomCongr σ.symm
   left_inv f := by ext; simp [Function.comp]
   right_inv m := by ext; simp [Function.comp]
   map_add' := domDomCongr_add σ
   map_smul' := domDomCongr_smul σ
-#align alternating_map.dom_dom_lcongr AlternatingMap.domDomLcongr
+#align alternating_map.dom_dom_lcongr AlternatingMap.domDomCongrₗ
 
 @[simp]
-theorem domDomLcongr_refl :
-    (domDomLcongr S (Equiv.refl ι) : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι) =
+theorem domDomCongrₗ_refl :
+    (domDomCongrₗ S (Equiv.refl ι) : M [Λ^ι]→ₗ[R] N ≃ₗ[S] M [Λ^ι]→ₗ[R] N) =
       LinearEquiv.refl _ _ :=
   rfl
-#align alternating_map.dom_dom_lcongr_refl AlternatingMap.domDomLcongr_refl
+#align alternating_map.dom_dom_lcongr_refl AlternatingMap.domDomCongrₗ_refl
 
 @[simp]
-theorem domDomLcongr_toAddEquiv (σ : ι ≃ ι') :
-    (↑(domDomLcongr S σ : AlternatingMap R M N ι ≃ₗ[S] _) : AlternatingMap R M N ι ≃+ _) =
+theorem domDomCongrₗ_toAddEquiv (σ : ι ≃ ι') :
+    (↑(domDomCongrₗ S σ : M [Λ^ι]→ₗ[R] N ≃ₗ[S] _) : M [Λ^ι]→ₗ[R] N ≃+ _) =
       domDomCongrEquiv σ :=
   rfl
-#align alternating_map.dom_dom_lcongr_to_add_equiv AlternatingMap.domDomLcongr_toAddEquiv
+#align alternating_map.dom_dom_lcongr_to_add_equiv AlternatingMap.domDomCongrₗ_toAddEquiv
 
 end DomDomLcongr
 
 /-- The results of applying `domDomCongr` to two maps are equal if and only if those maps are. -/
 @[simp]
-theorem domDomCongr_eq_iff (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
+theorem domDomCongr_eq_iff (σ : ι ≃ ι') (f g : M [Λ^ι]→ₗ[R] N) :
     f.domDomCongr σ = g.domDomCongr σ ↔ f = g :=
-  (domDomCongrEquiv σ : _ ≃+ AlternatingMap R M N ι').apply_eq_iff_eq
+  (domDomCongrEquiv σ : _ ≃+ M [Λ^ι']→ₗ[R] N).apply_eq_iff_eq
 #align alternating_map.dom_dom_congr_eq_iff AlternatingMap.domDomCongr_eq_iff
 
 @[simp]
-theorem domDomCongr_eq_zero_iff (σ : ι ≃ ι') (f : AlternatingMap R M N ι) :
+theorem domDomCongr_eq_zero_iff (σ : ι ≃ ι') (f : M [Λ^ι]→ₗ[R] N) :
     f.domDomCongr σ = 0 ↔ f = 0 :=
-  (domDomCongrEquiv σ : AlternatingMap R M N ι ≃+ AlternatingMap R M N ι').map_eq_zero_iff
+  (domDomCongrEquiv σ : M [Λ^ι]→ₗ[R] N ≃+ M [Λ^ι']→ₗ[R] N).map_eq_zero_iff
 #align alternating_map.dom_dom_congr_eq_zero_iff AlternatingMap.domDomCongr_eq_zero_iff
 
 theorem domDomCongr_perm [Fintype ι] [DecidableEq ι] (σ : Equiv.Perm ι) :
@@ -839,7 +839,7 @@ end DomDomCongr
 
 /-- If the arguments are linearly dependent then the result is `0`. -/
 theorem map_linearDependent {K : Type*} [Ring K] {M : Type*} [AddCommGroup M] [Module K M]
-    {N : Type*} [AddCommGroup N] [Module K N] [NoZeroSMulDivisors K N] (f : AlternatingMap K M N ι)
+    {N : Type*} [AddCommGroup N] [Module K N] [NoZeroSMulDivisors K N] (f : M [Λ^ι]→ₗ[K] N)
     (v : ι → M) (h : ¬LinearIndependent K v) : f v = 0 := by
   obtain ⟨s, g, h, i, hi, hz⟩ := not_linearIndependent_iff.mp h
   letI := Classical.decEq ι
@@ -861,13 +861,13 @@ section Fin
 open Fin
 
 /-- A version of `MultilinearMap.cons_add` for `AlternatingMap`. -/
-theorem map_vecCons_add {n : ℕ} (f : AlternatingMap R M N (Fin n.succ)) (m : Fin n → M) (x y : M) :
+theorem map_vecCons_add {n : ℕ} (f : M [Λ^Fin n.succ]→ₗ[R] N) (m : Fin n → M) (x y : M) :
     f (Matrix.vecCons (x + y) m) = f (Matrix.vecCons x m) + f (Matrix.vecCons y m) :=
   f.toMultilinearMap.cons_add _ _ _
 #align alternating_map.map_vec_cons_add AlternatingMap.map_vecCons_add
 
 /-- A version of `MultilinearMap.cons_smul` for `AlternatingMap`. -/
-theorem map_vecCons_smul {n : ℕ} (f : AlternatingMap R M N (Fin n.succ)) (m : Fin n → M) (c : R)
+theorem map_vecCons_smul {n : ℕ} (f : M [Λ^Fin n.succ]→ₗ[R] N) (m : Fin n → M) (c : R)
     (x : M) : f (Matrix.vecCons (c • x) m) = c • f (Matrix.vecCons x m) :=
   f.toMultilinearMap.cons_smul _ _ _
 #align alternating_map.map_vec_cons_smul AlternatingMap.map_vecCons_smul
@@ -897,7 +897,7 @@ private theorem alternization_map_eq_zero_of_eq_aux (m : MultilinearMap R (fun _
 
 /-- Produce an `AlternatingMap` out of a `MultilinearMap`, by summing over all argument
 permutations. -/
-def alternatization : MultilinearMap R (fun _ : ι => M) N' →+ AlternatingMap R M N' ι where
+def alternatization : MultilinearMap R (fun _ : ι => M) N' →+ M [Λ^ι]→ₗ[R] N' where
   toFun m :=
     { ∑ σ : Perm ι, Equiv.Perm.sign σ • m.domDomCongr σ with
       toFun := ⇑(∑ σ : Perm ι, Equiv.Perm.sign σ • m.domDomCongr σ)
@@ -934,7 +934,7 @@ namespace AlternatingMap
 
 /-- Alternatizing a multilinear map that is already alternating results in a scale factor of `n!`,
 where `n` is the number of inputs. -/
-theorem coe_alternatization [DecidableEq ι] [Fintype ι] (a : AlternatingMap R M N' ι) :
+theorem coe_alternatization [DecidableEq ι] [Fintype ι] (a : M [Λ^ι]→ₗ[R] N') :
     MultilinearMap.alternatization (a : MultilinearMap R (fun _ => M) N')
     = Nat.factorial (Fintype.card ι) • a := by
   apply AlternatingMap.coe_injective
@@ -972,7 +972,7 @@ variable [Module R' N₁] [Module R' N₂]
 
 /-- Two alternating maps indexed by a `Fintype` are equal if they are equal when all arguments
 are distinct basis vectors. -/
-theorem Basis.ext_alternating {f g : AlternatingMap R' N₁ N₂ ι} (e : Basis ι₁ R' N₁)
+theorem Basis.ext_alternating {f g : N₁ [Λ^ι]→ₗ[R'] N₂} (e : Basis ι₁ R' N₁)
     (h : ∀ v : ι → ι₁, Function.Injective v → (f fun i => e (v i)) = g fun i => e (v i)) :
     f = g := by
   classical
@@ -1004,8 +1004,8 @@ It can be thought of as a map $Hom(\bigwedge^{n+1} M, N) \to Hom(M, Hom(\bigwedg
 This is `MultilinearMap.curryLeft` for `AlternatingMap`. See also
 `AlternatingMap.curryLeftLinearMap`. -/
 @[simps]
-def curryLeft {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ)) :
-    M'' →ₗ[R'] AlternatingMap R' M'' N'' (Fin n) where
+def curryLeft {n : ℕ} (f : M'' [Λ^Fin n.succ]→ₗ[R'] N'') :
+    M'' →ₗ[R'] M'' [Λ^Fin n]→ₗ[R'] N'' where
   toFun m :=
     { f.toMultilinearMap.curryLeft m with
       toFun := fun v => f (Matrix.vecCons m v)
@@ -1018,18 +1018,18 @@ def curryLeft {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ)) :
 #align alternating_map.curry_left_apply_apply AlternatingMap.curryLeft_apply_apply
 
 @[simp]
-theorem curryLeft_zero {n : ℕ} : curryLeft (0 : AlternatingMap R' M'' N'' (Fin n.succ)) = 0 :=
+theorem curryLeft_zero {n : ℕ} : curryLeft (0 : M'' [Λ^Fin n.succ]→ₗ[R'] N'') = 0 :=
   rfl
 #align alternating_map.curry_left_zero AlternatingMap.curryLeft_zero
 
 @[simp]
-theorem curryLeft_add {n : ℕ} (f g : AlternatingMap R' M'' N'' (Fin n.succ)) :
+theorem curryLeft_add {n : ℕ} (f g : M'' [Λ^Fin n.succ]→ₗ[R'] N'') :
     curryLeft (f + g) = curryLeft f + curryLeft g :=
   rfl
 #align alternating_map.curry_left_add AlternatingMap.curryLeft_add
 
 @[simp]
-theorem curryLeft_smul {n : ℕ} (r : R') (f : AlternatingMap R' M'' N'' (Fin n.succ)) :
+theorem curryLeft_smul {n : ℕ} (r : R') (f : M'' [Λ^Fin n.succ]→ₗ[R'] N'') :
     curryLeft (r • f) = r • curryLeft f :=
   rfl
 #align alternating_map.curry_left_smul AlternatingMap.curryLeft_smul
@@ -1038,7 +1038,7 @@ theorem curryLeft_smul {n : ℕ} (r : R') (f : AlternatingMap R' M'' N'' (Fin n.
 does not work for this version. -/
 @[simps]
 def curryLeftLinearMap {n : ℕ} :
-    AlternatingMap R' M'' N'' (Fin n.succ) →ₗ[R'] M'' →ₗ[R'] AlternatingMap R' M'' N'' (Fin n) where
+    (M'' [Λ^Fin n.succ]→ₗ[R'] N'') →ₗ[R'] M'' →ₗ[R'] M'' [Λ^Fin n]→ₗ[R'] N'' where
   toFun f := f.curryLeft
   map_add' := curryLeft_add
   map_smul' := curryLeft_smul
@@ -1047,21 +1047,21 @@ def curryLeftLinearMap {n : ℕ} :
 
 /-- Currying with the same element twice gives the zero map. -/
 @[simp]
-theorem curryLeft_same {n : ℕ} (f : AlternatingMap R' M'' N'' (Fin n.succ.succ)) (m : M'') :
+theorem curryLeft_same {n : ℕ} (f : M'' [Λ^Fin n.succ.succ]→ₗ[R'] N'') (m : M'') :
     (f.curryLeft m).curryLeft m = 0 :=
   ext fun x => f.map_eq_zero_of_eq _ (by simp) Fin.zero_ne_one
 #align alternating_map.curry_left_same AlternatingMap.curryLeft_same
 
 @[simp]
 theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
-    (f : AlternatingMap R' M'' N'' (Fin n.succ)) (m : M'') :
+    (f : M'' [Λ^Fin n.succ]→ₗ[R'] N'') (m : M'') :
     (g.compAlternatingMap f).curryLeft m = g.compAlternatingMap (f.curryLeft m) :=
   rfl
 #align alternating_map.curry_left_comp_alternating_map AlternatingMap.curryLeft_compAlternatingMap
 
 @[simp]
 theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')
-    (f : AlternatingMap R' M'' N'' (Fin n.succ)) (m : M₂'') :
+    (f : M'' [Λ^Fin n.succ]→ₗ[R'] N'') (m : M₂'') :
     (f.compLinearMap g).curryLeft m = (f.curryLeft (g m)).compLinearMap g :=
   ext fun v => congr_arg f <| funext <| by
     refine' Fin.cases _ _
@@ -1072,7 +1072,7 @@ theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')
 /-- The space of constant maps is equivalent to the space of maps that are alternating with respect
 to an empty family. -/
 @[simps]
-def constLinearEquivOfIsEmpty [IsEmpty ι] : N'' ≃ₗ[R'] AlternatingMap R' M'' N'' ι where
+def constLinearEquivOfIsEmpty [IsEmpty ι] : N'' ≃ₗ[R'] (M'' [Λ^ι]→ₗ[R'] N'') where
   toFun := AlternatingMap.constOfIsEmpty R' M'' ι
   map_add' _ _ := rfl
   map_smul' _ _ := rfl

Change MultilinearMap.ofSubsingleton and other similar definitions so that they are now equivalences between linear maps and 1-multilinear maps.

@@ -434,19 +434,21 @@ end Module
 
 section
 
-variable (R M)
+variable (R M N)
 
-/-- The evaluation map from `ι → M` to `M` at a given `i` is alternating when `ι` is subsingleton.
--/
-@[simps]
-def ofSubsingleton [Subsingleton ι] (i : ι) : AlternatingMap R M M ι :=
-  { MultilinearMap.ofSubsingleton R M i with
-    toFun := Function.eval i
-    map_eq_zero_of_eq' := fun _ _ _ _ hij => (hij <| Subsingleton.elim _ _).elim }
+/-- The natural equivalence between linear maps from `M` to `N`
+and `1`-multilinear alternating maps from `M` to `N`. -/
+@[simps!]
+def ofSubsingleton [Subsingleton ι] (i : ι) : (M →ₗ[R] N) ≃ AlternatingMap R M N ι where
+  toFun f := ⟨MultilinearMap.ofSubsingleton R M N i f, fun _ _ _ _ ↦ absurd (Subsingleton.elim _ _)⟩
+  invFun f := (MultilinearMap.ofSubsingleton R M N i).symm f
+  left_inv _ := rfl
+  right_inv _ := coe_multilinearMap_injective <|
+    (MultilinearMap.ofSubsingleton R M N i).apply_symm_apply _
 #align alternating_map.of_subsingleton AlternatingMap.ofSubsingleton
-#align alternating_map.of_subsingleton_apply AlternatingMap.ofSubsingleton_apply
+#align alternating_map.of_subsingleton_apply AlternatingMap.ofSubsingleton_apply_apply
 
-variable (ι)
+variable (ι) {N}
 
 /-- The constant map is alternating when `ι` is empty. -/
 @[simps (config := .asFn)]

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -255,8 +255,7 @@ theorem smul_apply (c : S) (m : ι → M) : (c • f) m = c • f m :=
 #align alternating_map.smul_apply AlternatingMap.smul_apply
 
 @[norm_cast]
-theorem coe_smul (c : S) : (c • f : MultilinearMap R (fun _ : ι => M) N) =
-    c • (f : MultilinearMap R (fun _ : ι => M) N) :=
+theorem coe_smul (c : S) : ↑(c • f) = c • (f : MultilinearMap R (fun _ : ι => M) N) :=
   rfl
 #align alternating_map.coe_smul AlternatingMap.coe_smul
 

Use .asFn and .lemmasOnly as simps configuration options.

For reference, these are defined here:

https://github.com/leanprover-community/mathlib4/blob/4055c8b471380825f07416b12cb0cf266da44d84/Mathlib/Tactic/Simps/Basic.lean#L843-L851

@@ -450,7 +450,7 @@ def ofSubsingleton [Subsingleton ι] (i : ι) : AlternatingMap R M M ι :=
 variable (ι)
 
 /-- The constant map is alternating when `ι` is empty. -/
-@[simps (config := { fullyApplied := false })]
+@[simps (config := .asFn)]
 def constOfIsEmpty [IsEmpty ι] (m : N) : AlternatingMap R M N ι :=
   { MultilinearMap.constOfIsEmpty R _ m with
     toFun := Function.const _ m

More principled version of #7281.

@@ -16,6 +16,8 @@ taking values in the tensor product of the codomains of the original maps.
 
 #align_import linear_algebra.alternating from "leanprover-community/mathlib"@"0c1d80f5a86b36c1db32e021e8d19ae7809d5b79"
 
+suppress_compilation
+
 open BigOperators TensorProduct
 
 variable {ιa ιb : Type*} [Fintype ιa] [Fintype ιb]

@@ -954,7 +954,7 @@ theorem compMultilinearMap_alternatization (g : N' →ₗ[R] N'₂)
     MultilinearMap.alternatization (g.compMultilinearMap f)
       = g.compAlternatingMap (MultilinearMap.alternatization f) := by
   ext
-  simp [MultilinearMap.alternatization_def, map_sum]
+  simp [MultilinearMap.alternatization_def]
 #align linear_map.comp_multilinear_map_alternatization LinearMap.compMultilinearMap_alternatization
 
 end LinearMap

And fix some names in comments where this revealed issues

@@ -783,7 +783,7 @@ section DomDomLcongr
 
 variable (S : Type*) [Semiring S] [Module S N] [SMulCommClass R S N]
 
-/-- `alternating_map.dom_dom_congr` as a linear equivalence. -/
+/-- `AlternatingMap.domDomCongr` as a linear equivalence. -/
 @[simps apply symm_apply]
 def domDomLcongr (σ : ι ≃ ι') : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι' where
   toFun := domDomCongr σ

Note that _root_.map_sum is not marked as @[simp].

@@ -954,7 +954,7 @@ theorem compMultilinearMap_alternatization (g : N' →ₗ[R] N'₂)
     MultilinearMap.alternatization (g.compMultilinearMap f)
       = g.compAlternatingMap (MultilinearMap.alternatization f) := by
   ext
-  simp [MultilinearMap.alternatization_def]
+  simp [MultilinearMap.alternatization_def, map_sum]
 #align linear_map.comp_multilinear_map_alternatization LinearMap.compMultilinearMap_alternatization
 
 end LinearMap

I'm going to refactor/expand API about domCoprod, and I don't want to rebuild the whole library when I do it.

I'm going to refactor/expand API about domCoprod, and I don't want to rebuild the whole library when I do it.

@@ -3,12 +3,9 @@ Copyright (c) 2020 Zhangir Azerbayev. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Zhangir Azerbayev
 -/
-import Mathlib.GroupTheory.GroupAction.Quotient
 import Mathlib.GroupTheory.Perm.Sign
-import Mathlib.GroupTheory.Perm.Subgroup
-import Mathlib.LinearAlgebra.LinearIndependent
+import Mathlib.Data.Fintype.Perm
 import Mathlib.LinearAlgebra.Multilinear.Basis
-import Mathlib.LinearAlgebra.Multilinear.TensorProduct
 
 #align_import linear_algebra.alternating from "leanprover-community/mathlib"@"0c1d80f5a86b36c1db32e021e8d19ae7809d5b79"
 
@@ -27,7 +24,6 @@ arguments of the same type.
   matches the definitions over `MultilinearMap`s.
 * `MultilinearMap.domDomCongr`, for permutating the elements within a family.
 * `MultilinearMap.alternatization`, which makes an alternating map out of a non-alternating one.
-* `AlternatingMap.domCoprod`, which behaves as a product between two alternating maps.
 * `AlternatingMap.curryLeft`, for binding the leftmost argument of an alternating map indexed
   by `Fin n.succ`.
 
@@ -739,8 +735,7 @@ def domDomCongr (σ : ι ≃ ι') (f : AlternatingMap R M N ι) : AlternatingMap
 #align alternating_map.dom_dom_congr_apply AlternatingMap.domDomCongr_apply
 
 @[simp]
-theorem domDomCongr_refl (f : AlternatingMap R M N ι) : f.domDomCongr (Equiv.refl ι) = f :=
-  ext fun _ => rfl
+theorem domDomCongr_refl (f : AlternatingMap R M N ι) : f.domDomCongr (Equiv.refl ι) = f := rfl
 #align alternating_map.dom_dom_congr_refl AlternatingMap.domDomCongr_refl
 
 theorem domDomCongr_trans (σ₁ : ι ≃ ι') (σ₂ : ι' ≃ ι'') (f : AlternatingMap R M N ι) :
@@ -790,8 +785,7 @@ variable (S : Type*) [Semiring S] [Module S N] [SMulCommClass R S N]
 
 /-- `alternating_map.dom_dom_congr` as a linear equivalence. -/
 @[simps apply symm_apply]
-def domDomLcongr (σ : ι ≃ ι') : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι'
-    where
+def domDomLcongr (σ : ι ≃ ι') : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι' where
   toFun := domDomCongr σ
   invFun := domDomCongr σ.symm
   left_inv f := by ext; simp [Function.comp]
@@ -804,7 +798,7 @@ def domDomLcongr (σ : ι ≃ ι') : AlternatingMap R M N ι ≃ₗ[S] Alternati
 theorem domDomLcongr_refl :
     (domDomLcongr S (Equiv.refl ι) : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι) =
       LinearEquiv.refl _ _ :=
-  LinearEquiv.ext domDomCongr_refl
+  rfl
 #align alternating_map.dom_dom_lcongr_refl AlternatingMap.domDomLcongr_refl
 
 @[simp]
@@ -965,281 +959,6 @@ theorem compMultilinearMap_alternatization (g : N' →ₗ[R] N'₂)
 
 end LinearMap
 
-section Coprod
-
-open BigOperators
-
-open TensorProduct
-
-variable {ιa ιb : Type*} [Fintype ιa] [Fintype ιb]
-
-variable {R' : Type*} {Mᵢ N₁ N₂ : Type*} [CommSemiring R'] [AddCommGroup N₁] [Module R' N₁]
-  [AddCommGroup N₂] [Module R' N₂] [AddCommMonoid Mᵢ] [Module R' Mᵢ]
-
-namespace Equiv.Perm
-
-/-- Elements which are considered equivalent if they differ only by swaps within α or β  -/
-abbrev ModSumCongr (α β : Type*) :=
-  _ ⧸ (Equiv.Perm.sumCongrHom α β).range
-#align equiv.perm.mod_sum_congr Equiv.Perm.ModSumCongr
-
-theorem ModSumCongr.swap_smul_involutive {α β : Type*} [DecidableEq (Sum α β)] (i j : Sum α β) :
-    Function.Involutive (SMul.smul (Equiv.swap i j) : ModSumCongr α β → ModSumCongr α β) :=
-  fun σ => by
-    refine Quotient.inductionOn' σ fun σ => ?_
-    exact _root_.congr_arg Quotient.mk'' (Equiv.swap_mul_involutive i j σ)
-#align equiv.perm.mod_sum_congr.swap_smul_involutive Equiv.Perm.ModSumCongr.swap_smul_involutive
-
-end Equiv.Perm
-
-namespace AlternatingMap
-
-open Equiv
-
-variable [DecidableEq ιa] [DecidableEq ιb]
-
-/-- summand used in `AlternatingMap.domCoprod` -/
-def domCoprod.summand (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
-    (σ : Perm.ModSumCongr ιa ιb) : MultilinearMap R' (fun _ : Sum ιa ιb => Mᵢ) (N₁ ⊗[R'] N₂) :=
-  Quotient.liftOn' σ
-    (fun σ =>
-      Equiv.Perm.sign σ •
-        (MultilinearMap.domCoprod ↑a ↑b : MultilinearMap R' (fun _ => Mᵢ) (N₁ ⊗ N₂)).domDomCongr σ)
-    fun σ₁ σ₂ H => by
-    rw [QuotientGroup.leftRel_apply] at H
-    obtain ⟨⟨sl, sr⟩, h⟩ := H
-    ext v
-    simp only [MultilinearMap.domDomCongr_apply, MultilinearMap.domCoprod_apply,
-      coe_multilinearMap, MultilinearMap.smul_apply]
-    replace h := inv_mul_eq_iff_eq_mul.mp h.symm
-    have : Equiv.Perm.sign (σ₁ * Perm.sumCongrHom _ _ (sl, sr))
-      = Equiv.Perm.sign σ₁ * (Equiv.Perm.sign sl * Equiv.Perm.sign sr) := by simp
-    rw [h, this, mul_smul, mul_smul, smul_left_cancel_iff, ← TensorProduct.tmul_smul,
-      TensorProduct.smul_tmul']
-    simp only [Sum.map_inr, Perm.sumCongrHom_apply, Perm.sumCongr_apply, Sum.map_inl,
-      Function.comp_apply, Perm.coe_mul]
-    -- Porting note: Was `rw`.
-    erw [← a.map_congr_perm fun i => v (σ₁ _), ← b.map_congr_perm fun i => v (σ₁ _)]
-#align alternating_map.dom_coprod.summand AlternatingMap.domCoprod.summand
-
-theorem domCoprod.summand_mk'' (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb)
-    (σ : Equiv.Perm (Sum ιa ιb)) :
-    domCoprod.summand a b (Quotient.mk'' σ) =
-      Equiv.Perm.sign σ •
-        (MultilinearMap.domCoprod ↑a ↑b : MultilinearMap R' (fun _ => Mᵢ) (N₁ ⊗ N₂)).domDomCongr
-          σ :=
-  rfl
-#align alternating_map.dom_coprod.summand_mk' AlternatingMap.domCoprod.summand_mk''
-
-/-- Swapping elements in `σ` with equal values in `v` results in an addition that cancels -/
-theorem domCoprod.summand_add_swap_smul_eq_zero (a : AlternatingMap R' Mᵢ N₁ ιa)
-    (b : AlternatingMap R' Mᵢ N₂ ιb) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
-    {i j : Sum ιa ιb} (hv : v i = v j) (hij : i ≠ j) :
-    domCoprod.summand a b σ v + domCoprod.summand a b (swap i j • σ) v = 0 := by
-  refine Quotient.inductionOn' σ fun σ => ?_
-  dsimp only [Quotient.liftOn'_mk'', Quotient.map'_mk'', MulAction.Quotient.smul_mk,
-    domCoprod.summand]
-  rw [smul_eq_mul, Perm.sign_mul, Perm.sign_swap hij]
-  simp only [one_mul, neg_mul, Function.comp_apply, Units.neg_smul, Perm.coe_mul, Units.val_neg,
-    MultilinearMap.smul_apply, MultilinearMap.neg_apply, MultilinearMap.domDomCongr_apply,
-    MultilinearMap.domCoprod_apply]
-  convert add_right_neg (G := N₁ ⊗[R'] N₂) _ using 6 <;>
-    · ext k
-      rw [Equiv.apply_swap_eq_self hv]
-#align alternating_map.dom_coprod.summand_add_swap_smul_eq_zero AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero
-
-/-- Swapping elements in `σ` with equal values in `v` result in zero if the swap has no effect
-on the quotient. -/
-theorem domCoprod.summand_eq_zero_of_smul_invariant (a : AlternatingMap R' Mᵢ N₁ ιa)
-    (b : AlternatingMap R' Mᵢ N₂ ιb) (σ : Perm.ModSumCongr ιa ιb) {v : Sum ιa ιb → Mᵢ}
-    {i j : Sum ιa ιb} (hv : v i = v j) (hij : i ≠ j) :
-    swap i j • σ = σ → domCoprod.summand a b σ v = 0 := by
-  refine Quotient.inductionOn' σ fun σ => ?_
-  dsimp only [Quotient.liftOn'_mk'', Quotient.map'_mk'', MultilinearMap.smul_apply,
-    MultilinearMap.domDomCongr_apply, MultilinearMap.domCoprod_apply, domCoprod.summand]
-  intro hσ
-  cases' hi : σ⁻¹ i with val val <;> cases' hj : σ⁻¹ j with val_1 val_1 <;>
-    rw [Perm.inv_eq_iff_eq] at hi hj <;> substs hi hj <;> revert val val_1
-  -- Porting note: `on_goal` is not available in `case _ | _ =>`, so the proof gets tedious.
-  -- the term pairs with and cancels another term
-  case inl.inr =>
-    intro i' j' _ _ hσ
-    obtain ⟨⟨sl, sr⟩, hσ⟩ := QuotientGroup.leftRel_apply.mp (Quotient.exact' hσ)
-    replace hσ := Equiv.congr_fun hσ (Sum.inl i')
-    dsimp only at hσ
-    rw [smul_eq_mul, ← mul_swap_eq_swap_mul, mul_inv_rev, swap_inv, inv_mul_cancel_right] at hσ
-    simp at hσ
-  case inr.inl =>
-    intro i' j' _ _ hσ
-    obtain ⟨⟨sl, sr⟩, hσ⟩ := QuotientGroup.leftRel_apply.mp (Quotient.exact' hσ)
-    replace hσ := Equiv.congr_fun hσ (Sum.inr i')
-    dsimp only at hσ
-    rw [smul_eq_mul, ← mul_swap_eq_swap_mul, mul_inv_rev, swap_inv, inv_mul_cancel_right] at hσ
-    simp at hσ
-  -- the term does not pair but is zero
-  case inr.inr =>
-    intro i' j' hv hij _
-    convert smul_zero (M := ℤˣ) (A := N₁ ⊗[R'] N₂) _
-    convert TensorProduct.tmul_zero (R := R') (M := N₁) N₂ _
-    exact AlternatingMap.map_eq_zero_of_eq _ _ hv fun hij' => hij (hij' ▸ rfl)
-  case inl.inl =>
-    intro i' j' hv hij _
-    convert smul_zero (M := ℤˣ) (A := N₁ ⊗[R'] N₂) _
-    convert TensorProduct.zero_tmul (R := R') N₁ (N := N₂) _
-    exact AlternatingMap.map_eq_zero_of_eq _ _ hv fun hij' => hij (hij' ▸ rfl)
-#align alternating_map.dom_coprod.summand_eq_zero_of_smul_invariant AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant
-
-/-- Like `MultilinearMap.domCoprod`, but ensures the result is also alternating.
-
-Note that this is usually defined (for instance, as used in Proposition 22.24 in [Gallier2011Notes])
-over integer indices `ιa = Fin n` and `ιb = Fin m`, as
-$$
-(f \wedge g)(u_1, \ldots, u_{m+n}) =
-  \sum_{\operatorname{shuffle}(m, n)} \operatorname{sign}(\sigma)
-    f(u_{\sigma(1)}, \ldots, u_{\sigma(m)}) g(u_{\sigma(m+1)}, \ldots, u_{\sigma(m+n)}),
-$$
-where $\operatorname{shuffle}(m, n)$ consists of all permutations of $[1, m+n]$ such that
-$\sigma(1) < \cdots < \sigma(m)$ and $\sigma(m+1) < \cdots < \sigma(m+n)$.
-
-Here, we generalize this by replacing:
-* the product in the sum with a tensor product
-* the filtering of $[1, m+n]$ to shuffles with an isomorphic quotient
-* the additions in the subscripts of $\sigma$ with an index of type `Sum`
-
-The specialized version can be obtained by combining this definition with `finSumFinEquiv` and
-`LinearMap.mul'`.
--/
-@[simps]
-def domCoprod (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
-    AlternatingMap R' Mᵢ (N₁ ⊗[R'] N₂) (Sum ιa ιb) :=
-  { ∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ with
-    toFun := fun v => (⇑(∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ)) v
-    map_eq_zero_of_eq' := fun v i j hv hij => by
-      dsimp only
-      rw [MultilinearMap.sum_apply]
-      exact
-        Finset.sum_involution (fun σ _ => Equiv.swap i j • σ)
-          (fun σ _ => domCoprod.summand_add_swap_smul_eq_zero a b σ hv hij)
-          (fun σ _ => mt <| domCoprod.summand_eq_zero_of_smul_invariant a b σ hv hij)
-          (fun σ _ => Finset.mem_univ _) fun σ _ =>
-          Equiv.Perm.ModSumCongr.swap_smul_involutive i j σ }
-#align alternating_map.dom_coprod AlternatingMap.domCoprod
-#align alternating_map.dom_coprod_apply AlternatingMap.domCoprod_apply
-
-theorem domCoprod_coe (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
-    (↑(a.domCoprod b) : MultilinearMap R' (fun _ => Mᵢ) _) =
-      ∑ σ : Perm.ModSumCongr ιa ιb, domCoprod.summand a b σ :=
-  MultilinearMap.ext fun _ => rfl
-#align alternating_map.dom_coprod_coe AlternatingMap.domCoprod_coe
-
-/-- A more bundled version of `AlternatingMap.domCoprod` that maps
-`((ι₁ → N) → N₁) ⊗ ((ι₂ → N) → N₂)` to `(ι₁ ⊕ ι₂ → N) → N₁ ⊗ N₂`. -/
-def domCoprod' :
-    AlternatingMap R' Mᵢ N₁ ιa ⊗[R'] AlternatingMap R' Mᵢ N₂ ιb →ₗ[R']
-      AlternatingMap R' Mᵢ (N₁ ⊗[R'] N₂) (Sum ιa ιb) :=
-  TensorProduct.lift <| by
-    refine'
-      LinearMap.mk₂ R' domCoprod (fun m₁ m₂ n => _) (fun c m n => _) (fun m n₁ n₂ => _)
-        fun c m n => _ <;>
-    · ext
-      simp only [domCoprod_apply, add_apply, smul_apply, ← Finset.sum_add_distrib,
-        Finset.smul_sum, MultilinearMap.sum_apply, domCoprod.summand]
-      congr
-      ext σ
-      refine Quotient.inductionOn' σ fun σ => ?_
-      simp only [Quotient.liftOn'_mk'', coe_add, coe_smul, MultilinearMap.smul_apply,
-        ← MultilinearMap.domCoprod'_apply]
-      simp only [TensorProduct.add_tmul, ← TensorProduct.smul_tmul', TensorProduct.tmul_add,
-        TensorProduct.tmul_smul, LinearMap.map_add, LinearMap.map_smul]
-      first | rw [← smul_add] | rw [smul_comm]
-      rfl
-#align alternating_map.dom_coprod' AlternatingMap.domCoprod'
-
-@[simp]
-theorem domCoprod'_apply (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
-    domCoprod' (a ⊗ₜ[R'] b) = domCoprod a b :=
-  rfl
-#align alternating_map.dom_coprod'_apply AlternatingMap.domCoprod'_apply
-
-end AlternatingMap
-
-open Equiv
-
-/-- A helper lemma for `MultilinearMap.domCoprod_alternization`. -/
-theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableEq ιb]
-    (a : MultilinearMap R' (fun _ : ιa => Mᵢ) N₁) (b : MultilinearMap R' (fun _ : ιb => Mᵢ) N₂) :
-    MultilinearMap.domCoprod (MultilinearMap.alternatization a)
-      (MultilinearMap.alternatization b) =
-      ∑ σa : Perm ιa, ∑ σb : Perm ιb,
-        Equiv.Perm.sign σa • Equiv.Perm.sign σb •
-          MultilinearMap.domCoprod (a.domDomCongr σa) (b.domDomCongr σb) := by
-  simp_rw [← MultilinearMap.domCoprod'_apply, MultilinearMap.alternatization_coe]
-  simp_rw [TensorProduct.sum_tmul, TensorProduct.tmul_sum, _root_.map_sum,
-    ← TensorProduct.smul_tmul', TensorProduct.tmul_smul]
-  rfl
-#align multilinear_map.dom_coprod_alternization_coe MultilinearMap.domCoprod_alternization_coe
-
-open AlternatingMap
-
-/-- Computing the `MultilinearMap.alternatization` of the `MultilinearMap.domCoprod` is the same
-as computing the `AlternatingMap.domCoprod` of the `MultilinearMap.alternatization`s.
--/
-theorem MultilinearMap.domCoprod_alternization [DecidableEq ιa] [DecidableEq ιb]
-    (a : MultilinearMap R' (fun _ : ιa => Mᵢ) N₁) (b : MultilinearMap R' (fun _ : ιb => Mᵢ) N₂) :
-    MultilinearMap.alternatization (MultilinearMap.domCoprod a b) =
-      a.alternatization.domCoprod (MultilinearMap.alternatization b) := by
-  apply coe_multilinearMap_injective
-  rw [domCoprod_coe, MultilinearMap.alternatization_coe,
-    Finset.sum_partition (QuotientGroup.leftRel (Perm.sumCongrHom ιa ιb).range)]
-  congr 1
-  ext1 σ
-  refine Quotient.inductionOn' σ fun σ => ?_
-  -- unfold the quotient mess left by `Finset.sum_partition`
-  -- Porting note: Was `conv in .. => ..`.
-  erw
-    [@Finset.filter_congr _ _ (fun a => @Quotient.decidableEq _ _
-      (QuotientGroup.leftRelDecidable (MonoidHom.range (Perm.sumCongrHom ιa ιb)))
-      (Quotient.mk (QuotientGroup.leftRel (MonoidHom.range (Perm.sumCongrHom ιa ιb))) a)
-      (Quotient.mk'' σ)) _ (s := Finset.univ)
-    fun x _ => QuotientGroup.eq' (s := MonoidHom.range (Perm.sumCongrHom ιa ιb)) (a := x) (b := σ)]
-  -- eliminate a multiplication
-  rw [← Finset.map_univ_equiv (Equiv.mulLeft σ), Finset.filter_map, Finset.sum_map]
-  simp_rw [Equiv.coe_toEmbedding, Equiv.coe_mulLeft, (· ∘ ·), mul_inv_rev, inv_mul_cancel_right,
-    Subgroup.inv_mem_iff, MonoidHom.mem_range, Finset.univ_filter_exists,
-    Finset.sum_image (Perm.sumCongrHom_injective.injOn _)]
-  -- now we're ready to clean up the RHS, pulling out the summation
-  rw [domCoprod.summand_mk'', MultilinearMap.domCoprod_alternization_coe, ← Finset.sum_product',
-    Finset.univ_product_univ, ← MultilinearMap.domDomCongrEquiv_apply, _root_.map_sum,
-    Finset.smul_sum]
-  congr 1
-  ext1 ⟨al, ar⟩
-  dsimp only
-  -- pull out the pair of smuls on the RHS, by rewriting to `_ →ₗ[ℤ] _` and back
-  rw [← AddEquiv.coe_toAddMonoidHom, ← AddMonoidHom.coe_toIntLinearMap, LinearMap.map_smul_of_tower,
-    LinearMap.map_smul_of_tower, AddMonoidHom.coe_toIntLinearMap, AddEquiv.coe_toAddMonoidHom,
-    MultilinearMap.domDomCongrEquiv_apply]
-  -- pick up the pieces
-  rw [MultilinearMap.domDomCongr_mul, Perm.sign_mul, Perm.sumCongrHom_apply,
-    MultilinearMap.domCoprod_domDomCongr_sumCongr, Perm.sign_sumCongr, mul_smul, mul_smul]
-#align multilinear_map.dom_coprod_alternization MultilinearMap.domCoprod_alternization
-
-/-- Taking the `MultilinearMap.alternatization` of the `MultilinearMap.domCoprod` of two
-`AlternatingMap`s gives a scaled version of the `AlternatingMap.coprod` of those maps.
--/
-theorem MultilinearMap.domCoprod_alternization_eq [DecidableEq ιa] [DecidableEq ιb]
-    (a : AlternatingMap R' Mᵢ N₁ ιa) (b : AlternatingMap R' Mᵢ N₂ ιb) :
-    MultilinearMap.alternatization
-      (MultilinearMap.domCoprod a b : MultilinearMap R' (fun _ : Sum ιa ιb => Mᵢ) (N₁ ⊗ N₂)) =
-      ((Fintype.card ιa).factorial * (Fintype.card ιb).factorial) • a.domCoprod b := by
-  rw [MultilinearMap.domCoprod_alternization, coe_alternatization, coe_alternatization, mul_smul,
-    ← AlternatingMap.domCoprod'_apply, ← AlternatingMap.domCoprod'_apply,
-    ← TensorProduct.smul_tmul', TensorProduct.tmul_smul,
-    LinearMap.map_smul_of_tower AlternatingMap.domCoprod',
-    LinearMap.map_smul_of_tower AlternatingMap.domCoprod']
-#align multilinear_map.dom_coprod_alternization_eq MultilinearMap.domCoprod_alternization_eq
-
-end Coprod
-
 section Basis
 
 open AlternatingMap
@@ -1343,12 +1062,10 @@ theorem curryLeft_compAlternatingMap {n : ℕ} (g : N'' →ₗ[R'] N₂'')
 theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')
     (f : AlternatingMap R' M'' N'' (Fin n.succ)) (m : M₂'') :
     (f.compLinearMap g).curryLeft m = (f.curryLeft (g m)).compLinearMap g :=
-  ext fun v =>
-    congr_arg f <|
-      funext <| by
-        refine' Fin.cases _ _
-        · rfl
-        · simp
+  ext fun v => congr_arg f <| funext <| by
+    refine' Fin.cases _ _
+    · rfl
+    · simp
 #align alternating_map.curry_left_comp_linear_map AlternatingMap.curryLeft_compLinearMap
 
 /-- The space of constant maps is equivalent to the space of maps that are alternating with respect

Also _root_.map_smul when in the neighbourhood.

@@ -1174,8 +1174,8 @@ theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableE
         Equiv.Perm.sign σa • Equiv.Perm.sign σb •
           MultilinearMap.domCoprod (a.domDomCongr σa) (b.domDomCongr σb) := by
   simp_rw [← MultilinearMap.domCoprod'_apply, MultilinearMap.alternatization_coe]
-  simp_rw [TensorProduct.sum_tmul, TensorProduct.tmul_sum, LinearMap.map_sum, ←
-    TensorProduct.smul_tmul', TensorProduct.tmul_smul]
+  simp_rw [TensorProduct.sum_tmul, TensorProduct.tmul_sum, _root_.map_sum,
+    ← TensorProduct.smul_tmul', TensorProduct.tmul_smul]
   rfl
 #align multilinear_map.dom_coprod_alternization_coe MultilinearMap.domCoprod_alternization_coe
 

This forward-ports leanprover-community/mathlib#19236

@@ -10,7 +10,7 @@ import Mathlib.LinearAlgebra.LinearIndependent
 import Mathlib.LinearAlgebra.Multilinear.Basis
 import Mathlib.LinearAlgebra.Multilinear.TensorProduct
 
-#align_import linear_algebra.alternating from "leanprover-community/mathlib"@"bd65478311e4dfd41f48bf38c7e3b02fb75d0163"
+#align_import linear_algebra.alternating from "leanprover-community/mathlib"@"0c1d80f5a86b36c1db32e021e8d19ae7809d5b79"
 
 /-!
 # Alternating Maps
@@ -759,6 +759,13 @@ theorem domDomCongr_add (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :
   rfl
 #align alternating_map.dom_dom_congr_add AlternatingMap.domDomCongr_add
 
+@[simp]
+theorem domDomCongr_smul {S : Type*} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
+    (σ : ι ≃ ι') (c : S) (f : AlternatingMap R M N ι) :
+    (c • f).domDomCongr σ = c • f.domDomCongr σ :=
+  rfl
+#align alternating_map.dom_dom_congr_smul AlternatingMap.domDomCongr_smul
+
 /-- `AlternatingMap.domDomCongr` as an equivalence.
 
 This is declared separately because it does not work with dot notation. -/
@@ -777,6 +784,38 @@ def domDomCongrEquiv (σ : ι ≃ ι') : AlternatingMap R M N ι ≃+ Alternatin
 #align alternating_map.dom_dom_congr_equiv_apply AlternatingMap.domDomCongrEquiv_apply
 #align alternating_map.dom_dom_congr_equiv_symm_apply AlternatingMap.domDomCongrEquiv_symm_apply
 
+section DomDomLcongr
+
+variable (S : Type*) [Semiring S] [Module S N] [SMulCommClass R S N]
+
+/-- `alternating_map.dom_dom_congr` as a linear equivalence. -/
+@[simps apply symm_apply]
+def domDomLcongr (σ : ι ≃ ι') : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι'
+    where
+  toFun := domDomCongr σ
+  invFun := domDomCongr σ.symm
+  left_inv f := by ext; simp [Function.comp]
+  right_inv m := by ext; simp [Function.comp]
+  map_add' := domDomCongr_add σ
+  map_smul' := domDomCongr_smul σ
+#align alternating_map.dom_dom_lcongr AlternatingMap.domDomLcongr
+
+@[simp]
+theorem domDomLcongr_refl :
+    (domDomLcongr S (Equiv.refl ι) : AlternatingMap R M N ι ≃ₗ[S] AlternatingMap R M N ι) =
+      LinearEquiv.refl _ _ :=
+  LinearEquiv.ext domDomCongr_refl
+#align alternating_map.dom_dom_lcongr_refl AlternatingMap.domDomLcongr_refl
+
+@[simp]
+theorem domDomLcongr_toAddEquiv (σ : ι ≃ ι') :
+    (↑(domDomLcongr S σ : AlternatingMap R M N ι ≃ₗ[S] _) : AlternatingMap R M N ι ≃+ _) =
+      domDomCongrEquiv σ :=
+  rfl
+#align alternating_map.dom_dom_lcongr_to_add_equiv AlternatingMap.domDomLcongr_toAddEquiv
+
+end DomDomLcongr
+
 /-- The results of applying `domDomCongr` to two maps are equal if and only if those maps are. -/
 @[simp]
 theorem domDomCongr_eq_iff (σ : ι ≃ ι') (f g : AlternatingMap R M N ι) :

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

This has nice performance benefits.

@@ -48,21 +48,21 @@ using `map_swap` as a definition, and does not require `Neg N`.
 
 -- semiring / add_comm_monoid
 
-variable {R : Type _} [Semiring R]
+variable {R : Type*} [Semiring R]
 
-variable {M : Type _} [AddCommMonoid M] [Module R M]
+variable {M : Type*} [AddCommMonoid M] [Module R M]
 
-variable {N : Type _} [AddCommMonoid N] [Module R N]
+variable {N : Type*} [AddCommMonoid N] [Module R N]
 
-variable {P : Type _} [AddCommMonoid P] [Module R P]
+variable {P : Type*} [AddCommMonoid P] [Module R P]
 
 -- semiring / add_comm_group
 
-variable {M' : Type _} [AddCommGroup M'] [Module R M']
+variable {M' : Type*} [AddCommGroup M'] [Module R M']
 
-variable {N' : Type _} [AddCommGroup N'] [Module R N']
+variable {N' : Type*} [AddCommGroup N'] [Module R N']
 
-variable {ι ι' ι'' : Type _}
+variable {ι ι' ι'' : Type*}
 
 section
 
@@ -245,7 +245,7 @@ as `MultilinearMap`
 
 section SMul
 
-variable {S : Type _} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
+variable {S : Type*} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
 
 instance smul : SMul S (AlternatingMap R M N ι) :=
   ⟨fun c f =>
@@ -293,7 +293,7 @@ theorem coe_prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) :
 /-- Combine a family of alternating maps with the same domain and codomains `N i` into an
 alternating map taking values in the space of functions `Π i, N i`. -/
 @[simps!]
-def pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
+def pi {ι' : Type*} {N : ι' → Type*} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
     (f : ∀ i, AlternatingMap R M (N i) ι) : AlternatingMap R M (∀ i, N i) ι :=
   { MultilinearMap.pi fun a => (f a).toMultilinearMap with
     map_eq_zero_of_eq' := fun _ _ _ h hne => funext fun a => (f a).map_eq_zero_of_eq _ h hne }
@@ -301,7 +301,7 @@ def pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)] [∀ i,
 #align alternating_map.pi_apply AlternatingMap.pi_apply
 
 @[simp]
-theorem coe_pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
+theorem coe_pi {ι' : Type*} {N : ι' → Type*} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
     (f : ∀ i, AlternatingMap R M (N i) ι) :
     (pi f : MultilinearMap R (fun _ : ι => M) (∀ i, N i)) = MultilinearMap.pi fun a => f a :=
   rfl
@@ -310,7 +310,7 @@ theorem coe_pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)]
 /-- Given an alternating `R`-multilinear map `f` taking values in `R`, `f.smul_right z` is the map
 sending `m` to `f m • z`. -/
 @[simps!]
-def smulRight {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
+def smulRight {R M₁ M₂ ι : Type*} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
     [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) : AlternatingMap R M₁ M₂ ι :=
   { f.toMultilinearMap.smulRight z with
     map_eq_zero_of_eq' := fun v i j h hne => by simp [f.map_eq_zero_of_eq v h hne] }
@@ -318,7 +318,7 @@ def smulRight {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁] [A
 #align alternating_map.smul_right_apply AlternatingMap.smulRight_apply
 
 @[simp]
-theorem coe_smulRight {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
+theorem coe_smulRight {R M₁ M₂ ι : Type*} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
     [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) :
     (f.smulRight z : MultilinearMap R (fun _ : ι => M₁) M₂) = MultilinearMap.smulRight f z :=
   rfl
@@ -408,7 +408,7 @@ instance addCommGroup : AddCommGroup (AlternatingMap R M N' ι) :=
 #align alternating_map.add_comm_group AlternatingMap.addCommGroup
 section DistribMulAction
 
-variable {S : Type _} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
+variable {S : Type*} [Monoid S] [DistribMulAction S N] [SMulCommClass R S N]
 
 instance distribMulAction : DistribMulAction S (AlternatingMap R M N ι) where
   one_smul _ := ext fun _ => one_smul _ _
@@ -421,7 +421,7 @@ end DistribMulAction
 
 section Module
 
-variable {S : Type _} [Semiring S] [Module S N] [SMulCommClass R S N]
+variable {S : Type*} [Semiring S] [Module S N] [SMulCommClass R S N]
 
 /-- The space of multilinear maps over an algebra over `R` is a module over `R`, for the pointwise
 addition and scalar multiplication. -/
@@ -483,7 +483,7 @@ end AlternatingMap
 
 namespace LinearMap
 
-variable {N₂ : Type _} [AddCommMonoid N₂] [Module R N₂]
+variable {N₂ : Type*} [AddCommMonoid N₂] [Module R N₂]
 
 /-- Composing an alternating map with a linear map on the left gives again an alternating map. -/
 def compAlternatingMap (g : N →ₗ[R] N₂) : AlternatingMap R M N ι →+ AlternatingMap R M N₂ ι where
@@ -510,7 +510,7 @@ theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : AlternatingMap R M
   rfl
 #align linear_map.comp_alternating_map_apply LinearMap.compAlternatingMap_apply
 
-theorem smulRight_eq_comp {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁]
+theorem smulRight_eq_comp {R M₁ M₂ ι : Type*} [CommSemiring R] [AddCommMonoid M₁]
     [AddCommMonoid M₂] [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) :
     f.smulRight z = (LinearMap.id.smulRight z).compAlternatingMap f :=
   rfl
@@ -534,9 +534,9 @@ end LinearMap
 
 namespace AlternatingMap
 
-variable {M₂ : Type _} [AddCommMonoid M₂] [Module R M₂]
+variable {M₂ : Type*} [AddCommMonoid M₂] [Module R M₂]
 
-variable {M₃ : Type _} [AddCommMonoid M₃] [Module R M₃]
+variable {M₃ : Type*} [AddCommMonoid M₃] [Module R M₃]
 
 /-- Composing an alternating map with the same linear map on each argument gives again an
 alternating map. -/
@@ -605,7 +605,7 @@ theorem compLinearMap_inj (f : M₂ →ₗ[R] M) (hf : Function.Surjective f)
 section DomLcongr
 
 variable (ι R N)
-variable (S : Type _) [Semiring S] [Module S N] [SMulCommClass R S N]
+variable (S : Type*) [Semiring S] [Module S N] [SMulCommClass R S N]
 
 /-- Construct a linear equivalence between maps from a linear equivalence between domains. -/
 @[simps apply]
@@ -663,7 +663,7 @@ section
 
 open BigOperators
 
-theorem map_update_sum {α : Type _} [DecidableEq ι] (t : Finset α) (i : ι) (g : α → M) (m : ι → M) :
+theorem map_update_sum {α : Type*} [DecidableEq ι] (t : Finset α) (i : ι) (g : α → M) (m : ι → M) :
     f (update m i (∑ a in t, g a)) = ∑ a in t, f (update m i (g a)) :=
   f.toMultilinearMap.map_update_sum t i g m
 #align alternating_map.map_update_sum AlternatingMap.map_update_sum
@@ -804,8 +804,8 @@ theorem coe_domDomCongr (σ : ι ≃ ι') :
 end DomDomCongr
 
 /-- If the arguments are linearly dependent then the result is `0`. -/
-theorem map_linearDependent {K : Type _} [Ring K] {M : Type _} [AddCommGroup M] [Module K M]
-    {N : Type _} [AddCommGroup N] [Module K N] [NoZeroSMulDivisors K N] (f : AlternatingMap K M N ι)
+theorem map_linearDependent {K : Type*} [Ring K] {M : Type*} [AddCommGroup M] [Module K M]
+    {N : Type*} [AddCommGroup N] [Module K N] [NoZeroSMulDivisors K N] (f : AlternatingMap K M N ι)
     (v : ι → M) (h : ¬LinearIndependent K v) : f v = 0 := by
   obtain ⟨s, g, h, i, hi, hz⟩ := not_linearIndependent_iff.mp h
   letI := Classical.decEq ι
@@ -913,7 +913,7 @@ end AlternatingMap
 
 namespace LinearMap
 
-variable {N'₂ : Type _} [AddCommGroup N'₂] [Module R N'₂] [DecidableEq ι] [Fintype ι]
+variable {N'₂ : Type*} [AddCommGroup N'₂] [Module R N'₂] [DecidableEq ι] [Fintype ι]
 
 /-- Composition with a linear map before and after alternatization are equivalent. -/
 theorem compMultilinearMap_alternatization (g : N' →ₗ[R] N'₂)
@@ -932,19 +932,19 @@ open BigOperators
 
 open TensorProduct
 
-variable {ιa ιb : Type _} [Fintype ιa] [Fintype ιb]
+variable {ιa ιb : Type*} [Fintype ιa] [Fintype ιb]
 
-variable {R' : Type _} {Mᵢ N₁ N₂ : Type _} [CommSemiring R'] [AddCommGroup N₁] [Module R' N₁]
+variable {R' : Type*} {Mᵢ N₁ N₂ : Type*} [CommSemiring R'] [AddCommGroup N₁] [Module R' N₁]
   [AddCommGroup N₂] [Module R' N₂] [AddCommMonoid Mᵢ] [Module R' Mᵢ]
 
 namespace Equiv.Perm
 
 /-- Elements which are considered equivalent if they differ only by swaps within α or β  -/
-abbrev ModSumCongr (α β : Type _) :=
+abbrev ModSumCongr (α β : Type*) :=
   _ ⧸ (Equiv.Perm.sumCongrHom α β).range
 #align equiv.perm.mod_sum_congr Equiv.Perm.ModSumCongr
 
-theorem ModSumCongr.swap_smul_involutive {α β : Type _} [DecidableEq (Sum α β)] (i j : Sum α β) :
+theorem ModSumCongr.swap_smul_involutive {α β : Type*} [DecidableEq (Sum α β)] (i j : Sum α β) :
     Function.Involutive (SMul.smul (Equiv.swap i j) : ModSumCongr α β → ModSumCongr α β) :=
   fun σ => by
     refine Quotient.inductionOn' σ fun σ => ?_
@@ -1205,9 +1205,9 @@ section Basis
 
 open AlternatingMap
 
-variable {ι₁ : Type _} [Finite ι]
+variable {ι₁ : Type*} [Finite ι]
 
-variable {R' : Type _} {N₁ N₂ : Type _} [CommSemiring R'] [AddCommMonoid N₁] [AddCommMonoid N₂]
+variable {R' : Type*} {N₁ N₂ : Type*} [CommSemiring R'] [AddCommMonoid N₁] [AddCommMonoid N₂]
 
 variable [Module R' N₁] [Module R' N₂]
 
@@ -1232,7 +1232,7 @@ end Basis
 
 section Currying
 
-variable {R' : Type _} {M'' M₂'' N'' N₂'' : Type _} [CommSemiring R'] [AddCommMonoid M'']
+variable {R' : Type*} {M'' M₂'' N'' N₂'' : Type*} [CommSemiring R'] [AddCommMonoid M'']
   [AddCommMonoid M₂''] [AddCommMonoid N''] [AddCommMonoid N₂''] [Module R' M''] [Module R' M₂'']
   [Module R' N''] [Module R' N₂'']
 

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Zhangir Azerbayev. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Zhangir Azerbayev
-
-! This file was ported from Lean 3 source module linear_algebra.alternating
-! leanprover-community/mathlib commit bd65478311e4dfd41f48bf38c7e3b02fb75d0163
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.GroupTheory.GroupAction.Quotient
 import Mathlib.GroupTheory.Perm.Sign
@@ -15,6 +10,8 @@ import Mathlib.LinearAlgebra.LinearIndependent
 import Mathlib.LinearAlgebra.Multilinear.Basis
 import Mathlib.LinearAlgebra.Multilinear.TensorProduct
 
+#align_import linear_algebra.alternating from "leanprover-community/mathlib"@"bd65478311e4dfd41f48bf38c7e3b02fb75d0163"
+
 /-!
 # Alternating Maps
 

@@ -74,7 +74,8 @@ variable (R M N ι)
 /-- An alternating map is a multilinear map that vanishes when two of its arguments are equal.
 -/
 structure AlternatingMap extends MultilinearMap R (fun _ : ι => M) N where
-  map_eq_zero_of_eq' : ∀ (v : ι → M) (i j : ι) (_ : v i = v j) (_ : i ≠ j), toFun v = 0
+  /-- The map is alternating: if `v` has two equal coordinates, then `f v = 0`. -/
+  map_eq_zero_of_eq' : ∀ (v : ι → M) (i j : ι), v i = v j → i ≠ j → toFun v = 0
 #align alternating_map AlternatingMap
 
 end
@@ -358,6 +359,11 @@ theorem coe_zero : ((0 : AlternatingMap R M N ι) : MultilinearMap R (fun _ : ι
   rfl
 #align alternating_map.coe_zero AlternatingMap.coe_zero
 
+@[simp]
+theorem mk_zero :
+    mk (0 : MultilinearMap R (fun _ : ι ↦ M) N) (0 : AlternatingMap R M N ι).2 = 0 :=
+  rfl
+
 instance inhabited : Inhabited (AlternatingMap R M N ι) :=
   ⟨0⟩
 #align alternating_map.inhabited AlternatingMap.inhabited

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -232,7 +232,7 @@ theorem map_zero [Nonempty ι] : f 0 = 0 :=
 
 theorem map_eq_zero_of_not_injective (v : ι → M) (hv : ¬Function.Injective v) : f v = 0 := by
   rw [Function.Injective] at hv
-  push_neg  at hv
+  push_neg at hv
   rcases hv with ⟨i₁, i₂, heq, hne⟩
   exact f.map_eq_zero_of_eq v heq hne
 #align alternating_map.map_eq_zero_of_not_injective AlternatingMap.map_eq_zero_of_not_injective

Part 2 of #5001

@@ -482,7 +482,7 @@ namespace LinearMap
 
 variable {N₂ : Type _} [AddCommMonoid N₂] [Module R N₂]
 
-/-- Composing a alternating map with a linear map on the left gives again an alternating map. -/
+/-- Composing an alternating map with a linear map on the left gives again an alternating map. -/
 def compAlternatingMap (g : N →ₗ[R] N₂) : AlternatingMap R M N ι →+ AlternatingMap R M N₂ ι where
   toFun f :=
     { g.compMultilinearMap (f : MultilinearMap R (fun _ : ι => M) N) with
@@ -535,7 +535,7 @@ variable {M₂ : Type _} [AddCommMonoid M₂] [Module R M₂]
 
 variable {M₃ : Type _} [AddCommMonoid M₃] [Module R M₃]
 
-/-- Composing a alternating map with the same linear map on each argument gives again an
+/-- Composing an alternating map with the same linear map on each argument gives again an
 alternating map. -/
 def compLinearMap (f : AlternatingMap R M N ι) (g : M₂ →ₗ[R] M) : AlternatingMap R M₂ N ι :=
   { (f : MultilinearMap R (fun _ : ι => M) N).compLinearMap fun _ => g with

Forward-port leanprover-community/mathlib#19123

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Zhangir Azerbayev
 
 ! This file was ported from Lean 3 source module linear_algebra.alternating
-! leanprover-community/mathlib commit 78fdf68dcd2fdb3fe64c0dd6f88926a49418a6ea
+! leanprover-community/mathlib commit bd65478311e4dfd41f48bf38c7e3b02fb75d0163
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -448,6 +448,8 @@ def ofSubsingleton [Subsingleton ι] (i : ι) : AlternatingMap R M M ι :=
 #align alternating_map.of_subsingleton AlternatingMap.ofSubsingleton
 #align alternating_map.of_subsingleton_apply AlternatingMap.ofSubsingleton_apply
 
+variable (ι)
+
 /-- The constant map is alternating when `ι` is empty. -/
 @[simps (config := { fullyApplied := false })]
 def constOfIsEmpty [IsEmpty ι] (m : N) : AlternatingMap R M N ι :=
@@ -1311,7 +1313,7 @@ theorem curryLeft_compLinearMap {n : ℕ} (g : M₂'' →ₗ[R'] M'')
 to an empty family. -/
 @[simps]
 def constLinearEquivOfIsEmpty [IsEmpty ι] : N'' ≃ₗ[R'] AlternatingMap R' M'' N'' ι where
-  toFun := AlternatingMap.constOfIsEmpty R' M''
+  toFun := AlternatingMap.constOfIsEmpty R' M'' ι
   map_add' _ _ := rfl
   map_smul' _ _ := rfl
   invFun f := f 0

Forward-port leanprover-community/mathlib#19069

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Zhangir Azerbayev
 
 ! This file was ported from Lean 3 source module linear_algebra.alternating
-! leanprover-community/mathlib commit 284fdd2962e67d2932fa3a79ce19fcf92d38e228
+! leanprover-community/mathlib commit 78fdf68dcd2fdb3fe64c0dd6f88926a49418a6ea
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -57,6 +57,8 @@ variable {M : Type _} [AddCommMonoid M] [Module R M]
 
 variable {N : Type _} [AddCommMonoid N] [Module R N]
 
+variable {P : Type _} [AddCommMonoid P] [Module R P]
+
 -- semiring / add_comm_group
 
 variable {M' : Type _} [AddCommGroup M'] [Module R M']
@@ -275,6 +277,55 @@ instance isCentralScalar [DistribMulAction Sᵐᵒᵖ N] [IsCentralScalar S N] :
 
 end SMul
 
+/-- The cartesian product of two alternating maps, as an alternating map. -/
+@[simps!]
+def prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) : AlternatingMap R M (N × P) ι :=
+  { f.toMultilinearMap.prod g.toMultilinearMap with
+    map_eq_zero_of_eq' := fun _ _ _ h hne =>
+      Prod.ext (f.map_eq_zero_of_eq _ h hne) (g.map_eq_zero_of_eq _ h hne) }
+#align alternating_map.prod AlternatingMap.prod
+#align alternating_map.prod_apply AlternatingMap.prod_apply
+
+@[simp]
+theorem coe_prod (f : AlternatingMap R M N ι) (g : AlternatingMap R M P ι) :
+    (f.prod g : MultilinearMap R (fun _ : ι => M) (N × P)) = MultilinearMap.prod f g :=
+  rfl
+#align alternating_map.coe_prod AlternatingMap.coe_prod
+
+/-- Combine a family of alternating maps with the same domain and codomains `N i` into an
+alternating map taking values in the space of functions `Π i, N i`. -/
+@[simps!]
+def pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
+    (f : ∀ i, AlternatingMap R M (N i) ι) : AlternatingMap R M (∀ i, N i) ι :=
+  { MultilinearMap.pi fun a => (f a).toMultilinearMap with
+    map_eq_zero_of_eq' := fun _ _ _ h hne => funext fun a => (f a).map_eq_zero_of_eq _ h hne }
+#align alternating_map.pi AlternatingMap.pi
+#align alternating_map.pi_apply AlternatingMap.pi_apply
+
+@[simp]
+theorem coe_pi {ι' : Type _} {N : ι' → Type _} [∀ i, AddCommMonoid (N i)] [∀ i, Module R (N i)]
+    (f : ∀ i, AlternatingMap R M (N i) ι) :
+    (pi f : MultilinearMap R (fun _ : ι => M) (∀ i, N i)) = MultilinearMap.pi fun a => f a :=
+  rfl
+#align alternating_map.coe_pi AlternatingMap.coe_pi
+
+/-- Given an alternating `R`-multilinear map `f` taking values in `R`, `f.smul_right z` is the map
+sending `m` to `f m • z`. -/
+@[simps!]
+def smulRight {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
+    [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) : AlternatingMap R M₁ M₂ ι :=
+  { f.toMultilinearMap.smulRight z with
+    map_eq_zero_of_eq' := fun v i j h hne => by simp [f.map_eq_zero_of_eq v h hne] }
+#align alternating_map.smul_right AlternatingMap.smulRight
+#align alternating_map.smul_right_apply AlternatingMap.smulRight_apply
+
+@[simp]
+theorem coe_smulRight {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁] [AddCommMonoid M₂]
+    [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) :
+    (f.smulRight z : MultilinearMap R (fun _ : ι => M₁) M₂) = MultilinearMap.smulRight f z :=
+  rfl
+#align alternating_map.coe_smul_right AlternatingMap.coe_smulRight
+
 instance add : Add (AlternatingMap R M N ι) :=
   ⟨fun a b =>
     { (a + b : MultilinearMap R (fun _ : ι => M) N) with
@@ -454,6 +505,12 @@ theorem compAlternatingMap_apply (g : N →ₗ[R] N₂) (f : AlternatingMap R M
   rfl
 #align linear_map.comp_alternating_map_apply LinearMap.compAlternatingMap_apply
 
+theorem smulRight_eq_comp {R M₁ M₂ ι : Type _} [CommSemiring R] [AddCommMonoid M₁]
+    [AddCommMonoid M₂] [Module R M₁] [Module R M₂] (f : AlternatingMap R M₁ R ι) (z : M₂) :
+    f.smulRight z = (LinearMap.id.smulRight z).compAlternatingMap f :=
+  rfl
+#align linear_map.smul_right_eq_comp LinearMap.smulRight_eq_comp
+
 @[simp]
 theorem subtype_compAlternatingMap_codRestrict (f : AlternatingMap R M N ι) (p : Submodule R N)
     (h) : p.subtype.compAlternatingMap (f.codRestrict p h) = f :=

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

@@ -1005,7 +1005,7 @@ Here, we generalize this by replacing:
 * the filtering of $[1, m+n]$ to shuffles with an isomorphic quotient
 * the additions in the subscripts of $\sigma$ with an index of type `Sum`
 
-The specialized version can be obtained by combining this definition with `fin_sum_fin_equiv` and
+The specialized version can be obtained by combining this definition with `finSumFinEquiv` and
 `LinearMap.mul'`.
 -/
 @[simps]

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

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

@@ -627,16 +627,16 @@ theorem map_update_update [DecidableEq ι] {i j : ι} (hij : i ≠ j) (m : M) :
     (by rw [Function.update_same, Function.update_noteq hij, Function.update_same]) hij
 #align alternating_map.map_update_update AlternatingMap.map_update_update
 
-theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f (v ∘ Equiv.swap i j) + f v = 0 :=
-  by
+theorem map_swap_add [DecidableEq ι] {i j : ι} (hij : i ≠ j) :
+    f (v ∘ Equiv.swap i j) + f v = 0 := by
   rw [Equiv.comp_swap_eq_update]
   convert f.map_update_update v hij (v i + v j)
   simp [f.map_update_self _ hij, f.map_update_self _ hij.symm,
     Function.update_comm hij (v i + v j) (v _) v, Function.update_comm hij.symm (v i) (v i) v]
 #align alternating_map.map_swap_add AlternatingMap.map_swap_add
 
-theorem map_add_swap [DecidableEq ι] {i j : ι} (hij : i ≠ j) : f v + f (v ∘ Equiv.swap i j) = 0 :=
-  by
+theorem map_add_swap [DecidableEq ι] {i j : ι} (hij : i ≠ j) :
+    f v + f (v ∘ Equiv.swap i j) = 0 := by
   rw [add_comm]
   exact f.map_swap_add v hij
 #align alternating_map.map_add_swap AlternatingMap.map_add_swap
@@ -840,8 +840,7 @@ namespace AlternatingMap
 where `n` is the number of inputs. -/
 theorem coe_alternatization [DecidableEq ι] [Fintype ι] (a : AlternatingMap R M N' ι) :
     MultilinearMap.alternatization (a : MultilinearMap R (fun _ => M) N')
-      = Nat.factorial (Fintype.card ι) • a :=
-  by
+    = Nat.factorial (Fintype.card ι) • a := by
   apply AlternatingMap.coe_injective
   simp_rw [MultilinearMap.alternatization_def, ← coe_domDomCongr, domDomCongr_perm, coe_smul,
     smul_smul, Int.units_mul_self, one_smul, Finset.sum_const, Finset.card_univ, Fintype.card_perm,
@@ -1153,8 +1152,8 @@ variable [Module R' N₁] [Module R' N₂]
 /-- Two alternating maps indexed by a `Fintype` are equal if they are equal when all arguments
 are distinct basis vectors. -/
 theorem Basis.ext_alternating {f g : AlternatingMap R' N₁ N₂ ι} (e : Basis ι₁ R' N₁)
-    (h : ∀ v : ι → ι₁, Function.Injective v → (f fun i => e (v i)) = g fun i => e (v i)) : f = g :=
-  by
+    (h : ∀ v : ι → ι₁, Function.Injective v → (f fun i => e (v i)) = g fun i => e (v i)) :
+    f = g := by
   classical
     refine' AlternatingMap.coe_multilinearMap_injective (Basis.ext_multilinear e fun v => _)
     by_cases hi : Function.Injective v

closes #3680, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Stepping.20through.20simp_rw/near/326712986

@@ -1075,7 +1075,7 @@ theorem MultilinearMap.domCoprod_alternization_coe [DecidableEq ιa] [DecidableE
           MultilinearMap.domCoprod (a.domDomCongr σa) (b.domDomCongr σb) := by
   simp_rw [← MultilinearMap.domCoprod'_apply, MultilinearMap.alternatization_coe]
   simp_rw [TensorProduct.sum_tmul, TensorProduct.tmul_sum, LinearMap.map_sum, ←
-    TensorProduct.smul_tmul', TensorProduct.tmul_smul, LinearMap.map_smul_of_tower]
+    TensorProduct.smul_tmul', TensorProduct.tmul_smul]
   rfl
 #align multilinear_map.dom_coprod_alternization_coe MultilinearMap.domCoprod_alternization_coe
 

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>