data.mv_polynomial.monad ⟷ Mathlib.Data.MvPolynomial.Monad

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

@@ -412,8 +412,8 @@ theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r :
 #print MvPolynomial.bind₂_monomial /-
 theorem bind₂_monomial (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) (r : R) :
     bind₂ f (monomial d r) = f r * monomial d 1 := by
-  simp only [monomial_eq, RingHom.map_mul, bind₂_C_right, Finsupp.prod, RingHom.map_prod,
-    RingHom.map_pow, bind₂_X_right, C_1, one_mul]
+  simp only [monomial_eq, RingHom.map_mul, bind₂_C_right, Finsupp.prod, map_prod, RingHom.map_pow,
+    bind₂_X_right, C_1, one_mul]
 #align mv_polynomial.bind₂_monomial MvPolynomial.bind₂_monomial
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Robert Y. Lewis
 -/
-import Data.MvPolynomial.Rename
-import Data.MvPolynomial.Degrees
+import Algebra.MvPolynomial.Rename
+import Algebra.MvPolynomial.Degrees
 
 #align_import data.mv_polynomial.monad from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Robert Y. Lewis
 -/
 import Data.MvPolynomial.Rename
-import Data.MvPolynomial.Variables
+import Data.MvPolynomial.Degrees
 
 #align_import data.mv_polynomial.monad from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 

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

@@ -467,7 +467,9 @@ end
 
 #print MvPolynomial.mem_vars_bind₁ /-
 theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
-    (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by classical
+    (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by
+  classical simpa only [exists_prop, Finset.mem_biUnion, mem_support_iff, Ne.def] using
+    vars_bind₁ f φ h
 #align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁
 -/
 

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

@@ -467,9 +467,7 @@ end
 
 #print MvPolynomial.mem_vars_bind₁ /-
 theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
-    (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by
-  classical simpa only [exists_prop, Finset.mem_biUnion, mem_support_iff, Ne.def] using
-    vars_bind₁ f φ h
+    (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by classical
 #align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁
 -/
 

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

@@ -232,7 +232,7 @@ theorem join₂_comp_map (f : R →+* MvPolynomial σ S) : join₂.comp (map f)
 
 #print MvPolynomial.aeval_id_rename /-
 theorem aeval_id_rename (f : σ → MvPolynomial τ R) (p : MvPolynomial σ R) :
-    aeval id (rename f p) = aeval f p := by rw [aeval_rename, Function.comp.left_id]
+    aeval id (rename f p) = aeval f p := by rw [aeval_rename, Function.id_comp]
 #align mv_polynomial.aeval_id_rename MvPolynomial.aeval_id_rename
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Robert Y. Lewis
 -/
-import Mathbin.Data.MvPolynomial.Rename
-import Mathbin.Data.MvPolynomial.Variables
+import Data.MvPolynomial.Rename
+import Data.MvPolynomial.Variables
 
 #align_import data.mv_polynomial.monad from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Robert Y. Lewis
-
-! This file was ported from Lean 3 source module data.mv_polynomial.monad
-! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.MvPolynomial.Rename
 import Mathbin.Data.MvPolynomial.Variables
 
+#align_import data.mv_polynomial.monad from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
+
 /-!
 
 # Monad operations on `mv_polynomial`

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

@@ -116,39 +116,51 @@ def join₂ : MvPolynomial σ (MvPolynomial σ R) →+* MvPolynomial σ R :=
 #align mv_polynomial.join₂ MvPolynomial.join₂
 -/
 
+#print MvPolynomial.aeval_eq_bind₁ /-
 @[simp]
 theorem aeval_eq_bind₁ (f : σ → MvPolynomial τ R) : aeval f = bind₁ f :=
   rfl
 #align mv_polynomial.aeval_eq_bind₁ MvPolynomial.aeval_eq_bind₁
+-/
 
+#print MvPolynomial.eval₂Hom_C_eq_bind₁ /-
 @[simp]
 theorem eval₂Hom_C_eq_bind₁ (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind₁ f :=
   rfl
 #align mv_polynomial.eval₂_hom_C_eq_bind₁ MvPolynomial.eval₂Hom_C_eq_bind₁
+-/
 
+#print MvPolynomial.eval₂Hom_eq_bind₂ /-
 @[simp]
 theorem eval₂Hom_eq_bind₂ (f : R →+* MvPolynomial σ S) : eval₂Hom f X = bind₂ f :=
   rfl
 #align mv_polynomial.eval₂_hom_eq_bind₂ MvPolynomial.eval₂Hom_eq_bind₂
+-/
 
 section
 
 variable (σ R)
 
+#print MvPolynomial.aeval_id_eq_join₁ /-
 @[simp]
 theorem aeval_id_eq_join₁ : aeval id = @join₁ σ R _ :=
   rfl
 #align mv_polynomial.aeval_id_eq_join₁ MvPolynomial.aeval_id_eq_join₁
+-/
 
+#print MvPolynomial.eval₂Hom_C_id_eq_join₁ /-
 theorem eval₂Hom_C_id_eq_join₁ (φ : MvPolynomial (MvPolynomial σ R) R) :
     eval₂Hom C id φ = join₁ φ :=
   rfl
 #align mv_polynomial.eval₂_hom_C_id_eq_join₁ MvPolynomial.eval₂Hom_C_id_eq_join₁
+-/
 
+#print MvPolynomial.eval₂Hom_id_X_eq_join₂ /-
 @[simp]
 theorem eval₂Hom_id_X_eq_join₂ : eval₂Hom (RingHom.id _) X = @join₂ σ R _ :=
   rfl
 #align mv_polynomial.eval₂_hom_id_X_eq_join₂ MvPolynomial.eval₂Hom_id_X_eq_join₂
+-/
 
 end
 
@@ -158,98 +170,137 @@ end
 attribute [-simp] aeval_eq_bind₁ eval₂_hom_C_eq_bind₁ eval₂_hom_eq_bind₂ aeval_id_eq_join₁
   eval₂_hom_id_X_eq_join₂
 
+#print MvPolynomial.bind₁_X_right /-
 @[simp]
 theorem bind₁_X_right (f : σ → MvPolynomial τ R) (i : σ) : bind₁ f (X i) = f i :=
   aeval_X f i
 #align mv_polynomial.bind₁_X_right MvPolynomial.bind₁_X_right
+-/
 
+#print MvPolynomial.bind₂_X_right /-
 @[simp]
 theorem bind₂_X_right (f : R →+* MvPolynomial σ S) (i : σ) : bind₂ f (X i) = X i :=
   eval₂Hom_X' f X i
 #align mv_polynomial.bind₂_X_right MvPolynomial.bind₂_X_right
+-/
 
+#print MvPolynomial.bind₁_X_left /-
 @[simp]
 theorem bind₁_X_left : bind₁ (X : σ → MvPolynomial σ R) = AlgHom.id R _ := by ext1 i; simp
 #align mv_polynomial.bind₁_X_left MvPolynomial.bind₁_X_left
+-/
 
 variable (f : σ → MvPolynomial τ R)
 
+#print MvPolynomial.bind₁_C_right /-
 @[simp]
 theorem bind₁_C_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (C x) = C x := by
   simp [bind₁, algebra_map_eq]
 #align mv_polynomial.bind₁_C_right MvPolynomial.bind₁_C_right
+-/
 
+#print MvPolynomial.bind₂_C_right /-
 @[simp]
 theorem bind₂_C_right (f : R →+* MvPolynomial σ S) (r : R) : bind₂ f (C r) = f r :=
   eval₂Hom_C f X r
 #align mv_polynomial.bind₂_C_right MvPolynomial.bind₂_C_right
+-/
 
+#print MvPolynomial.bind₂_C_left /-
 @[simp]
 theorem bind₂_C_left : bind₂ (C : R →+* MvPolynomial σ R) = RingHom.id _ := by ext : 2 <;> simp
 #align mv_polynomial.bind₂_C_left MvPolynomial.bind₂_C_left
+-/
 
+#print MvPolynomial.bind₂_comp_C /-
 @[simp]
 theorem bind₂_comp_C (f : R →+* MvPolynomial σ S) : (bind₂ f).comp C = f :=
   RingHom.ext <| bind₂_C_right _
 #align mv_polynomial.bind₂_comp_C MvPolynomial.bind₂_comp_C
+-/
 
+#print MvPolynomial.join₂_map /-
 @[simp]
 theorem join₂_map (f : R →+* MvPolynomial σ S) (φ : MvPolynomial σ R) :
     join₂ (map f φ) = bind₂ f φ := by simp only [join₂, bind₂, eval₂_hom_map_hom, RingHom.id_comp]
 #align mv_polynomial.join₂_map MvPolynomial.join₂_map
+-/
 
+#print MvPolynomial.join₂_comp_map /-
 @[simp]
 theorem join₂_comp_map (f : R →+* MvPolynomial σ S) : join₂.comp (map f) = bind₂ f :=
   RingHom.ext <| join₂_map _
 #align mv_polynomial.join₂_comp_map MvPolynomial.join₂_comp_map
+-/
 
+#print MvPolynomial.aeval_id_rename /-
 theorem aeval_id_rename (f : σ → MvPolynomial τ R) (p : MvPolynomial σ R) :
     aeval id (rename f p) = aeval f p := by rw [aeval_rename, Function.comp.left_id]
 #align mv_polynomial.aeval_id_rename MvPolynomial.aeval_id_rename
+-/
 
+#print MvPolynomial.join₁_rename /-
 @[simp]
 theorem join₁_rename (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     join₁ (rename f φ) = bind₁ f φ :=
   aeval_id_rename _ _
 #align mv_polynomial.join₁_rename MvPolynomial.join₁_rename
+-/
 
+#print MvPolynomial.bind₁_id /-
 @[simp]
 theorem bind₁_id : bind₁ (@id (MvPolynomial σ R)) = join₁ :=
   rfl
 #align mv_polynomial.bind₁_id MvPolynomial.bind₁_id
+-/
 
+#print MvPolynomial.bind₂_id /-
 @[simp]
 theorem bind₂_id : bind₂ (RingHom.id (MvPolynomial σ R)) = join₂ :=
   rfl
 #align mv_polynomial.bind₂_id MvPolynomial.bind₂_id
+-/
 
+#print MvPolynomial.bind₁_bind₁ /-
 theorem bind₁_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R)
     (φ : MvPolynomial σ R) : (bind₁ g) (bind₁ f φ) = bind₁ (fun i => bind₁ g (f i)) φ := by
   simp [bind₁, ← comp_aeval]
 #align mv_polynomial.bind₁_bind₁ MvPolynomial.bind₁_bind₁
+-/
 
+#print MvPolynomial.bind₁_comp_bind₁ /-
 theorem bind₁_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R) :
     (bind₁ g).comp (bind₁ f) = bind₁ fun i => bind₁ g (f i) := by ext1; apply bind₁_bind₁
 #align mv_polynomial.bind₁_comp_bind₁ MvPolynomial.bind₁_comp_bind₁
+-/
 
+#print MvPolynomial.bind₂_comp_bind₂ /-
 theorem bind₂_comp_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPolynomial σ T) :
     (bind₂ g).comp (bind₂ f) = bind₂ ((bind₂ g).comp f) := by ext : 2 <;> simp
 #align mv_polynomial.bind₂_comp_bind₂ MvPolynomial.bind₂_comp_bind₂
+-/
 
+#print MvPolynomial.bind₂_bind₂ /-
 theorem bind₂_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPolynomial σ T)
     (φ : MvPolynomial σ R) : (bind₂ g) (bind₂ f φ) = bind₂ ((bind₂ g).comp f) φ :=
   RingHom.congr_fun (bind₂_comp_bind₂ f g) φ
 #align mv_polynomial.bind₂_bind₂ MvPolynomial.bind₂_bind₂
+-/
 
+#print MvPolynomial.rename_comp_bind₁ /-
 theorem rename_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) :
     (rename g).comp (bind₁ f) = bind₁ fun i => rename g <| f i := by ext1 i; simp
 #align mv_polynomial.rename_comp_bind₁ MvPolynomial.rename_comp_bind₁
+-/
 
+#print MvPolynomial.rename_bind₁ /-
 theorem rename_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) (φ : MvPolynomial σ R) :
     rename g (bind₁ f φ) = bind₁ (fun i => rename g <| f i) φ :=
   AlgHom.congr_fun (rename_comp_bind₁ f g) φ
 #align mv_polynomial.rename_bind₁ MvPolynomial.rename_bind₁
+-/
 
+#print MvPolynomial.map_bind₂ /-
 theorem map_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* T) (φ : MvPolynomial σ R) :
     map g (bind₂ f φ) = bind₂ ((map g).comp f) φ :=
   by
@@ -257,92 +308,128 @@ theorem map_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* T) (φ : MvPoly
   congr 1 with : 1
   simp only [Function.comp_apply, map_X]
 #align mv_polynomial.map_bind₂ MvPolynomial.map_bind₂
+-/
 
+#print MvPolynomial.bind₁_comp_rename /-
 theorem bind₁_comp_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ → τ) :
     (bind₁ f).comp (rename g) = bind₁ (f ∘ g) := by ext1 i; simp
 #align mv_polynomial.bind₁_comp_rename MvPolynomial.bind₁_comp_rename
+-/
 
+#print MvPolynomial.bind₁_rename /-
 theorem bind₁_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ → τ) (φ : MvPolynomial σ R) :
     bind₁ f (rename g φ) = bind₁ (f ∘ g) φ :=
   AlgHom.congr_fun (bind₁_comp_rename f g) φ
 #align mv_polynomial.bind₁_rename MvPolynomial.bind₁_rename
+-/
 
+#print MvPolynomial.bind₂_map /-
 theorem bind₂_map (f : S →+* MvPolynomial σ T) (g : R →+* S) (φ : MvPolynomial σ R) :
     bind₂ f (map g φ) = bind₂ (f.comp g) φ := by simp [bind₂]
 #align mv_polynomial.bind₂_map MvPolynomial.bind₂_map
+-/
 
+#print MvPolynomial.map_comp_C /-
 @[simp]
 theorem map_comp_C (f : R →+* S) : (map f).comp (C : R →+* MvPolynomial σ R) = C.comp f := by ext1;
   apply map_C
 #align mv_polynomial.map_comp_C MvPolynomial.map_comp_C
+-/
 
+#print MvPolynomial.hom_bind₁ /-
 -- mixing the two monad structures
 theorem hom_bind₁ (f : MvPolynomial τ R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     f (bind₁ g φ) = eval₂Hom (f.comp C) (fun i => f (g i)) φ := by
   rw [bind₁, map_aeval, algebra_map_eq]
 #align mv_polynomial.hom_bind₁ MvPolynomial.hom_bind₁
+-/
 
+#print MvPolynomial.map_bind₁ /-
 theorem map_bind₁ (f : R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     map f (bind₁ g φ) = bind₁ (fun i : σ => (map f) (g i)) (map f φ) := by
   rw [hom_bind₁, map_comp_C, ← eval₂_hom_map_hom]; rfl
 #align mv_polynomial.map_bind₁ MvPolynomial.map_bind₁
+-/
 
+#print MvPolynomial.eval₂Hom_comp_C /-
 @[simp]
 theorem eval₂Hom_comp_C (f : R →+* S) (g : σ → S) : (eval₂Hom f g).comp C = f := by ext1 r;
   exact eval₂_C f g r
 #align mv_polynomial.eval₂_hom_comp_C MvPolynomial.eval₂Hom_comp_C
+-/
 
+#print MvPolynomial.eval₂Hom_bind₁ /-
 theorem eval₂Hom_bind₁ (f : R →+* S) (g : τ → S) (h : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     eval₂Hom f g (bind₁ h φ) = eval₂Hom f (fun i => eval₂Hom f g (h i)) φ := by
   rw [hom_bind₁, eval₂_hom_comp_C]
 #align mv_polynomial.eval₂_hom_bind₁ MvPolynomial.eval₂Hom_bind₁
+-/
 
+#print MvPolynomial.aeval_bind₁ /-
 theorem aeval_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     aeval f (bind₁ g φ) = aeval (fun i => aeval f (g i)) φ :=
   eval₂Hom_bind₁ _ _ _ _
 #align mv_polynomial.aeval_bind₁ MvPolynomial.aeval_bind₁
+-/
 
+#print MvPolynomial.aeval_comp_bind₁ /-
 theorem aeval_comp_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R) :
     (aeval f).comp (bind₁ g) = aeval fun i => aeval f (g i) := by ext1; apply aeval_bind₁
 #align mv_polynomial.aeval_comp_bind₁ MvPolynomial.aeval_comp_bind₁
+-/
 
+#print MvPolynomial.eval₂Hom_comp_bind₂ /-
 theorem eval₂Hom_comp_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPolynomial σ S) :
     (eval₂Hom f g).comp (bind₂ h) = eval₂Hom ((eval₂Hom f g).comp h) g := by ext : 2 <;> simp
 #align mv_polynomial.eval₂_hom_comp_bind₂ MvPolynomial.eval₂Hom_comp_bind₂
+-/
 
+#print MvPolynomial.eval₂Hom_bind₂ /-
 theorem eval₂Hom_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPolynomial σ S)
     (φ : MvPolynomial σ R) : eval₂Hom f g (bind₂ h φ) = eval₂Hom ((eval₂Hom f g).comp h) g φ :=
   RingHom.congr_fun (eval₂Hom_comp_bind₂ f g h) φ
 #align mv_polynomial.eval₂_hom_bind₂ MvPolynomial.eval₂Hom_bind₂
+-/
 
+#print MvPolynomial.aeval_bind₂ /-
 theorem aeval_bind₂ [Algebra S T] (f : σ → T) (g : R →+* MvPolynomial σ S) (φ : MvPolynomial σ R) :
     aeval f (bind₂ g φ) = eval₂Hom ((↑(aeval f : _ →ₐ[S] _) : _ →+* _).comp g) f φ :=
   eval₂Hom_bind₂ _ _ _ _
 #align mv_polynomial.aeval_bind₂ MvPolynomial.aeval_bind₂
+-/
 
+#print MvPolynomial.eval₂Hom_C_left /-
 theorem eval₂Hom_C_left (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind₁ f :=
   rfl
 #align mv_polynomial.eval₂_hom_C_left MvPolynomial.eval₂Hom_C_left
+-/
 
+#print MvPolynomial.bind₁_monomial /-
 theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r : R) :
     bind₁ f (monomial d r) = C r * ∏ i in d.support, f i ^ d i := by
   simp only [monomial_eq, AlgHom.map_mul, bind₁_C_right, Finsupp.prod, AlgHom.map_prod,
     AlgHom.map_pow, bind₁_X_right]
 #align mv_polynomial.bind₁_monomial MvPolynomial.bind₁_monomial
+-/
 
+#print MvPolynomial.bind₂_monomial /-
 theorem bind₂_monomial (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) (r : R) :
     bind₂ f (monomial d r) = f r * monomial d 1 := by
   simp only [monomial_eq, RingHom.map_mul, bind₂_C_right, Finsupp.prod, RingHom.map_prod,
     RingHom.map_pow, bind₂_X_right, C_1, one_mul]
 #align mv_polynomial.bind₂_monomial MvPolynomial.bind₂_monomial
+-/
 
+#print MvPolynomial.bind₂_monomial_one /-
 @[simp]
 theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) :
     bind₂ f (monomial d 1) = monomial d 1 := by rw [bind₂_monomial, f.map_one, one_mul]
 #align mv_polynomial.bind₂_monomial_one MvPolynomial.bind₂_monomial_one
+-/
 
 section
 
+#print MvPolynomial.vars_bind₁ /-
 theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     (bind₁ f φ).vars ⊆ φ.vars.biUnion fun i => (f i).vars :=
   by
@@ -377,14 +464,17 @@ theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPol
     rintro ⟨d, hd, ⟨i, hi, hj⟩⟩
     exact ⟨i, (mem_vars _).mpr ⟨d, hd, hi⟩, hj⟩
 #align mv_polynomial.vars_bind₁ MvPolynomial.vars_bind₁
+-/
 
 end
 
+#print MvPolynomial.mem_vars_bind₁ /-
 theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
     (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by
   classical simpa only [exists_prop, Finset.mem_biUnion, mem_support_iff, Ne.def] using
     vars_bind₁ f φ h
 #align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁
+-/
 
 #print MvPolynomial.monad /-
 instance monad : Monad fun σ => MvPolynomial σ R

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -358,7 +358,6 @@ theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPol
         _ ≤
         φ.vars.bUnion fun i : σ => (f i).vars :=
       _
-    
   -- proof below
   · apply Finset.biUnion_mono
     intro d hd
@@ -370,7 +369,6 @@ theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPol
         simp only [Finset.empty_union, vars_C, Finset.le_iff_subset, Finset.Subset.refl]
       _ ≤ d.support.bUnion fun i : σ => (f i ^ d i).vars := (vars_prod _)
       _ ≤ d.support.bUnion fun i : σ => (f i).vars := _
-      
     apply Finset.biUnion_mono
     intro i hi
     apply vars_pow

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

@@ -385,7 +385,7 @@ end
 theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
     (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by
   classical simpa only [exists_prop, Finset.mem_biUnion, mem_support_iff, Ne.def] using
-      vars_bind₁ f φ h
+    vars_bind₁ f φ h
 #align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁
 
 #print MvPolynomial.monad /-

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

@@ -155,8 +155,8 @@ end
 -- In this file, we don't want to use these simp lemmas,
 -- because we first need to show how these new definitions interact
 -- and the proofs fall back on unfolding the definitions and call simp afterwards
-attribute [-simp]
-  aeval_eq_bind₁ eval₂_hom_C_eq_bind₁ eval₂_hom_eq_bind₂ aeval_id_eq_join₁ eval₂_hom_id_X_eq_join₂
+attribute [-simp] aeval_eq_bind₁ eval₂_hom_C_eq_bind₁ eval₂_hom_eq_bind₂ aeval_id_eq_join₁
+  eval₂_hom_id_X_eq_join₂
 
 @[simp]
 theorem bind₁_X_right (f : σ → MvPolynomial τ R) (i : σ) : bind₁ f (X i) = f i :=

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

@@ -53,7 +53,7 @@ since it is not a monad in `Type` but in `CommRing` (or rather `CommSemiRing`).
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
 noncomputable section
 

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

@@ -116,31 +116,16 @@ def join₂ : MvPolynomial σ (MvPolynomial σ R) →+* MvPolynomial σ R :=
 #align mv_polynomial.join₂ MvPolynomial.join₂
 -/
 
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 @[simp]
 theorem aeval_eq_bind₁ (f : σ → MvPolynomial τ R) : aeval f = bind₁ f :=
   rfl
 #align mv_polynomial.aeval_eq_bind₁ MvPolynomial.aeval_eq_bind₁
 
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 @[simp]
 theorem eval₂Hom_C_eq_bind₁ (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind₁ f :=
   rfl
 #align mv_polynomial.eval₂_hom_C_eq_bind₁ MvPolynomial.eval₂Hom_C_eq_bind₁
 
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 @[simp]
 theorem eval₂Hom_eq_bind₂ (f : R →+* MvPolynomial σ S) : eval₂Hom f X = bind₂ f :=
   rfl
@@ -150,31 +135,16 @@ section
 
 variable (σ R)
 
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 @[simp]
 theorem aeval_id_eq_join₁ : aeval id = @join₁ σ R _ :=
   rfl
 #align mv_polynomial.aeval_id_eq_join₁ MvPolynomial.aeval_id_eq_join₁
 
-/- warning: mv_polynomial.eval₂_hom_C_id_eq_join₁ -> MvPolynomial.eval₂Hom_C_id_eq_join₁ is a dubious translation:
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 theorem eval₂Hom_C_id_eq_join₁ (φ : MvPolynomial (MvPolynomial σ R) R) :
     eval₂Hom C id φ = join₁ φ :=
   rfl
 #align mv_polynomial.eval₂_hom_C_id_eq_join₁ MvPolynomial.eval₂Hom_C_id_eq_join₁
 
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 @[simp]
 theorem eval₂Hom_id_X_eq_join₂ : eval₂Hom (RingHom.id _) X = @join₂ σ R _ :=
   rfl
@@ -188,182 +158,98 @@ end
 attribute [-simp]
   aeval_eq_bind₁ eval₂_hom_C_eq_bind₁ eval₂_hom_eq_bind₂ aeval_id_eq_join₁ eval₂_hom_id_X_eq_join₂
 
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 @[simp]
 theorem bind₁_X_right (f : σ → MvPolynomial τ R) (i : σ) : bind₁ f (X i) = f i :=
   aeval_X f i
 #align mv_polynomial.bind₁_X_right MvPolynomial.bind₁_X_right
 
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 @[simp]
 theorem bind₂_X_right (f : R →+* MvPolynomial σ S) (i : σ) : bind₂ f (X i) = X i :=
   eval₂Hom_X' f X i
 #align mv_polynomial.bind₂_X_right MvPolynomial.bind₂_X_right
 
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 @[simp]
 theorem bind₁_X_left : bind₁ (X : σ → MvPolynomial σ R) = AlgHom.id R _ := by ext1 i; simp
 #align mv_polynomial.bind₁_X_left MvPolynomial.bind₁_X_left
 
 variable (f : σ → MvPolynomial τ R)
 
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 @[simp]
 theorem bind₁_C_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (C x) = C x := by
   simp [bind₁, algebra_map_eq]
 #align mv_polynomial.bind₁_C_right MvPolynomial.bind₁_C_right
 
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 @[simp]
 theorem bind₂_C_right (f : R →+* MvPolynomial σ S) (r : R) : bind₂ f (C r) = f r :=
   eval₂Hom_C f X r
 #align mv_polynomial.bind₂_C_right MvPolynomial.bind₂_C_right
 
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 @[simp]
 theorem bind₂_C_left : bind₂ (C : R →+* MvPolynomial σ R) = RingHom.id _ := by ext : 2 <;> simp
 #align mv_polynomial.bind₂_C_left MvPolynomial.bind₂_C_left
 
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 @[simp]
 theorem bind₂_comp_C (f : R →+* MvPolynomial σ S) : (bind₂ f).comp C = f :=
   RingHom.ext <| bind₂_C_right _
 #align mv_polynomial.bind₂_comp_C MvPolynomial.bind₂_comp_C
 
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 @[simp]
 theorem join₂_map (f : R →+* MvPolynomial σ S) (φ : MvPolynomial σ R) :
     join₂ (map f φ) = bind₂ f φ := by simp only [join₂, bind₂, eval₂_hom_map_hom, RingHom.id_comp]
 #align mv_polynomial.join₂_map MvPolynomial.join₂_map
 
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 @[simp]
 theorem join₂_comp_map (f : R →+* MvPolynomial σ S) : join₂.comp (map f) = bind₂ f :=
   RingHom.ext <| join₂_map _
 #align mv_polynomial.join₂_comp_map MvPolynomial.join₂_comp_map
 
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 theorem aeval_id_rename (f : σ → MvPolynomial τ R) (p : MvPolynomial σ R) :
     aeval id (rename f p) = aeval f p := by rw [aeval_rename, Function.comp.left_id]
 #align mv_polynomial.aeval_id_rename MvPolynomial.aeval_id_rename
 
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 @[simp]
 theorem join₁_rename (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     join₁ (rename f φ) = bind₁ f φ :=
   aeval_id_rename _ _
 #align mv_polynomial.join₁_rename MvPolynomial.join₁_rename
 
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 @[simp]
 theorem bind₁_id : bind₁ (@id (MvPolynomial σ R)) = join₁ :=
   rfl
 #align mv_polynomial.bind₁_id MvPolynomial.bind₁_id
 
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 @[simp]
 theorem bind₂_id : bind₂ (RingHom.id (MvPolynomial σ R)) = join₂ :=
   rfl
 #align mv_polynomial.bind₂_id MvPolynomial.bind₂_id
 
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 theorem bind₁_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R)
     (φ : MvPolynomial σ R) : (bind₁ g) (bind₁ f φ) = bind₁ (fun i => bind₁ g (f i)) φ := by
   simp [bind₁, ← comp_aeval]
 #align mv_polynomial.bind₁_bind₁ MvPolynomial.bind₁_bind₁
 
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 theorem bind₁_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R) :
     (bind₁ g).comp (bind₁ f) = bind₁ fun i => bind₁ g (f i) := by ext1; apply bind₁_bind₁
 #align mv_polynomial.bind₁_comp_bind₁ MvPolynomial.bind₁_comp_bind₁
 
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 theorem bind₂_comp_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPolynomial σ T) :
     (bind₂ g).comp (bind₂ f) = bind₂ ((bind₂ g).comp f) := by ext : 2 <;> simp
 #align mv_polynomial.bind₂_comp_bind₂ MvPolynomial.bind₂_comp_bind₂
 
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 theorem bind₂_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPolynomial σ T)
     (φ : MvPolynomial σ R) : (bind₂ g) (bind₂ f φ) = bind₂ ((bind₂ g).comp f) φ :=
   RingHom.congr_fun (bind₂_comp_bind₂ f g) φ
 #align mv_polynomial.bind₂_bind₂ MvPolynomial.bind₂_bind₂
 
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 theorem rename_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) :
     (rename g).comp (bind₁ f) = bind₁ fun i => rename g <| f i := by ext1 i; simp
 #align mv_polynomial.rename_comp_bind₁ MvPolynomial.rename_comp_bind₁
 
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 theorem rename_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) (φ : MvPolynomial σ R) :
     rename g (bind₁ f φ) = bind₁ (fun i => rename g <| f i) φ :=
   AlgHom.congr_fun (rename_comp_bind₁ f g) φ
 #align mv_polynomial.rename_bind₁ MvPolynomial.rename_bind₁
 
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 theorem map_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* T) (φ : MvPolynomial σ R) :
     map g (bind₂ f φ) = bind₂ ((map g).comp f) φ :=
   by
@@ -372,147 +258,84 @@ theorem map_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* T) (φ : MvPoly
   simp only [Function.comp_apply, map_X]
 #align mv_polynomial.map_bind₂ MvPolynomial.map_bind₂
 
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 theorem bind₁_comp_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ → τ) :
     (bind₁ f).comp (rename g) = bind₁ (f ∘ g) := by ext1 i; simp
 #align mv_polynomial.bind₁_comp_rename MvPolynomial.bind₁_comp_rename
 
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 theorem bind₁_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ → τ) (φ : MvPolynomial σ R) :
     bind₁ f (rename g φ) = bind₁ (f ∘ g) φ :=
   AlgHom.congr_fun (bind₁_comp_rename f g) φ
 #align mv_polynomial.bind₁_rename MvPolynomial.bind₁_rename
 
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 theorem bind₂_map (f : S →+* MvPolynomial σ T) (g : R →+* S) (φ : MvPolynomial σ R) :
     bind₂ f (map g φ) = bind₂ (f.comp g) φ := by simp [bind₂]
 #align mv_polynomial.bind₂_map MvPolynomial.bind₂_map
 
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 @[simp]
 theorem map_comp_C (f : R →+* S) : (map f).comp (C : R →+* MvPolynomial σ R) = C.comp f := by ext1;
   apply map_C
 #align mv_polynomial.map_comp_C MvPolynomial.map_comp_C
 
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 -- mixing the two monad structures
 theorem hom_bind₁ (f : MvPolynomial τ R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     f (bind₁ g φ) = eval₂Hom (f.comp C) (fun i => f (g i)) φ := by
   rw [bind₁, map_aeval, algebra_map_eq]
 #align mv_polynomial.hom_bind₁ MvPolynomial.hom_bind₁
 
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 theorem map_bind₁ (f : R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     map f (bind₁ g φ) = bind₁ (fun i : σ => (map f) (g i)) (map f φ) := by
   rw [hom_bind₁, map_comp_C, ← eval₂_hom_map_hom]; rfl
 #align mv_polynomial.map_bind₁ MvPolynomial.map_bind₁
 
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 @[simp]
 theorem eval₂Hom_comp_C (f : R →+* S) (g : σ → S) : (eval₂Hom f g).comp C = f := by ext1 r;
   exact eval₂_C f g r
 #align mv_polynomial.eval₂_hom_comp_C MvPolynomial.eval₂Hom_comp_C
 
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 theorem eval₂Hom_bind₁ (f : R →+* S) (g : τ → S) (h : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     eval₂Hom f g (bind₁ h φ) = eval₂Hom f (fun i => eval₂Hom f g (h i)) φ := by
   rw [hom_bind₁, eval₂_hom_comp_C]
 #align mv_polynomial.eval₂_hom_bind₁ MvPolynomial.eval₂Hom_bind₁
 
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 theorem aeval_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     aeval f (bind₁ g φ) = aeval (fun i => aeval f (g i)) φ :=
   eval₂Hom_bind₁ _ _ _ _
 #align mv_polynomial.aeval_bind₁ MvPolynomial.aeval_bind₁
 
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 theorem aeval_comp_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R) :
     (aeval f).comp (bind₁ g) = aeval fun i => aeval f (g i) := by ext1; apply aeval_bind₁
 #align mv_polynomial.aeval_comp_bind₁ MvPolynomial.aeval_comp_bind₁
 
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 theorem eval₂Hom_comp_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPolynomial σ S) :
     (eval₂Hom f g).comp (bind₂ h) = eval₂Hom ((eval₂Hom f g).comp h) g := by ext : 2 <;> simp
 #align mv_polynomial.eval₂_hom_comp_bind₂ MvPolynomial.eval₂Hom_comp_bind₂
 
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 theorem eval₂Hom_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPolynomial σ S)
     (φ : MvPolynomial σ R) : eval₂Hom f g (bind₂ h φ) = eval₂Hom ((eval₂Hom f g).comp h) g φ :=
   RingHom.congr_fun (eval₂Hom_comp_bind₂ f g h) φ
 #align mv_polynomial.eval₂_hom_bind₂ MvPolynomial.eval₂Hom_bind₂
 
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 theorem aeval_bind₂ [Algebra S T] (f : σ → T) (g : R →+* MvPolynomial σ S) (φ : MvPolynomial σ R) :
     aeval f (bind₂ g φ) = eval₂Hom ((↑(aeval f : _ →ₐ[S] _) : _ →+* _).comp g) f φ :=
   eval₂Hom_bind₂ _ _ _ _
 #align mv_polynomial.aeval_bind₂ MvPolynomial.aeval_bind₂
 
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 theorem eval₂Hom_C_left (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind₁ f :=
   rfl
 #align mv_polynomial.eval₂_hom_C_left MvPolynomial.eval₂Hom_C_left
 
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 theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r : R) :
     bind₁ f (monomial d r) = C r * ∏ i in d.support, f i ^ d i := by
   simp only [monomial_eq, AlgHom.map_mul, bind₁_C_right, Finsupp.prod, AlgHom.map_prod,
     AlgHom.map_pow, bind₁_X_right]
 #align mv_polynomial.bind₁_monomial MvPolynomial.bind₁_monomial
 
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 theorem bind₂_monomial (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) (r : R) :
     bind₂ f (monomial d r) = f r * monomial d 1 := by
   simp only [monomial_eq, RingHom.map_mul, bind₂_C_right, Finsupp.prod, RingHom.map_prod,
     RingHom.map_pow, bind₂_X_right, C_1, one_mul]
 #align mv_polynomial.bind₂_monomial MvPolynomial.bind₂_monomial
 
-/- warning: mv_polynomial.bind₂_monomial_one -> MvPolynomial.bind₂_monomial_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_monomial_one MvPolynomial.bind₂_monomial_oneₓ'. -/
 @[simp]
 theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) :
     bind₂ f (monomial d 1) = monomial d 1 := by rw [bind₂_monomial, f.map_one, one_mul]
@@ -520,9 +343,6 @@ theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ)
 
 section
 
-/- warning: mv_polynomial.vars_bind₁ -> MvPolynomial.vars_bind₁ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_bind₁ MvPolynomial.vars_bind₁ₓ'. -/
 theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     (bind₁ f φ).vars ⊆ φ.vars.biUnion fun i => (f i).vars :=
   by
@@ -562,9 +382,6 @@ theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPol
 
 end
 
-/- warning: mv_polynomial.mem_vars_bind₁ -> MvPolynomial.mem_vars_bind₁ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁ₓ'. -/
 theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
     (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by
   classical simpa only [exists_prop, Finset.mem_biUnion, mem_support_iff, Ne.def] using

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

@@ -214,10 +214,7 @@ but is expected to have type
   forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R], Eq.{max (succ u2) (succ u1)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.bind₁.{u2, u2, u1} σ σ R _inst_1 (MvPolynomial.X.{u1, u2} R σ _inst_1)) (AlgHom.id.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_X_left MvPolynomial.bind₁_X_leftₓ'. -/
 @[simp]
-theorem bind₁_X_left : bind₁ (X : σ → MvPolynomial σ R) = AlgHom.id R _ :=
-  by
-  ext1 i
-  simp
+theorem bind₁_X_left : bind₁ (X : σ → MvPolynomial σ R) = AlgHom.id R _ := by ext1 i; simp
 #align mv_polynomial.bind₁_X_left MvPolynomial.bind₁_X_left
 
 variable (f : σ → MvPolynomial τ R)
@@ -328,10 +325,7 @@ theorem bind₁_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ →
 <too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_comp_bind₁ MvPolynomial.bind₁_comp_bind₁ₓ'. -/
 theorem bind₁_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R) :
-    (bind₁ g).comp (bind₁ f) = bind₁ fun i => bind₁ g (f i) :=
-  by
-  ext1
-  apply bind₁_bind₁
+    (bind₁ g).comp (bind₁ f) = bind₁ fun i => bind₁ g (f i) := by ext1; apply bind₁_bind₁
 #align mv_polynomial.bind₁_comp_bind₁ MvPolynomial.bind₁_comp_bind₁
 
 /- warning: mv_polynomial.bind₂_comp_bind₂ -> MvPolynomial.bind₂_comp_bind₂ is a dubious translation:
@@ -356,10 +350,7 @@ theorem bind₂_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPolynomia
 <too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.rename_comp_bind₁ MvPolynomial.rename_comp_bind₁ₓ'. -/
 theorem rename_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) :
-    (rename g).comp (bind₁ f) = bind₁ fun i => rename g <| f i :=
-  by
-  ext1 i
-  simp
+    (rename g).comp (bind₁ f) = bind₁ fun i => rename g <| f i := by ext1 i; simp
 #align mv_polynomial.rename_comp_bind₁ MvPolynomial.rename_comp_bind₁
 
 /- warning: mv_polynomial.rename_bind₁ -> MvPolynomial.rename_bind₁ is a dubious translation:
@@ -388,10 +379,7 @@ but is expected to have type
   forall {σ : Type.{u2}} {τ : Type.{u1}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {υ : Type.{u4}} (f : τ -> (MvPolynomial.{u4, u3} υ R _inst_1)) (g : σ -> τ), Eq.{max (max (succ u2) (succ u3)) (succ u4)} (AlgHom.{u3, max u3 u2, max u3 u4} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (AlgHom.comp.{u3, max u3 u2, max u1 u3, max u3 u4} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.bind₁.{u1, u4, u3} τ υ R _inst_1 f) (MvPolynomial.rename.{u2, u1, u3} σ τ R _inst_1 g)) (MvPolynomial.bind₁.{u2, u4, u3} σ υ R _inst_1 (Function.comp.{succ u2, succ u1, max (succ u3) (succ u4)} σ τ (MvPolynomial.{u4, u3} υ R _inst_1) f g))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_comp_rename MvPolynomial.bind₁_comp_renameₓ'. -/
 theorem bind₁_comp_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ → τ) :
-    (bind₁ f).comp (rename g) = bind₁ (f ∘ g) :=
-  by
-  ext1 i
-  simp
+    (bind₁ f).comp (rename g) = bind₁ (f ∘ g) := by ext1 i; simp
 #align mv_polynomial.bind₁_comp_rename MvPolynomial.bind₁_comp_rename
 
 /- warning: mv_polynomial.bind₁_rename -> MvPolynomial.bind₁_rename is a dubious translation:
@@ -416,9 +404,7 @@ but is expected to have type
   forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (RingHom.{u3, max u2 u1} R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (RingHom.comp.{u3, max u3 u1, max u2 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (MvPolynomial.map.{u3, u2, u1} R S σ _inst_1 _inst_2 f) (MvPolynomial.C.{u3, u1} R σ _inst_1)) (RingHom.comp.{u3, u2, max u1 u2} R S (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (MvPolynomial.C.{u2, u1} S σ _inst_2) f)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_comp_C MvPolynomial.map_comp_Cₓ'. -/
 @[simp]
-theorem map_comp_C (f : R →+* S) : (map f).comp (C : R →+* MvPolynomial σ R) = C.comp f :=
-  by
-  ext1
+theorem map_comp_C (f : R →+* S) : (map f).comp (C : R →+* MvPolynomial σ R) = C.comp f := by ext1;
   apply map_C
 #align mv_polynomial.map_comp_C MvPolynomial.map_comp_C
 
@@ -435,10 +421,8 @@ theorem hom_bind₁ (f : MvPolynomial τ R →+* S) (g : σ → MvPolynomial τ
 <too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_bind₁ MvPolynomial.map_bind₁ₓ'. -/
 theorem map_bind₁ (f : R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
-    map f (bind₁ g φ) = bind₁ (fun i : σ => (map f) (g i)) (map f φ) :=
-  by
-  rw [hom_bind₁, map_comp_C, ← eval₂_hom_map_hom]
-  rfl
+    map f (bind₁ g φ) = bind₁ (fun i : σ => (map f) (g i)) (map f φ) := by
+  rw [hom_bind₁, map_comp_C, ← eval₂_hom_map_hom]; rfl
 #align mv_polynomial.map_bind₁ MvPolynomial.map_bind₁
 
 /- warning: mv_polynomial.eval₂_hom_comp_C -> MvPolynomial.eval₂Hom_comp_C is a dubious translation:
@@ -448,9 +432,7 @@ but is expected to have type
   forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (g : σ -> S), Eq.{max (succ u3) (succ u2)} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHom.comp.{u3, max u1 u3, u2} R (MvPolynomial.{u1, u3} σ R _inst_1) S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (MvPolynomial.eval₂Hom.{u3, u2, u1} R S σ _inst_1 _inst_2 f g) (MvPolynomial.C.{u3, u1} R σ _inst_1)) f
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_comp_C MvPolynomial.eval₂Hom_comp_Cₓ'. -/
 @[simp]
-theorem eval₂Hom_comp_C (f : R →+* S) (g : σ → S) : (eval₂Hom f g).comp C = f :=
-  by
-  ext1 r
+theorem eval₂Hom_comp_C (f : R →+* S) (g : σ → S) : (eval₂Hom f g).comp C = f := by ext1 r;
   exact eval₂_C f g r
 #align mv_polynomial.eval₂_hom_comp_C MvPolynomial.eval₂Hom_comp_C
 
@@ -474,10 +456,7 @@ theorem aeval_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R
 <too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_comp_bind₁ MvPolynomial.aeval_comp_bind₁ₓ'. -/
 theorem aeval_comp_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R) :
-    (aeval f).comp (bind₁ g) = aeval fun i => aeval f (g i) :=
-  by
-  ext1
-  apply aeval_bind₁
+    (aeval f).comp (bind₁ g) = aeval fun i => aeval f (g i) := by ext1; apply aeval_bind₁
 #align mv_polynomial.aeval_comp_bind₁ MvPolynomial.aeval_comp_bind₁
 
 /- warning: mv_polynomial.eval₂_hom_comp_bind₂ -> MvPolynomial.eval₂Hom_comp_bind₂ is a dubious translation:

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

@@ -128,10 +128,7 @@ theorem aeval_eq_bind₁ (f : σ → MvPolynomial τ R) : aeval f = bind₁ f :=
 #align mv_polynomial.aeval_eq_bind₁ MvPolynomial.aeval_eq_bind₁
 
 /- warning: mv_polynomial.eval₂_hom_C_eq_bind₁ -> MvPolynomial.eval₂Hom_C_eq_bind₁ is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_C_eq_bind₁ MvPolynomial.eval₂Hom_C_eq_bind₁ₓ'. -/
 @[simp]
 theorem eval₂Hom_C_eq_bind₁ (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind₁ f :=
@@ -165,10 +162,7 @@ theorem aeval_id_eq_join₁ : aeval id = @join₁ σ R _ :=
 #align mv_polynomial.aeval_id_eq_join₁ MvPolynomial.aeval_id_eq_join₁
 
 /- warning: mv_polynomial.eval₂_hom_C_id_eq_join₁ -> MvPolynomial.eval₂Hom_C_id_eq_join₁ is a dubious translation:
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (AlgHom.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (AlgHom.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u1, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.join₁.{u1, u2} σ R _inst_1) φ)
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_C_id_eq_join₁ MvPolynomial.eval₂Hom_C_id_eq_join₁ₓ'. -/
 theorem eval₂Hom_C_id_eq_join₁ (φ : MvPolynomial (MvPolynomial σ R) R) :
     eval₂Hom C id φ = join₁ φ :=
@@ -195,10 +189,7 @@ attribute [-simp]
   aeval_eq_bind₁ eval₂_hom_C_eq_bind₁ eval₂_hom_eq_bind₂ aeval_id_eq_join₁ eval₂_hom_id_X_eq_join₂
 
 /- warning: mv_polynomial.bind₁_X_right -> MvPolynomial.bind₁_X_right is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_X_right MvPolynomial.bind₁_X_rightₓ'. -/
 @[simp]
 theorem bind₁_X_right (f : σ → MvPolynomial τ R) (i : σ) : bind₁ f (X i) = f i :=
@@ -232,10 +223,7 @@ theorem bind₁_X_left : bind₁ (X : σ → MvPolynomial σ R) = AlgHom.id R _
 variable (f : σ → MvPolynomial τ R)
 
 /- warning: mv_polynomial.bind₁_C_right -> MvPolynomial.bind₁_C_right is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_C_right MvPolynomial.bind₁_C_rightₓ'. -/
 @[simp]
 theorem bind₁_C_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (C x) = C x := by
@@ -243,10 +231,7 @@ theorem bind₁_C_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (C x) = C
 #align mv_polynomial.bind₁_C_right MvPolynomial.bind₁_C_right
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_C_right MvPolynomial.bind₂_C_rightₓ'. -/
 @[simp]
 theorem bind₂_C_right (f : R →+* MvPolynomial σ S) (r : R) : bind₂ f (C r) = f r :=
@@ -275,10 +260,7 @@ theorem bind₂_comp_C (f : R →+* MvPolynomial σ S) : (bind₂ f).comp C = f
 #align mv_polynomial.bind₂_comp_C MvPolynomial.bind₂_comp_C
 
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S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} 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(MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))))))) (MvPolynomial.map.{u3, max u1 u2, u1} R (MvPolynomial.{u1, u2} σ S _inst_2) σ _inst_1 (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2) f) φ)) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), max (succ u1) (succ u2)} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) 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u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u3, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.bind₂.{u1, u3, u2} σ R S _inst_1 _inst_2 f) φ)
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.join₂_map MvPolynomial.join₂_mapₓ'. -/
 @[simp]
 theorem join₂_map (f : R →+* MvPolynomial σ S) (φ : MvPolynomial σ R) :
@@ -297,20 +279,14 @@ theorem join₂_comp_map (f : R →+* MvPolynomial σ S) : join₂.comp (map f)
 #align mv_polynomial.join₂_comp_map MvPolynomial.join₂_comp_map
 
 /- warning: mv_polynomial.aeval_id_rename -> MvPolynomial.aeval_id_rename is a dubious translation:
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u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.aeval.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} τ R _inst_1) σ _inst_1 (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) f) p)
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_id_rename MvPolynomial.aeval_id_renameₓ'. -/
 theorem aeval_id_rename (f : σ → MvPolynomial τ R) (p : MvPolynomial σ R) :
     aeval id (rename f p) = aeval f p := by rw [aeval_rename, Function.comp.left_id]
 #align mv_polynomial.aeval_id_rename MvPolynomial.aeval_id_rename
 
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(MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ)
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.join₁_rename MvPolynomial.join₁_renameₓ'. -/
 @[simp]
 theorem join₁_rename (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
@@ -341,10 +317,7 @@ theorem bind₂_id : bind₂ (RingHom.id (MvPolynomial σ R)) = join₂ :=
 #align mv_polynomial.bind₂_id MvPolynomial.bind₂_id
 
 /- warning: mv_polynomial.bind₁_bind₁ -> MvPolynomial.bind₁_bind₁ is a dubious translation:
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(MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u2 u4, max (max u3 u2) u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u3, u4, u2} τ υ R _inst_1 g) (f i))) φ)
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_bind₁ MvPolynomial.bind₁_bind₁ₓ'. -/
 theorem bind₁_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R)
     (φ : MvPolynomial σ R) : (bind₁ g) (bind₁ f φ) = bind₁ (fun i => bind₁ g (f i)) φ := by
@@ -352,10 +325,7 @@ theorem bind₁_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ →
 #align mv_polynomial.bind₁_bind₁ MvPolynomial.bind₁_bind₁
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_comp_bind₁ MvPolynomial.bind₁_comp_bind₁ₓ'. -/
 theorem bind₁_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R) :
     (bind₁ g).comp (bind₁ f) = bind₁ fun i => bind₁ g (f i) :=
@@ -375,10 +345,7 @@ theorem bind₂_comp_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPoly
 #align mv_polynomial.bind₂_comp_bind₂ MvPolynomial.bind₂_comp_bind₂
 
 /- warning: mv_polynomial.bind₂_bind₂ -> MvPolynomial.bind₂_bind₂ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_bind₂ MvPolynomial.bind₂_bind₂ₓ'. -/
 theorem bind₂_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPolynomial σ T)
     (φ : MvPolynomial σ R) : (bind₂ g) (bind₂ f φ) = bind₂ ((bind₂ g).comp f) φ :=
@@ -386,10 +353,7 @@ theorem bind₂_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPolynomia
 #align mv_polynomial.bind₂_bind₂ MvPolynomial.bind₂_bind₂
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.rename_comp_bind₁ MvPolynomial.rename_comp_bind₁ₓ'. -/
 theorem rename_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) :
     (rename g).comp (bind₁ f) = bind₁ fun i => rename g <| f i :=
@@ -399,10 +363,7 @@ theorem rename_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ
 #align mv_polynomial.rename_comp_bind₁ MvPolynomial.rename_comp_bind₁
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.rename_bind₁ MvPolynomial.rename_bind₁ₓ'. -/
 theorem rename_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) (φ : MvPolynomial σ R) :
     rename g (bind₁ f φ) = bind₁ (fun i => rename g <| f i) φ :=
@@ -410,10 +371,7 @@ theorem rename_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ →
 #align mv_polynomial.rename_bind₁ MvPolynomial.rename_bind₁
 
 /- warning: mv_polynomial.map_bind₂ -> MvPolynomial.map_bind₂ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_bind₂ MvPolynomial.map_bind₂ₓ'. -/
 theorem map_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* T) (φ : MvPolynomial σ R) :
     map g (bind₂ f φ) = bind₂ ((map g).comp f) φ :=
@@ -437,10 +395,7 @@ theorem bind₁_comp_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ
 #align mv_polynomial.bind₁_comp_rename MvPolynomial.bind₁_comp_rename
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_rename MvPolynomial.bind₁_renameₓ'. -/
 theorem bind₁_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ → τ) (φ : MvPolynomial σ R) :
     bind₁ f (rename g φ) = bind₁ (f ∘ g) φ :=
@@ -448,10 +403,7 @@ theorem bind₁_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ →
 #align mv_polynomial.bind₁_rename MvPolynomial.bind₁_rename
 
 /- warning: mv_polynomial.bind₂_map -> MvPolynomial.bind₂_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_map MvPolynomial.bind₂_mapₓ'. -/
 theorem bind₂_map (f : S →+* MvPolynomial σ T) (g : R →+* S) (φ : MvPolynomial σ R) :
     bind₂ f (map g φ) = bind₂ (f.comp g) φ := by simp [bind₂]
@@ -471,10 +423,7 @@ theorem map_comp_C (f : R →+* S) : (map f).comp (C : R →+* MvPolynomial σ R
 #align mv_polynomial.map_comp_C MvPolynomial.map_comp_C
 
 /- warning: mv_polynomial.hom_bind₁ -> MvPolynomial.hom_bind₁ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.hom_bind₁ MvPolynomial.hom_bind₁ₓ'. -/
 -- mixing the two monad structures
 theorem hom_bind₁ (f : MvPolynomial τ R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
@@ -483,10 +432,7 @@ theorem hom_bind₁ (f : MvPolynomial τ R →+* S) (g : σ → MvPolynomial τ
 #align mv_polynomial.hom_bind₁ MvPolynomial.hom_bind₁
 
 /- warning: mv_polynomial.map_bind₁ -> MvPolynomial.map_bind₁ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_bind₁ MvPolynomial.map_bind₁ₓ'. -/
 theorem map_bind₁ (f : R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     map f (bind₁ g φ) = bind₁ (fun i : σ => (map f) (g i)) (map f φ) :=
@@ -509,10 +455,7 @@ theorem eval₂Hom_comp_C (f : R →+* S) (g : σ → S) : (eval₂Hom f g).comp
 #align mv_polynomial.eval₂_hom_comp_C MvPolynomial.eval₂Hom_comp_C
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_bind₁ MvPolynomial.eval₂Hom_bind₁ₓ'. -/
 theorem eval₂Hom_bind₁ (f : R →+* S) (g : τ → S) (h : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     eval₂Hom f g (bind₁ h φ) = eval₂Hom f (fun i => eval₂Hom f g (h i)) φ := by
@@ -520,10 +463,7 @@ theorem eval₂Hom_bind₁ (f : R →+* S) (g : τ → S) (h : σ → MvPolynomi
 #align mv_polynomial.eval₂_hom_bind₁ MvPolynomial.eval₂Hom_bind₁
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_bind₁ MvPolynomial.aeval_bind₁ₓ'. -/
 theorem aeval_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     aeval f (bind₁ g φ) = aeval (fun i => aeval f (g i)) φ :=
@@ -531,10 +471,7 @@ theorem aeval_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R
 #align mv_polynomial.aeval_bind₁ MvPolynomial.aeval_bind₁
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_comp_bind₁ MvPolynomial.aeval_comp_bind₁ₓ'. -/
 theorem aeval_comp_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R) :
     (aeval f).comp (bind₁ g) = aeval fun i => aeval f (g i) :=
@@ -554,10 +491,7 @@ theorem eval₂Hom_comp_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPo
 #align mv_polynomial.eval₂_hom_comp_bind₂ MvPolynomial.eval₂Hom_comp_bind₂
 
 /- warning: mv_polynomial.eval₂_hom_bind₂ -> MvPolynomial.eval₂Hom_bind₂ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_bind₂ MvPolynomial.eval₂Hom_bind₂ₓ'. -/
 theorem eval₂Hom_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPolynomial σ S)
     (φ : MvPolynomial σ R) : eval₂Hom f g (bind₂ h φ) = eval₂Hom ((eval₂Hom f g).comp h) g φ :=
@@ -565,10 +499,7 @@ theorem eval₂Hom_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPolynom
 #align mv_polynomial.eval₂_hom_bind₂ MvPolynomial.eval₂Hom_bind₂
 
 /- warning: mv_polynomial.aeval_bind₂ -> MvPolynomial.aeval_bind₂ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_bind₂ MvPolynomial.aeval_bind₂ₓ'. -/
 theorem aeval_bind₂ [Algebra S T] (f : σ → T) (g : R →+* MvPolynomial σ S) (φ : MvPolynomial σ R) :
     aeval f (bind₂ g φ) = eval₂Hom ((↑(aeval f : _ →ₐ[S] _) : _ →+* _).comp g) f φ :=
@@ -576,20 +507,14 @@ theorem aeval_bind₂ [Algebra S T] (f : σ → T) (g : R →+* MvPolynomial σ
 #align mv_polynomial.aeval_bind₂ MvPolynomial.aeval_bind₂
 
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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_C_left MvPolynomial.eval₂Hom_C_leftₓ'. -/
 theorem eval₂Hom_C_left (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind₁ f :=
   rfl
 #align mv_polynomial.eval₂_hom_C_left MvPolynomial.eval₂Hom_C_left
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_monomial MvPolynomial.bind₁_monomialₓ'. -/
 theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r : R) :
     bind₁ f (monomial d r) = C r * ∏ i in d.support, f i ^ d i := by
@@ -598,10 +523,7 @@ theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r :
 #align mv_polynomial.bind₁_monomial MvPolynomial.bind₁_monomial
 
 /- warning: mv_polynomial.bind₂_monomial -> MvPolynomial.bind₂_monomial is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_monomial MvPolynomial.bind₂_monomialₓ'. -/
 theorem bind₂_monomial (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) (r : R) :
     bind₂ f (monomial d r) = f r * monomial d 1 := by
@@ -610,10 +532,7 @@ theorem bind₂_monomial (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) (r
 #align mv_polynomial.bind₂_monomial MvPolynomial.bind₂_monomial
 
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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_monomial_one MvPolynomial.bind₂_monomial_oneₓ'. -/
 @[simp]
 theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) :
@@ -623,10 +542,7 @@ theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ)
 section
 
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σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ)) (Finset.biUnion.{u1, u3} σ τ (fun (a : τ) (b : τ) => _inst_4 a b) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u2, u3} R τ _inst_1 (f i)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_bind₁ MvPolynomial.vars_bind₁ₓ'. -/
 theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     (bind₁ f φ).vars ⊆ φ.vars.biUnion fun i => (f i).vars :=
@@ -668,10 +584,7 @@ theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPol
 end
 
 /- warning: mv_polynomial.mem_vars_bind₁ -> MvPolynomial.mem_vars_bind₁ is a dubious translation:
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R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} 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R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ))) -> (Exists.{succ u1} σ (fun (i : σ) => And (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ)) (Membership.mem.{u3, u3} τ (Finset.{u3} τ) (Finset.instMembershipFinset.{u3} τ) j (MvPolynomial.vars.{u2, u3} R τ _inst_1 (f i)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁ₓ'. -/
 theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
     (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by

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

@@ -168,7 +168,7 @@ theorem aeval_id_eq_join₁ : aeval id = @join₁ σ R _ :=
 lean 3 declaration is
   forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1), Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.eval₂Hom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1) (MvPolynomial.C.{u2, u1} R σ _inst_1) (id.{succ (max u1 u2)} (MvPolynomial.{u1, u2} σ R _inst_1))) φ) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) => (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) ([anonymous].{u2, max u1 u2, max u1 u2} R (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.join₁.{u1, u2} σ R _inst_1) φ)
 but is expected to have type
-  forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (fun (_x : MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 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R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u1, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.join₁.{u1, u2} σ R _inst_1) φ)
+  forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (fun (_x : MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 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_inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (AlgHom.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (AlgHom.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u1, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.join₁.{u1, u2} σ R _inst_1) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_C_id_eq_join₁ MvPolynomial.eval₂Hom_C_id_eq_join₁ₓ'. -/
 theorem eval₂Hom_C_id_eq_join₁ (φ : MvPolynomial (MvPolynomial σ R) R) :
     eval₂Hom C id φ = join₁ φ :=
@@ -198,7 +198,7 @@ attribute [-simp]
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (i : σ), Eq.{max (succ u2) (succ u3)} (MvPolynomial.{u2, u3} τ R _inst_1) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) (MvPolynomial.X.{u3, u1} R σ _inst_1 i)) (f i)
 but is expected to have type
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(MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 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R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) (MvPolynomial.X.{u2, u1} R σ _inst_1 i)) (f i)
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (i : σ), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.X.{u2, u1} R σ _inst_1 i)) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) 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R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) (MvPolynomial.X.{u2, u1} R σ _inst_1 i)) (f i)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_X_right MvPolynomial.bind₁_X_rightₓ'. -/
 @[simp]
 theorem bind₁_X_right (f : σ → MvPolynomial τ R) (i : σ) : bind₁ f (X i) = f i :=
@@ -235,7 +235,7 @@ variable (f : σ → MvPolynomial τ R)
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (x : R), Eq.{max (succ u2) (succ u3)} (MvPolynomial.{u2, u3} τ R _inst_1) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) (coeFn.{max (succ u3) (succ (max u1 u3)), max (succ u3) (succ (max u1 u3))} (RingHom.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (fun (_x : RingHom.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u3} σ R _inst_1)) (RingHom.hasCoeToFun.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (MvPolynomial.C.{u3, u1} R σ _inst_1) x)) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (RingHom.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))) (fun (_x : RingHom.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))) => R -> (MvPolynomial.{u2, u3} τ R _inst_1)) (RingHom.hasCoeToFun.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))) (MvPolynomial.C.{u3, u2} R τ _inst_1) x)
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) a) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (MvPolynomial.C.{u2, u1} R σ _inst_1) x)) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R 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u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (MulHomClass.toFunLike.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) R (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) R (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (MvPolynomial.C.{u2, u3} R τ _inst_1) x)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_C_right MvPolynomial.bind₁_C_rightₓ'. -/
 @[simp]
 theorem bind₁_C_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (C x) = C x := by
@@ -300,7 +300,7 @@ theorem join₂_comp_map (f : R →+* MvPolynomial σ S) : join₂.comp (map f)
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (p : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u2) (succ u3)} (MvPolynomial.{u2, u3} τ R _inst_1) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, max u2 u3} R R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, max u2 u3} R R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u2 u3, max u2 u3} R (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, max u2 u3} R R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.aeval.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (id.{succ (max u2 u3)} (MvPolynomial.{u2, u3} τ R _inst_1))) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, max u2 u3} R R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, max u2 u3} R R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, max u2 u3} R R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.rename.{u1, max u2 u3, u3} σ (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1 f) p)) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.aeval.{u3, max u2 u3, u1} R (MvPolynomial.{u2, u3} τ R _inst_1) σ _inst_1 (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) f) p)
 but is expected to have type
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_inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.aeval.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} τ R _inst_1) σ _inst_1 (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) f) p)
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (p : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, max u3 u2} R R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (a : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) a) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1)) 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_inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1))))))) 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.aeval.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} τ R _inst_1) σ _inst_1 (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) f) p)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_id_rename MvPolynomial.aeval_id_renameₓ'. -/
 theorem aeval_id_rename (f : σ → MvPolynomial τ R) (p : MvPolynomial σ R) :
     aeval id (rename f p) = aeval f p := by rw [aeval_rename, Function.comp.left_id]
@@ -310,7 +310,7 @@ theorem aeval_id_rename (f : σ → MvPolynomial τ R) (p : MvPolynomial σ R) :
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u2) (succ u3)} (MvPolynomial.{u2, u3} τ R _inst_1) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, max u2 u3} R R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, max u2 u3} R R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u2 u3, max u2 u3} R (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 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(MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, max u2 u3} R R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, max u2 u3} R R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{max u2 u3, u3} (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, max u2 u3} R R (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.rename.{u1, max u2 u3, u3} σ (MvPolynomial.{u2, u3} τ R _inst_1) R _inst_1 f) φ)) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ)
 but is expected to have type
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+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{max u2 u3, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u2, u2, 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(MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} 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R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.join₁_rename MvPolynomial.join₁_renameₓ'. -/
 @[simp]
 theorem join₁_rename (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
@@ -344,7 +344,7 @@ theorem bind₂_id : bind₂ (RingHom.id (MvPolynomial σ R)) = join₂ :=
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {υ : Type.{u4}} (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (g : τ -> (MvPolynomial.{u4, u3} υ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u4) (succ u3)} (MvPolynomial.{u4, u3} υ R _inst_1) (coeFn.{max (succ (max u2 u3)) (succ (max u4 u3)), max (succ (max u2 u3)) (succ (max u4 u3))} (AlgHom.{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u2, u4, u3} τ υ R _inst_1 g) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ)) (coeFn.{max (succ (max u1 u3)) (succ (max u4 u3)), max (succ (max u1 u3)) (succ (max u4 u3))} (AlgHom.{u3, max u1 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u1 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u4, u3} σ υ R _inst_1 (fun (i : σ) => coeFn.{max (succ (max u2 u3)) (succ (max u4 u3)), max (succ (max u2 u3)) (succ (max u4 u3))} (AlgHom.{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u2, u4, u3} τ υ R _inst_1 g) (f i))) φ)
 but is expected to have type
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(MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R 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(MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u4, u2, max u3 u2, max u2 u4} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u2 u4, max (max u3 u2) u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u3, u4, u2} τ υ R _inst_1 g) (f i))) φ)
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {υ : Type.{u4}} (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (g : τ -> (MvPolynomial.{u4, u2} υ R _inst_1)) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u2) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} τ R _inst_1) => MvPolynomial.{u4, u2} υ R _inst_1) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (a : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) a) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, 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R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u2 u4, max (max u3 u2) u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u3, u4, u2} τ υ R _inst_1 g) (f i))) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_bind₁ MvPolynomial.bind₁_bind₁ₓ'. -/
 theorem bind₁_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R)
     (φ : MvPolynomial σ R) : (bind₁ g) (bind₁ f φ) = bind₁ (fun i => bind₁ g (f i)) φ := by
@@ -355,7 +355,7 @@ theorem bind₁_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ →
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {υ : Type.{u4}} (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (g : τ -> (MvPolynomial.{u4, u3} υ R _inst_1)), Eq.{max (succ (max u1 u3)) (succ (max u4 u3))} (AlgHom.{u3, max u1 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (AlgHom.comp.{u3, max u1 u3, max u2 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.bind₁.{u2, u4, u3} τ υ R _inst_1 g) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f)) (MvPolynomial.bind₁.{u1, u4, u3} σ υ R _inst_1 (fun (i : σ) => coeFn.{max (succ (max u2 u3)) (succ (max u4 u3)), max (succ (max u2 u3)) (succ (max u4 u3))} (AlgHom.{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u2, u4, u3} τ υ R _inst_1 g) (f i)))
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {υ : Type.{u4}} (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (g : τ -> (MvPolynomial.{u4, u2} υ R _inst_1)), Eq.{max (max (succ u1) (succ u2)) (succ u4)} (AlgHom.{u2, max u2 u1, max u2 u4} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.comp.{u2, max u2 u1, max u3 u2, max u2 u4} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.bind₁.{u3, u4, u2} τ υ R _inst_1 g) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f)) (MvPolynomial.bind₁.{u1, u4, u2} σ υ R _inst_1 (fun (i : σ) => FunLike.coe.{max (max (succ u3) (succ u2)) (succ u4), max (succ u3) (succ u2), max (succ u2) (succ u4)} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u3, u2} τ R _inst_1) (fun (_x : MvPolynomial.{u3, u2} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u3, u2} τ R _inst_1) => MvPolynomial.{u4, u2} υ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u4, u2, max u3 u2, max u2 u4} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u4, u2, max u3 u2, max u2 u4} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u4, u2, max u3 u2, max u2 u4} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u2 u4, max (max u3 u2) u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u3, u4, u2} τ υ R _inst_1 g) (f i)))
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {υ : Type.{u4}} (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (g : τ -> (MvPolynomial.{u4, u2} υ R _inst_1)), Eq.{max (max (succ u1) (succ u2)) (succ u4)} (AlgHom.{u2, max u2 u1, max u2 u4} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.comp.{u2, max u2 u1, max u3 u2, max u2 u4} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.bind₁.{u3, u4, u2} τ υ R _inst_1 g) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f)) (MvPolynomial.bind₁.{u1, u4, u2} σ υ R _inst_1 (fun (i : σ) => FunLike.coe.{max (max (succ u3) (succ u2)) (succ u4), max (succ u3) (succ u2), max (succ u2) (succ u4)} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 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(MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (AddMonoid.toZero.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u4, u2, max u3 u2, max u2 u4} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u4, u2, max u3 u2, max u2 u4} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u2 u4, max (max u3 u2) u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u3, u4, u2} τ υ R _inst_1 g) (f i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_comp_bind₁ MvPolynomial.bind₁_comp_bind₁ₓ'. -/
 theorem bind₁_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R) :
     (bind₁ g).comp (bind₁ f) = bind₁ fun i => bind₁ g (f i) :=
@@ -389,7 +389,7 @@ theorem bind₂_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPolynomia
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {υ : Type.{u4}} (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (g : τ -> υ), Eq.{max (succ (max u1 u3)) (succ (max u4 u3))} (AlgHom.{u3, max u1 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (AlgHom.comp.{u3, max u1 u3, max u2 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.rename.{u2, u4, u3} τ υ R _inst_1 g) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f)) (MvPolynomial.bind₁.{u1, u4, u3} σ υ R _inst_1 (fun (i : σ) => coeFn.{max (succ (max u2 u3)) (succ (max u4 u3)), max (succ (max u2 u3)) (succ (max u4 u3))} (AlgHom.{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.rename.{u2, u4, u3} τ υ R _inst_1 g) (f i)))
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {υ : Type.{u4}} (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (g : τ -> υ), Eq.{max (max (succ u1) (succ u2)) (succ u4)} (AlgHom.{u2, max u2 u1, max u4 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.comp.{u2, max u2 u1, max u3 u2, max u4 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.rename.{u3, u4, u2} τ υ R _inst_1 g) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f)) (MvPolynomial.bind₁.{u1, u4, u2} σ υ R _inst_1 (fun (i : σ) => FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), max (succ u4) (succ u2)} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u3, u2} τ R _inst_1) (fun (_x : MvPolynomial.{u3, u2} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u3, u2} τ R _inst_1) => MvPolynomial.{u4, u2} υ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u2, u2, max u3 u2, max u4 u2} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (AddMonoid.toZero.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (AddCommMonoid.toAddMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (AddMonoid.toAddZeroClass.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (AddCommMonoid.toAddMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))))) (Module.toDistribMulAction.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u2, max u3 u2, max u4 u2} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u2, u2, max u3 u2, max u4 u2} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u4 u2, max (max u3 u4) u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u4 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.rename.{u3, u4, u2} τ υ R _inst_1 g) (f i)))
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {υ : Type.{u4}} (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (g : τ -> υ), Eq.{max (max (succ u1) (succ u2)) (succ u4)} (AlgHom.{u2, max u2 u1, max u4 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.comp.{u2, max u2 u1, max u3 u2, max u4 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.rename.{u3, u4, u2} τ υ R _inst_1 g) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f)) (MvPolynomial.bind₁.{u1, u4, u2} σ υ R _inst_1 (fun (i : σ) => FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u2), max (succ u4) (succ u2)} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} 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_inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} 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(Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))))) (Module.toDistribMulAction.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u2, max u3 u2, max u4 u2} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u2, u2, max u3 u2, max u4 u2} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u4 u2, max (max u3 u4) u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u4 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.rename.{u3, u4, u2} τ υ R _inst_1 g) (f i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.rename_comp_bind₁ MvPolynomial.rename_comp_bind₁ₓ'. -/
 theorem rename_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) :
     (rename g).comp (bind₁ f) = bind₁ fun i => rename g <| f i :=
@@ -402,7 +402,7 @@ theorem rename_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {υ : Type.{u4}} (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (g : τ -> υ) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u4) (succ u3)} (MvPolynomial.{u4, u3} υ R _inst_1) (coeFn.{max (succ (max u2 u3)) (succ (max u4 u3)), max (succ (max u2 u3)) (succ (max u4 u3))} (AlgHom.{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.rename.{u2, u4, u3} τ υ R _inst_1 g) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ)) (coeFn.{max 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(MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u1 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u4, u3} σ υ R _inst_1 (fun (i : σ) => coeFn.{max (succ (max u2 u3)) (succ (max u4 u3)), max (succ (max u2 u3)) (succ (max u4 u3))} (AlgHom.{u3, max u2 u3, max u4 u3} R 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_inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.rename.{u2, u4, u3} τ υ R _inst_1 g) (f i))) φ)
 but is expected to have type
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(MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (AddMonoid.toZero.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) 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(MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))))) (Module.toDistribMulAction.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u2, max u3 u2, max u4 u2} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u2, u2, max u3 u2, max u4 u2} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u4 u2, max (max u3 u4) u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u4 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.rename.{u3, u4, u2} τ υ R _inst_1 g) (f i))) φ)
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {υ : Type.{u4}} (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (g : τ -> υ) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u2) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} τ R _inst_1) => MvPolynomial.{u4, u2} υ R _inst_1) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (a : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) a) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) 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u4) u2, u2, max u3 u2, max u4 u2} (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u4 u2} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u4 u2, max (max u3 u4) u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u4 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.rename.{u3, u4, u2} τ υ R _inst_1 g) (f i))) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.rename_bind₁ MvPolynomial.rename_bind₁ₓ'. -/
 theorem rename_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) (φ : MvPolynomial σ R) :
     rename g (bind₁ f φ) = bind₁ (fun i => rename g <| f i) φ :=
@@ -440,7 +440,7 @@ theorem bind₁_comp_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {υ : Type.{u4}} (f : τ -> (MvPolynomial.{u4, u3} υ R _inst_1)) (g : σ -> τ) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u4) (succ u3)} (MvPolynomial.{u4, u3} υ R _inst_1) (coeFn.{max (succ (max u2 u3)) (succ (max u4 u3)), max (succ (max u2 u3)) (succ (max u4 u3))} (AlgHom.{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u2, u4, u3} τ υ R _inst_1 f) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.rename.{u1, u2, u3} σ τ R _inst_1 g) φ)) (coeFn.{max (succ (max u1 u3)) (succ (max u4 u3)), max (succ (max u1 u3)) (succ (max u4 u3))} (AlgHom.{u3, max u1 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u1 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u4, u3} σ υ R _inst_1 (Function.comp.{succ u1, succ u2, max (succ u4) (succ u3)} σ τ (MvPolynomial.{u4, u3} υ R _inst_1) f g)) φ)
 but is expected to have type
-  forall {σ : Type.{u2}} {τ : Type.{u1}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {υ : Type.{u4}} (f : τ -> (MvPolynomial.{u4, u3} υ R _inst_1)) (g : σ -> τ) (φ : MvPolynomial.{u2, u3} σ R _inst_1), Eq.{max (succ u3) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u3} τ R _inst_1) => MvPolynomial.{u4, u3} υ R _inst_1) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u3, max u3 u2, max u3 u1} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u1, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.{u2, u3} σ R _inst_1) (fun (a : MvPolynomial.{u2, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u3} σ R _inst_1) => MvPolynomial.{u1, u3} τ R _inst_1) a) (SMulHomClass.toFunLike.{max (max u2 u1) u3, u3, max u2 u3, max u1 u3} (AlgHom.{u3, max u3 u2, max u3 u1} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u1, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u1, u3} τ R _inst_1) (SMulZeroClass.toSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) 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_inst_1)))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))) (Algebra.toModule.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u3 u4} R (MvPolynomial.{u4, u3} υ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u4} 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(CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (AlgHom.{u3, max u3 u2, max u3 u4} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (AlgHom.algHomClass.{u3, max u2 u3, max u3 u4} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (MvPolynomial.bind₁.{u2, u4, u3} σ υ R _inst_1 (Function.comp.{succ u2, succ u1, max (succ u3) (succ u4)} σ τ (MvPolynomial.{u4, u3} υ R _inst_1) f g)) φ)
+  forall {σ : Type.{u2}} {τ : Type.{u1}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {υ : Type.{u4}} (f : τ -> (MvPolynomial.{u4, u3} υ R _inst_1)) (g : σ -> τ) (φ : MvPolynomial.{u2, u3} σ R _inst_1), Eq.{max (succ u3) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u3} τ R _inst_1) => MvPolynomial.{u4, u3} υ R _inst_1) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u3, max u3 u2, max u3 u1} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u1, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.{u2, u3} σ R _inst_1) (fun (a : MvPolynomial.{u2, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u3} σ R _inst_1) => MvPolynomial.{u1, u3} τ R _inst_1) a) (SMulHomClass.toFunLike.{max (max u2 u1) u3, u3, max u2 u3, max u1 u3} (AlgHom.{u3, max u3 u2, max u3 u1} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u1, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u1, u3} τ R _inst_1) (SMulZeroClass.toSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) 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(MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))) (Algebra.toModule.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max u1 u3} R (MvPolynomial.{u1, u3} τ R _inst_1) (AddMonoid.toZero.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u1 u3} R (MvPolynomial.{u1, u3} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u1 u3} R (MvPolynomial.{u1, u3} τ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _inst_1)))))) (Module.toDistribMulAction.{u3, max u1 u3} R (MvPolynomial.{u1, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _inst_1))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u3, u3, max u2 u3, max u1 u3} (AlgHom.{u3, max u3 u2, max u3 u1} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u1, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u1, u3} τ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} 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(CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)))))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))) (Algebra.toModule.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u3 u4} R (MvPolynomial.{u4, u3} υ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1))))) (Algebra.toModule.{u3, max u3 u4} R (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u2 u3) u4, u3, max u2 u3, max u3 u4} (AlgHom.{u3, max u3 u2, max u3 u4} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))) (Algebra.toModule.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u3 u4} R (MvPolynomial.{u4, u3} υ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1))))) (Algebra.toModule.{u3, max u3 u4} R (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u3 u4, max (max u2 u3) u4} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (AlgHom.{u3, max u3 u2, max u3 u4} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (AlgHom.algHomClass.{u3, max u2 u3, max u3 u4} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (MvPolynomial.bind₁.{u2, u4, u3} σ υ R _inst_1 (Function.comp.{succ u2, succ u1, max (succ u3) (succ u4)} σ τ (MvPolynomial.{u4, u3} υ R _inst_1) f g)) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_rename MvPolynomial.bind₁_renameₓ'. -/
 theorem bind₁_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ → τ) (φ : MvPolynomial σ R) :
     bind₁ f (rename g φ) = bind₁ (f ∘ g) φ :=
@@ -474,7 +474,7 @@ theorem map_comp_C (f : R →+* S) : (map f).comp (C : R →+* MvPolynomial σ R
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u4} S] (f : RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (g : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{succ u4} S (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (fun (_x : RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) f (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 g) φ)) (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (RingHom.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (fun (_x : RingHom.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (MvPolynomial.eval₂Hom.{u3, u4, u1} R S σ _inst_1 _inst_2 (RingHom.comp.{u3, max u2 u3, u4} R (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) f (MvPolynomial.C.{u3, u2} R τ _inst_1)) (fun (i : σ) => coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (fun (_x : RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) f (g i))) φ)
 but is expected to have type
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(MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u3 u4) u2, max u3 u4, u2} (RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u3 u4, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f (g i))) φ)
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u4}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (g : σ -> (MvPolynomial.{u3, u4} τ R _inst_1)) (φ : MvPolynomial.{u1, u4} σ R _inst_1), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u4} τ R _inst_1) => S) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u1) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u4, max u4 u1, max u4 u3} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u3, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) 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u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) S (NonUnitalNonAssocSemiring.toMul.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u3 u4) u2, max u3 u4, u2} (RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u3 u4) u2, max u3 u4, u2} (RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u3 u4, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f (g i))) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.hom_bind₁ MvPolynomial.hom_bind₁ₓ'. -/
 -- mixing the two monad structures
 theorem hom_bind₁ (f : MvPolynomial τ R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
@@ -486,7 +486,7 @@ theorem hom_bind₁ (f : MvPolynomial τ R →+* S) (g : σ → MvPolynomial τ
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u4} S] (f : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (g : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u2) (succ u4)} (MvPolynomial.{u2, u4} τ S _inst_2) (coeFn.{max (succ (max u2 u3)) (succ (max u2 u4)), max (succ (max u2 u3)) (succ (max u2 u4))} (RingHom.{max u2 u3, max u2 u4} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u4} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)))) (fun (_x : RingHom.{max u2 u3, max u2 u4} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u4} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u2, u4} τ S _inst_2)) (RingHom.hasCoeToFun.{max u2 u3, max u2 u4} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u4} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)))) (MvPolynomial.map.{u3, u4, u2} R S τ _inst_1 _inst_2 f) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 g) φ)) (coeFn.{max (succ (max u1 u4)) (succ (max u2 u4)), max (succ (max u1 u4)) (succ (max u2 u4))} (AlgHom.{u4, max u1 u4, max u2 u4} S (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.{u2, u4} τ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) (MvPolynomial.algebra.{u4, u4, u2} S S τ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2))) (fun (_x : AlgHom.{u4, max u1 u4, max u2 u4} S (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.{u2, u4} τ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) (MvPolynomial.algebra.{u4, u4, u2} S S τ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2))) => (MvPolynomial.{u1, u4} σ S _inst_2) -> (MvPolynomial.{u2, u4} τ S _inst_2)) ([anonymous].{u4, max u1 u4, max u2 u4} S (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.{u2, u4} τ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) (MvPolynomial.algebra.{u4, u4, u2} S S τ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2))) (MvPolynomial.bind₁.{u1, u2, u4} σ τ S _inst_2 (fun (i : σ) => coeFn.{max (succ (max u2 u3)) (succ (max u2 u4)), max (succ (max u2 u3)) (succ (max u2 u4))} (RingHom.{max u2 u3, max u2 u4} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u4} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)))) (fun (_x : RingHom.{max u2 u3, max u2 u4} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u4} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u2, u4} τ S _inst_2)) (RingHom.hasCoeToFun.{max u2 u3, max u2 u4} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u4} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)))) (MvPolynomial.map.{u3, u4, u2} R S τ _inst_1 _inst_2 f) (g i))) (coeFn.{max (succ (max u1 u3)) (succ (max u1 u4)), max (succ (max u1 u3)) (succ (max u1 u4))} (RingHom.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u1, u4} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (MvPolynomial.map.{u3, u4, u1} R S σ _inst_1 _inst_2 f) φ))
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (g : σ -> (MvPolynomial.{u2, u4} τ R _inst_1)) (φ : MvPolynomial.{u1, u4} σ R _inst_1), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u4} τ R _inst_1) => MvPolynomial.{u2, u3} τ S _inst_2) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), max (succ u2) (succ u4)} (AlgHom.{u4, max u4 u1, max u4 u2} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) 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u4 u1, max u3 u1} (RingHom.{max u4 u1, max u3 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u4 u3) u1, max u4 u1, max u3 u1} (RingHom.{max u4 u1, max u3 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.{u1, u4} σ R _inst_1) 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σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u4 u1, max u3 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))))) (MvPolynomial.map.{u4, u3, u1} R S σ _inst_1 _inst_2 f) φ))
+  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (g : σ -> (MvPolynomial.{u2, u4} τ R _inst_1)) (φ : MvPolynomial.{u1, u4} σ R _inst_1), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u4} τ R _inst_1) => MvPolynomial.{u2, u3} τ S _inst_2) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), max (succ u2) (succ u4)} (AlgHom.{u4, max u4 u1, max u4 u2} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u1 u3, max u2 u3, max (max u1 u2) u3} S (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u2, u3} τ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) (MvPolynomial.algebra.{u3, u3, u2} S S τ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) (AlgHom.{u3, max u3 u1, max u3 u2} S (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u2, u3} τ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) (MvPolynomial.algebra.{u3, u3, u2} S S τ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2))) (AlgHom.algHomClass.{u3, max u1 u3, max u2 u3} S (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u2, u3} τ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) (MvPolynomial.algebra.{u3, u3, u2} S S τ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2))))))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ S _inst_2 (fun (i : σ) => FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)))) (MvPolynomial.{u2, u4} τ R _inst_1) (fun (_x : MvPolynomial.{u2, u4} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u4} τ R _inst_1) => MvPolynomial.{u2, u3} τ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u4 u3) u2, max u4 u2, max u3 u2} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u2} 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(Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u4 u3) u2, max u4 u2, max u3 u2} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)))) (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.{u2, u3} τ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u4 u3) u2, max u4 u2, max u3 u2} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)))) (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2))) (RingHom.instRingHomClassRingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2))))))) (MvPolynomial.map.{u4, u3, u2} R S τ _inst_1 _inst_2 f) (g i))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (succ u4) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u4 u1, max u3 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.{u1, u4} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u4} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u4} σ R _inst_1) => MvPolynomial.{u1, u3} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u4 u3) u1, max 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(NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u4 u3) u1, max u4 u1, max u3 u1} (RingHom.{max u4 u1, max u3 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u4 u3) u1, max u4 u1, max u3 u1} (RingHom.{max u4 u1, max u3 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u4 u1, max u3 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))))) (MvPolynomial.map.{u4, u3, u1} R S σ _inst_1 _inst_2 f) φ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_bind₁ MvPolynomial.map_bind₁ₓ'. -/
 theorem map_bind₁ (f : R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     map f (bind₁ g φ) = bind₁ (fun i : σ => (map f) (g i)) (map f φ) :=
@@ -512,7 +512,7 @@ theorem eval₂Hom_comp_C (f : R →+* S) (g : σ → S) : (eval₂Hom f g).comp
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u4} S] (f : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (g : τ -> S) (h : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{succ u4} S (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (fun (_x : RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R 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_inst_1 _inst_2 f g) (h i))) φ)
 but is expected to have type
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(CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u1 u4, u3} (MvPolynomial.{u1, u4} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (MvPolynomial.eval₂Hom.{u4, u3, u1} R S σ _inst_1 _inst_2 f (fun (i : σ) => FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} (RingHom.{max u4 u2, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) 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(MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u4) u3, max u2 u4, u3} (RingHom.{max u4 u2, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u2, u4} τ R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u4) u3, max u2 u4, u3} (RingHom.{max u4 u2, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u2 u4, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (MvPolynomial.eval₂Hom.{u4, u3, u2} R S τ _inst_1 _inst_2 f g) (h i))) φ)
+  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (g : τ -> S) (h : σ -> (MvPolynomial.{u2, u4} τ R _inst_1)) (φ : MvPolynomial.{u1, u4} σ R _inst_1), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u4} τ R _inst_1) => S) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), max (succ u2) (succ u4)} (AlgHom.{u4, max u4 u1, max u4 u2} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) 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_inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) 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σ R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u4) u3, max u1 u4, u3} (RingHom.{max u4 u1, u3} (MvPolynomial.{u1, u4} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u4} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u1 u4, u3} (MvPolynomial.{u1, u4} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (MvPolynomial.eval₂Hom.{u4, u3, u1} R S σ _inst_1 _inst_2 f (fun (i : σ) => FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), succ u3} (RingHom.{max u4 u2, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u2, u4} τ R _inst_1) (fun (_x : MvPolynomial.{u2, u4} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u4} τ R _inst_1) => S) _x) (MulHomClass.toFunLike.{max (max u2 u4) u3, max u2 u4, u3} (RingHom.{max u4 u2, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u2, u4} τ R _inst_1) S (NonUnitalNonAssocSemiring.toMul.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u4) u3, max u2 u4, u3} (RingHom.{max u4 u2, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u2, u4} τ R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u4) u3, max u2 u4, u3} (RingHom.{max u4 u2, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u2 u4, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (MvPolynomial.eval₂Hom.{u4, u3, u2} R S τ _inst_1 _inst_2 f g) (h i))) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_bind₁ MvPolynomial.eval₂Hom_bind₁ₓ'. -/
 theorem eval₂Hom_bind₁ (f : R →+* S) (g : τ → S) (h : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     eval₂Hom f g (bind₁ h φ) = eval₂Hom f (fun i => eval₂Hom f g (h i)) φ := by
@@ -523,7 +523,7 @@ theorem eval₂Hom_bind₁ (f : R →+* S) (g : τ → S) (h : σ → MvPolynomi
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u4} S] [_inst_4 : Algebra.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_2)] (f : τ -> S) (g : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{succ u4} S (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (AlgHom.{u3, max u2 u3, u4} R (MvPolynomial.{u2, u3} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u3, max u2 u3, u4} R (MvPolynomial.{u2, u3} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) => (MvPolynomial.{u2, u3} τ R _inst_1) -> S) ([anonymous].{u3, max u2 u3, u4} R (MvPolynomial.{u2, u3} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) (MvPolynomial.aeval.{u3, u4, u2} R S τ _inst_1 _inst_2 _inst_4 f) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 g) φ)) (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (AlgHom.{u3, max u1 u3, u4} R (MvPolynomial.{u1, u3} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u3, max u1 u3, u4} R (MvPolynomial.{u1, u3} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) => (MvPolynomial.{u1, u3} σ R _inst_1) -> S) ([anonymous].{u3, max u1 u3, u4} R (MvPolynomial.{u1, u3} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) (MvPolynomial.aeval.{u3, u4, u1} R S σ _inst_1 _inst_2 _inst_4 (fun (i : σ) => coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (AlgHom.{u3, max u2 u3, u4} R (MvPolynomial.{u2, u3} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u3, max u2 u3, u4} R (MvPolynomial.{u2, u3} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) => (MvPolynomial.{u2, u3} τ R _inst_1) -> S) ([anonymous].{u3, max u2 u3, u4} R (MvPolynomial.{u2, u3} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) (MvPolynomial.aeval.{u3, u4, u2} R S τ _inst_1 _inst_2 _inst_4 f) (g i))) φ)
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] [_inst_4 : Algebra.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] (f : τ -> S) (g : σ -> (MvPolynomial.{u2, u4} τ R _inst_1)) (φ : MvPolynomial.{u1, u4} σ R _inst_1), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u4} τ R _inst_1) => S) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), max (succ u2) (succ u4)} (AlgHom.{u4, max u4 u1, max u4 u2} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) 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_inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1))))))) (SMulZeroClass.toSMul.{u4, u3} R S (AddMonoid.toZero.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (DistribSMul.toSMulZeroClass.{u4, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u4, u3} R S (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} S 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(MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R S (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u2 u3) u4, u4, max u2 u4, u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) R (MvPolynomial.{u2, u4} τ R _inst_1) S (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R S (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, max u2 u4, u3, max (max u2 u3) u4} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4 (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u4, max u2 u4, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4))))) (MvPolynomial.aeval.{u4, u3, u2} R S τ _inst_1 _inst_2 _inst_4 f) (g i))) φ)
+  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] [_inst_4 : Algebra.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] (f : τ -> S) (g : σ -> (MvPolynomial.{u2, u4} τ R _inst_1)) (φ : MvPolynomial.{u1, u4} σ R _inst_1), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u4} τ R _inst_1) => S) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), max (succ u2) (succ u4)} (AlgHom.{u4, max u4 u1, max u4 u2} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) 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u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) 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(CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, max u1 u4, u3, max (max u1 u3) u4} R (MvPolynomial.{u1, u4} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4 (AlgHom.{u4, max u4 u1, u3} R (MvPolynomial.{u1, u4} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u4, max u1 u4, u3} R (MvPolynomial.{u1, u4} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4))))) (MvPolynomial.aeval.{u4, u3, u1} R S σ _inst_1 _inst_2 _inst_4 (fun (i : σ) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) (MvPolynomial.{u2, u4} τ R _inst_1) (fun (_x : MvPolynomial.{u2, u4} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u4} τ R _inst_1) => S) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u4, u4, max u2 u4, u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) R (MvPolynomial.{u2, u4} τ R _inst_1) S (SMulZeroClass.toSMul.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (AddMonoid.toZero.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1))))))) (SMulZeroClass.toSMul.{u4, u3} R S (AddMonoid.toZero.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (DistribSMul.toSMulZeroClass.{u4, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u4, u3} R S (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))))) (Module.toDistribMulAction.{u4, u3} R S (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u4, u4, max u2 u4, u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) R (MvPolynomial.{u2, u4} τ R _inst_1) S (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R S (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u2 u3) u4, u4, max u2 u4, u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) R (MvPolynomial.{u2, u4} τ R _inst_1) S (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R S (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, max u2 u4, u3, max (max u2 u3) u4} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4 (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u4, max u2 u4, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4))))) (MvPolynomial.aeval.{u4, u3, u2} R S τ _inst_1 _inst_2 _inst_4 f) (g i))) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_bind₁ MvPolynomial.aeval_bind₁ₓ'. -/
 theorem aeval_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     aeval f (bind₁ g φ) = aeval (fun i => aeval f (g i)) φ :=
@@ -534,7 +534,7 @@ theorem aeval_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u4} S] [_inst_4 : Algebra.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_2)] (f : τ -> S) (g : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)), Eq.{max (succ (max u1 u3)) (succ u4)} (AlgHom.{u3, max u1 u3, u4} R (MvPolynomial.{u1, u3} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) (AlgHom.comp.{u3, max u1 u3, max u2 u3, u4} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4 (MvPolynomial.aeval.{u3, u4, u2} R S τ _inst_1 _inst_2 _inst_4 f) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 g)) (MvPolynomial.aeval.{u3, u4, u1} R S σ _inst_1 _inst_2 _inst_4 (fun (i : σ) => coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (AlgHom.{u3, max u2 u3, u4} R (MvPolynomial.{u2, u3} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u3, max u2 u3, u4} R (MvPolynomial.{u2, u3} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) => (MvPolynomial.{u2, u3} τ R _inst_1) -> S) ([anonymous].{u3, max u2 u3, u4} R (MvPolynomial.{u2, u3} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u4} S _inst_2) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) _inst_4) (MvPolynomial.aeval.{u3, u4, u2} R S τ _inst_1 _inst_2 _inst_4 f) (g i)))
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] [_inst_4 : Algebra.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] (f : τ -> S) (g : σ -> (MvPolynomial.{u2, u4} τ R _inst_1)), Eq.{max (max (succ u1) (succ u4)) (succ u3)} (AlgHom.{u4, max u4 u1, u3} R (MvPolynomial.{u1, u4} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) (AlgHom.comp.{u4, max u4 u1, max u2 u4, u3} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4 (MvPolynomial.aeval.{u4, u3, u2} R S τ _inst_1 _inst_2 _inst_4 f) (MvPolynomial.bind₁.{u1, u2, u4} σ τ R _inst_1 g)) (MvPolynomial.aeval.{u4, u3, u1} R S σ _inst_1 _inst_2 _inst_4 (fun (i : σ) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) (MvPolynomial.{u2, u4} τ R _inst_1) (fun (_x : MvPolynomial.{u2, u4} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u4} τ R _inst_1) => S) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u4, u4, max u2 u4, u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) R (MvPolynomial.{u2, u4} τ R _inst_1) S (SMulZeroClass.toSMul.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (AddMonoid.toZero.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1))))))) (SMulZeroClass.toSMul.{u4, u3} R S (AddMonoid.toZero.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (DistribSMul.toSMulZeroClass.{u4, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u4, u3} R S (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))))) (Module.toDistribMulAction.{u4, u3} R S (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u4, u4, max u2 u4, u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) R (MvPolynomial.{u2, u4} τ R _inst_1) S (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R S (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u2 u3) u4, u4, max u2 u4, u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) R (MvPolynomial.{u2, u4} τ R _inst_1) S (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R S (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, max u2 u4, u3, max (max u2 u3) u4} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4 (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u4, max u2 u4, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4))))) (MvPolynomial.aeval.{u4, u3, u2} R S τ _inst_1 _inst_2 _inst_4 f) (g i)))
+  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] [_inst_4 : Algebra.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] (f : τ -> S) (g : σ -> (MvPolynomial.{u2, u4} τ R _inst_1)), Eq.{max (max (succ u1) (succ u4)) (succ u3)} (AlgHom.{u4, max u4 u1, u3} R (MvPolynomial.{u1, u4} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) (AlgHom.comp.{u4, max u4 u1, max u2 u4, u3} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4 (MvPolynomial.aeval.{u4, u3, u2} R S τ _inst_1 _inst_2 _inst_4 f) (MvPolynomial.bind₁.{u1, u2, u4} σ τ R _inst_1 g)) (MvPolynomial.aeval.{u4, u3, u1} R S σ _inst_1 _inst_2 _inst_4 (fun (i : σ) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u4), succ u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) (MvPolynomial.{u2, u4} τ R _inst_1) (fun (_x : MvPolynomial.{u2, u4} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u4} τ R _inst_1) => S) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u4, u4, max u2 u4, u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) R (MvPolynomial.{u2, u4} τ R _inst_1) S (SMulZeroClass.toSMul.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (AddMonoid.toZero.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1))))))) (SMulZeroClass.toSMul.{u4, u3} R S (AddMonoid.toZero.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (DistribSMul.toSMulZeroClass.{u4, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u4, u3} R S (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))))) (Module.toDistribMulAction.{u4, u3} R S (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u4, u4, max u2 u4, u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) R (MvPolynomial.{u2, u4} τ R _inst_1) S (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R S (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u2 u3) u4, u4, max u2 u4, u3} (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) R (MvPolynomial.{u2, u4} τ R _inst_1) S (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, u3} R S (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u4, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, max u2 u4, u3, max (max u2 u3) u4} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4 (AlgHom.{u4, max u4 u2, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u4, max u2 u4, u3} R (MvPolynomial.{u2, u4} τ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) _inst_4))))) (MvPolynomial.aeval.{u4, u3, u2} R S τ _inst_1 _inst_2 _inst_4 f) (g i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_comp_bind₁ MvPolynomial.aeval_comp_bind₁ₓ'. -/
 theorem aeval_comp_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R) :
     (aeval f).comp (bind₁ g) = aeval fun i => aeval f (g i) :=
@@ -568,7 +568,7 @@ theorem eval₂Hom_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPolynom
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} {T : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u4} T] [_inst_4 : Algebra.{u3, u4} S T _inst_2 (CommSemiring.toSemiring.{u4} T _inst_3)] (f : σ -> T) (g : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u4} T (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (AlgHom.{u3, max u1 u3, u4} S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4) (fun (_x : AlgHom.{u3, max u1 u3, u4} S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4) => (MvPolynomial.{u1, u3} σ S _inst_2) -> T) ([anonymous].{u3, max u1 u3, u4} S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4) (MvPolynomial.aeval.{u3, u4, u1} S T σ _inst_2 _inst_3 _inst_4 f) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max 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 but is expected to have type
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(Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3)) (RingHomClass.toRingHom.{max (max u1 u4) u3, max u1 u4, u3} (AlgHom.{u4, max u4 u1, u3} S (MvPolynomial.{u1, u4} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u3} T _inst_3) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) _inst_4) (MvPolynomial.{u1, u4} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3)) (AlgHomClass.toRingHomClass.{max (max u1 u4) u3, u4, max u1 u4, u3} (AlgHom.{u4, max u4 u1, u3} S (MvPolynomial.{u1, u4} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u3} T _inst_3) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) _inst_4) S (MvPolynomial.{u1, u4} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u3} T _inst_3) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) _inst_4 (AlgHom.algHomClass.{u4, max u1 u4, u3} S (MvPolynomial.{u1, u4} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u3} T _inst_3) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) _inst_4)) (MvPolynomial.aeval.{u4, u3, u1} S T σ _inst_2 _inst_3 _inst_4 f)) g) f) φ)
+  forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u4}} {T : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u3} T] [_inst_4 : Algebra.{u4, u3} S T _inst_2 (CommSemiring.toSemiring.{u3} T _inst_3)] (f : σ -> T) (g : RingHom.{u2, max u4 u1} R (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u4} σ S _inst_2) => T) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u2), max (succ u1) (succ u4)} (RingHom.{max u2 u1, max u4 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) 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(MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u2) u4, max u1 u2, max u1 u4} (RingHom.{max u2 u1, max u4 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u2) u4, max u1 u2, max u1 u4} (RingHom.{max u2 u1, max u4 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) 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σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) _inst_4)) (MvPolynomial.aeval.{u4, u3, u1} S T σ _inst_2 _inst_3 _inst_4 f)) g) f) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_bind₂ MvPolynomial.aeval_bind₂ₓ'. -/
 theorem aeval_bind₂ [Algebra S T] (f : σ → T) (g : R →+* MvPolynomial σ S) (φ : MvPolynomial σ R) :
     aeval f (bind₂ g φ) = eval₂Hom ((↑(aeval f : _ →ₐ[S] _) : _ →+* _).comp g) f φ :=
@@ -589,7 +589,7 @@ theorem eval₂Hom_C_left (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero) (r : R), Eq.{max (succ u2) (succ u3)} (MvPolynomial.{u2, u3} τ R _inst_1) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ 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 but is expected to have type
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(MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (MvPolynomial.C.{u2, u3} R τ _inst_1) r) (Finset.prod.{max u3 u2, u1} (MvPolynomial.{u3, u2} τ R _inst_1) σ (CommSemiring.toCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => HPow.hPow.{max u3 u2, 0, max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) i) (MvPolynomial.{u3, u2} τ R _inst_1) (instHPow.{max u3 u2, 0} (MvPolynomial.{u3, u2} τ R _inst_1) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) i) (Monoid.Pow.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toMonoidWithZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (f i) (FunLike.coe.{succ u1, succ u1, 1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (_x : σ) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) _x) (Finsupp.funLike.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i))))
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (d : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (r : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) R (MvPolynomial.{u3, u2} τ R _inst_1) 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(MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (MvPolynomial.C.{u2, u3} R τ _inst_1) r) (Finset.prod.{max u3 u2, u1} (MvPolynomial.{u3, u2} τ R _inst_1) σ (CommSemiring.toCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => HPow.hPow.{max u3 u2, 0, max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) ((fun 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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_monomial MvPolynomial.bind₁_monomialₓ'. -/
 theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r : R) :
     bind₁ f (monomial d r) = C r * ∏ i in d.support, f i ^ d i := by
@@ -601,7 +601,7 @@ theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero) (r : R), Eq.{max (succ u1) (succ u3)} (MvPolynomial.{u1, u3} σ S _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) 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σ S _inst_2) (CommSemiring.toSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u3} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (MvPolynomial.module.{u3, u3, u1} S S σ (CommSemiring.toSemiring.{u3} S _inst_2) _inst_2 (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (MvPolynomial.monomial.{u3, u1} S σ _inst_2 d) (OfNat.ofNat.{u3} S 1 (OfNat.mk.{u3} S 1 (One.one.{u3} S (AddMonoidWithOne.toOne.{u3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))))))))))
 but is expected to have type
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(Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPolynomial.{u1, u3} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u3, max u1 u3} R R R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MvPolynomial.monomial.{u3, u1} R σ _inst_1 d) r)) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ S _inst_2) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : S) => MvPolynomial.{u1, u2} σ S _inst_2) (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (LinearMap.{u3, u3, u3, max u3 u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, 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=> (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : S) => MvPolynomial.{u1, u2} σ S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u1 u2} S S S (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (MvPolynomial.module.{u2, u2, u1} S S σ (CommSemiring.toSemiring.{u2} S _inst_2) _inst_2 (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MvPolynomial.monomial.{u2, u1} S σ _inst_2 d) (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_monomial MvPolynomial.bind₂_monomialₓ'. -/
 theorem bind₂_monomial (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) (r : R) :
     bind₂ f (monomial d r) = f r * monomial d 1 := by
@@ -613,7 +613,7 @@ theorem bind₂_monomial (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) (r
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero), Eq.{max (succ u1) (succ u3)} (MvPolynomial.{u1, u3} σ S _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.bind₂.{u1, u2, u3} σ R S _inst_1 _inst_2 f) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPolynomial.monomial.{u2, u1} R σ _inst_1 d) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))))) (coeFn.{max (succ u3) (succ (max u1 u3)), max (succ u3) (succ (max u1 u3))} (LinearMap.{u3, u3, u3, max u1 u3} S S (CommSemiring.toSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u3} S _inst_2) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) S (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (MvPolynomial.module.{u3, u3, u1} S S σ (CommSemiring.toSemiring.{u3} S _inst_2) _inst_2 (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (fun (_x : LinearMap.{u3, u3, u3, max u1 u3} S S (CommSemiring.toSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u3} S _inst_2) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) S (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (MvPolynomial.module.{u3, u3, u1} S S σ (CommSemiring.toSemiring.{u3} S _inst_2) _inst_2 (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) => S -> (MvPolynomial.{u1, u3} σ S _inst_2)) (LinearMap.hasCoeToFun.{u3, u3, u3, max u1 u3} S S S (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u3} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (MvPolynomial.module.{u3, u3, u1} S S σ (CommSemiring.toSemiring.{u3} S _inst_2) _inst_2 (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (MvPolynomial.monomial.{u3, u1} S σ _inst_2 d) (OfNat.ofNat.{u3} S 1 (OfNat.mk.{u3} S 1 (One.one.{u3} S (AddMonoidWithOne.toOne.{u3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))))))
 but is expected to have type
-  forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, max u2 u1} R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (d : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (LinearMap.{u3, u3, u3, max u3 u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u3} σ R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u3, u3, u3, max u1 u3} R R R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MvPolynomial.monomial.{u3, u1} R σ _inst_1 d) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), max (succ u1) (succ u2)} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MvPolynomial.monomial.{u3, u1} R σ _inst_1 d) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), max (succ u1) (succ u2)} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u3, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.bind₂.{u1, u3, u2} σ R S _inst_1 _inst_2 f) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (LinearMap.{u3, u3, u3, max u3 u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPolynomial.{u1, u3} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u3, max u1 u3} R R R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MvPolynomial.monomial.{u3, u1} R σ _inst_1 d) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} S S (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (MvPolynomial.{u1, u2} σ S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (MvPolynomial.module.{u2, u2, u1} S S σ (CommSemiring.toSemiring.{u2} S _inst_2) _inst_2 (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : S) => MvPolynomial.{u1, u2} σ S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u1 u2} S S S (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (MvPolynomial.module.{u2, u2, u1} S S σ (CommSemiring.toSemiring.{u2} S _inst_2) _inst_2 (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MvPolynomial.monomial.{u2, u1} S σ _inst_2 d) (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_monomial_one MvPolynomial.bind₂_monomial_oneₓ'. -/
 @[simp]
 theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) :
@@ -626,7 +626,7 @@ section
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] [_inst_4 : DecidableEq.{succ u2} τ] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} τ) (Finset.hasSubset.{u2} τ) (MvPolynomial.vars.{u3, u2} R τ _inst_1 (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ)) (Finset.biUnion.{u1, u2} σ τ (fun (a : τ) (b : τ) => _inst_4 a b) (MvPolynomial.vars.{u3, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u3, u2} R τ _inst_1 (f i)))
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] [_inst_4 : DecidableEq.{succ u3} τ] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (φ : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u3} (Finset.{u3} τ) (Finset.instHasSubsetFinset.{u3} τ) (MvPolynomial.vars.{u2, u3} R τ _inst_1 (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ)) (Finset.biUnion.{u1, u3} σ τ (fun (a : τ) (b : τ) => _inst_4 a b) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u2, u3} R τ _inst_1 (f i)))
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] [_inst_4 : DecidableEq.{succ u3} τ] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (φ : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u3} (Finset.{u3} τ) (Finset.instHasSubsetFinset.{u3} τ) (MvPolynomial.vars.{u2, u3} R τ _inst_1 (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ)) (Finset.biUnion.{u1, u3} σ τ (fun (a : τ) (b : τ) => _inst_4 a b) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u2, u3} R τ _inst_1 (f i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_bind₁ MvPolynomial.vars_bind₁ₓ'. -/
 theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     (bind₁ f φ).vars ⊆ φ.vars.biUnion fun i => (f i).vars :=
@@ -671,7 +671,7 @@ end
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1) {j : τ}, (Membership.Mem.{u2, u2} τ (Finset.{u2} τ) (Finset.hasMem.{u2} τ) j (MvPolynomial.vars.{u3, u2} R τ _inst_1 (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ))) -> (Exists.{succ u1} σ (fun (i : σ) => And (Membership.Mem.{u1, u1} σ (Finset.{u1} σ) (Finset.hasMem.{u1} σ) i (MvPolynomial.vars.{u3, u1} R σ _inst_1 φ)) (Membership.Mem.{u2, u2} τ (Finset.{u2} τ) (Finset.hasMem.{u2} τ) j (MvPolynomial.vars.{u3, u2} R τ _inst_1 (f i)))))
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (φ : MvPolynomial.{u1, u2} σ R _inst_1) {j : τ}, (Membership.mem.{u3, u3} τ (Finset.{u3} τ) (Finset.instMembershipFinset.{u3} τ) j (MvPolynomial.vars.{u2, u3} R τ _inst_1 (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ))) -> (Exists.{succ u1} σ (fun (i : σ) => And (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ)) (Membership.mem.{u3, u3} τ (Finset.{u3} τ) (Finset.instMembershipFinset.{u3} τ) j (MvPolynomial.vars.{u2, u3} R τ _inst_1 (f i)))))
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (φ : MvPolynomial.{u1, u2} σ R _inst_1) {j : τ}, (Membership.mem.{u3, u3} τ (Finset.{u3} τ) (Finset.instMembershipFinset.{u3} τ) j (MvPolynomial.vars.{u2, u3} R τ _inst_1 (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ))) -> (Exists.{succ u1} σ (fun (i : σ) => And (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ)) (Membership.mem.{u3, u3} τ (Finset.{u3} τ) (Finset.instMembershipFinset.{u3} τ) j (MvPolynomial.vars.{u2, u3} R τ _inst_1 (f i)))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁ₓ'. -/
 theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
     (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -626,7 +626,7 @@ section
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] [_inst_4 : DecidableEq.{succ u2} τ] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} τ) (Finset.hasSubset.{u2} τ) (MvPolynomial.vars.{u3, u2} R τ _inst_1 (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ)) (Finset.biUnion.{u1, u2} σ τ (fun (a : τ) (b : τ) => _inst_4 a b) (MvPolynomial.vars.{u3, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u3, u2} R τ _inst_1 (f i)))
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (_inst_4 : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (f : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u3} (Finset.{u3} τ) (Finset.instHasSubsetFinset.{u3} τ) (MvPolynomial.vars.{u2, u3} R τ _inst_1 (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (a : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) a) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 _inst_4) f)) (Finset.biUnion.{u1, u3} σ τ (fun (a : τ) (b : τ) => Classical.propDecidable (Eq.{succ u3} τ a b)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 f) (fun (i : σ) => MvPolynomial.vars.{u2, u3} R τ _inst_1 (_inst_4 i)))
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] [_inst_4 : DecidableEq.{succ u3} τ] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (φ : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u3} (Finset.{u3} τ) (Finset.instHasSubsetFinset.{u3} τ) (MvPolynomial.vars.{u2, u3} R τ _inst_1 (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ)) (Finset.biUnion.{u1, u3} σ τ (fun (a : τ) (b : τ) => _inst_4 a b) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u2, u3} R τ _inst_1 (f i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_bind₁ MvPolynomial.vars_bind₁ₓ'. -/
 theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     (bind₁ f φ).vars ⊆ φ.vars.biUnion fun i => (f i).vars :=

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

@@ -168,7 +168,7 @@ theorem aeval_id_eq_join₁ : aeval id = @join₁ σ R _ :=
 lean 3 declaration is
   forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1), Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) 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(MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) => (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) ([anonymous].{u2, max u1 u2, max u1 u2} R (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.join₁.{u1, u2} σ R _inst_1) φ)
 but is expected to have type
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u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (AlgHom.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} 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R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u1, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.join₁.{u1, u2} σ R _inst_1) φ)
+  forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 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_inst_1))))))) (MvPolynomial.eval₂Hom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1) (MvPolynomial.C.{u2, u1} R σ _inst_1) (id.{succ (max u1 u2)} (MvPolynomial.{u1, u2} σ R _inst_1))) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (AlgHom.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) 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u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (AlgHom.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u1, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u2 u1, max u2 u1} R (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.join₁.{u1, u2} σ R _inst_1) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_C_id_eq_join₁ MvPolynomial.eval₂Hom_C_id_eq_join₁ₓ'. -/
 theorem eval₂Hom_C_id_eq_join₁ (φ : MvPolynomial (MvPolynomial σ R) R) :
     eval₂Hom C id φ = join₁ φ :=
@@ -209,7 +209,7 @@ theorem bind₁_X_right (f : σ → MvPolynomial τ R) (i : σ) : bind₁ f (X i
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (i : σ), Eq.{max (succ u1) (succ u3)} (MvPolynomial.{u1, u3} σ S _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.bind₂.{u1, u2, u3} σ R S _inst_1 _inst_2 f) (MvPolynomial.X.{u2, u1} R σ _inst_1 i)) (MvPolynomial.X.{u3, u1} S σ _inst_2 i)
 but is expected to have type
-  forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, max u2 u1} R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (i : σ), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.X.{u3, u1} R σ _inst_1 i)) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), max (succ u1) (succ u2)} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u3, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.bind₂.{u1, u3, u2} σ R S _inst_1 _inst_2 f) (MvPolynomial.X.{u3, u1} R σ _inst_1 i)) (MvPolynomial.X.{u2, u1} S σ _inst_2 i)
+  forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, max u2 u1} R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (i : σ), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.X.{u3, u1} R σ _inst_1 i)) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), max (succ u1) (succ u2)} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u3, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.bind₂.{u1, u3, u2} σ R S _inst_1 _inst_2 f) (MvPolynomial.X.{u3, u1} R σ _inst_1 i)) (MvPolynomial.X.{u2, u1} S σ _inst_2 i)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_X_right MvPolynomial.bind₂_X_rightₓ'. -/
 @[simp]
 theorem bind₂_X_right (f : R →+* MvPolynomial σ S) (i : σ) : bind₂ f (X i) = X i :=
@@ -235,7 +235,7 @@ variable (f : σ → MvPolynomial τ R)
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (x : R), Eq.{max (succ u2) (succ u3)} (MvPolynomial.{u2, u3} τ R _inst_1) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) (coeFn.{max (succ u3) (succ (max u1 u3)), max (succ u3) (succ (max u1 u3))} (RingHom.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (fun (_x : RingHom.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u3} σ R _inst_1)) (RingHom.hasCoeToFun.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (MvPolynomial.C.{u3, u1} R σ _inst_1) x)) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (RingHom.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))) (fun (_x : RingHom.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))) => R -> (MvPolynomial.{u2, u3} τ R _inst_1)) (RingHom.hasCoeToFun.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))) (MvPolynomial.C.{u3, u2} R τ _inst_1) x)
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) a) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R 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_inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ 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(CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (MvPolynomial.C.{u2, u1} R σ _inst_1) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (MulHomClass.toFunLike.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) R (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) R (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (MvPolynomial.C.{u2, u3} R τ _inst_1) x)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_C_right MvPolynomial.bind₁_C_rightₓ'. -/
 @[simp]
 theorem bind₁_C_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (C x) = C x := by
@@ -246,7 +246,7 @@ theorem bind₁_C_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (C x) = C
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (r : R), Eq.{max (succ u1) (succ u3)} (MvPolynomial.{u1, u3} σ S _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.bind₂.{u1, u2, u3} σ R S _inst_1 _inst_2 f) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r)) (coeFn.{max (succ u2) (succ (max u1 u3)), max (succ u2) (succ (max u1 u3))} (RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => R -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) f r)
 but is expected to have type
-  forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, max u2 u1} R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (r : R), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (RingHom.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) 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+  forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, max u2 u1} R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (r : R), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (RingHom.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u3, max u1 u2} (RingHom.{u3, max u2 u1} R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) R (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, u3, max u1 u2} (RingHom.{u3, max u2 u1} R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{u3, max u1 u2} R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) f r)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_C_right MvPolynomial.bind₂_C_rightₓ'. -/
 @[simp]
 theorem bind₂_C_right (f : R →+* MvPolynomial σ S) (r : R) : bind₂ f (C r) = f r :=
@@ -278,7 +278,7 @@ theorem bind₂_comp_C (f : R →+* MvPolynomial σ S) : (bind₂ f).comp C = f
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u1) (succ u3)} (MvPolynomial.{u1, u3} σ S _inst_2) (coeFn.{succ (max u1 u3), succ (max u1 u3)} (RingHom.{max u1 u3, max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u3, u1} (MvPolynomial.{u1, u3} σ S _inst_2) σ (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u3, max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u3, u1} (MvPolynomial.{u1, u3} σ S _inst_2) σ (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u3, max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u3, u1} (MvPolynomial.{u1, u3} σ S _inst_2) σ (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.join₂.{u1, u3} σ S _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u3, u1} (MvPolynomial.{u1, u3} σ S _inst_2) σ (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u3, u1} (MvPolynomial.{u1, u3} σ S _inst_2) σ (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, max u1 u3} σ (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u3, u1} (MvPolynomial.{u1, u3} σ S _inst_2) σ (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) (MvPolynomial.map.{u2, max u1 u3, u1} R (MvPolynomial.{u1, u3} σ S _inst_2) σ _inst_1 (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2) f) φ)) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.bind₂.{u1, u2, u3} σ R S _inst_1 _inst_2 f) φ)
 but is expected to have type
-  forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, max u2 u1} R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, max u2 u1} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) => MvPolynomial.{u1, u2} σ S _inst_2) (FunLike.coe.{max (max (max (succ u1) (succ u3)) (succ u2)) (succ u1), max (succ u3) (succ u1), max (succ u1) (succ u2)} (RingHom.{max u3 u1, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (a : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) a) (MulHomClass.toFunLike.{max (max (max u1 u3) u2) u1, max u3 u1, max u1 u2} (RingHom.{max u3 u1, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} 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S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} 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(MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))))))) (MvPolynomial.map.{u3, max u1 u2, u1} R (MvPolynomial.{u1, u2} σ S _inst_2) σ _inst_1 (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2) f) φ)) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), max (succ u1) (succ u2)} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u3, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.bind₂.{u1, u3, u2} σ R S _inst_1 _inst_2 f) φ)
+  forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, max u2 u1} R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, max u2 u1} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) => MvPolynomial.{u1, u2} σ S _inst_2) (FunLike.coe.{max (max (max (succ u1) (succ u3)) (succ u2)) (succ u1), max (succ u3) (succ u1), max (succ u1) (succ u2)} (RingHom.{max u3 u1, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (a : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) a) (MulHomClass.toFunLike.{max (max (max u1 u3) u2) u1, max u3 u1, max u1 u2} (RingHom.{max u3 u1, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u1 u3) u2) u1, max u3 u1, max u1 u2} (RingHom.{max u3 u1, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max (max (max u1 u3) u2) u1, max u3 u1, max u1 u2} (RingHom.{max u3 u1, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (RingHom.instRingHomClassRingHom.{max u3 u1, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))))))) (MvPolynomial.map.{u3, max u1 u2, u1} R (MvPolynomial.{u1, u2} σ S _inst_2) σ _inst_1 (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2) f) φ)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u1, max u2 u1} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u2 u1} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u2 u1} σ (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ S _inst_2) σ (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, max u2 u1} σ (MvPolynomial.{u1, u2} σ S _inst_2) 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_inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u3, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.bind₂.{u1, u3, u2} σ R S _inst_1 _inst_2 f) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.join₂_map MvPolynomial.join₂_mapₓ'. -/
 @[simp]
 theorem join₂_map (f : R →+* MvPolynomial σ S) (φ : MvPolynomial σ R) :
@@ -378,7 +378,7 @@ theorem bind₂_comp_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPoly
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} {T : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u4} T] (f : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (g : RingHom.{u3, max u1 u4} S (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u1) (succ u4)} (MvPolynomial.{u1, u4} σ T _inst_3) (coeFn.{max (succ (max u1 u3)) (succ (max u1 u4)), max (succ (max u1 u3)) (succ (max u1 u4))} (RingHom.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (fun (_x : RingHom.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) => (MvPolynomial.{u1, u3} σ S _inst_2) -> (MvPolynomial.{u1, u4} σ T _inst_3)) (RingHom.hasCoeToFun.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (MvPolynomial.bind₂.{u1, u3, u4} σ S T _inst_2 _inst_3 g) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.bind₂.{u1, u2, u3} σ R S _inst_1 _inst_2 f) φ)) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u4)), max (succ (max u1 u2)) (succ (max u1 u4))} (RingHom.{max u1 u2, max u1 u4} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (fun (_x : RingHom.{max u1 u2, max u1 u4} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u4} σ T _inst_3)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u4} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (MvPolynomial.bind₂.{u1, u2, u4} σ R T _inst_1 _inst_3 (RingHom.comp.{u2, max u1 u3, max u1 u4} R (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3))) (MvPolynomial.bind₂.{u1, u3, u4} σ S T _inst_2 _inst_3 g) f)) φ)
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} {T : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u1} T] (f : RingHom.{u4, max u3 u2} R (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (g : RingHom.{u3, max u1 u2} S (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3)))) (φ : MvPolynomial.{u2, u4} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u3} σ S _inst_2) => MvPolynomial.{u2, u1} σ T _inst_3) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), max (succ u2) (succ u3)} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (MvPolynomial.{u2, u4} σ R _inst_1) (fun (a : MvPolynomial.{u2, u4} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u4} σ R _inst_1) => MvPolynomial.{u2, u3} σ S _inst_2) a) (MulHomClass.toFunLike.{max (max u2 u4) u3, max u2 u4, max u2 u3} (RingHom.{max u4 u2, max u3 u2} 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_inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u4) u3, max u2 u4, max u2 u3} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) 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(MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3)))) (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u1} σ T _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u4) u1, max u2 u4, max u2 u1} (RingHom.{max u4 u2, max u1 u2} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3)))) (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3))) (RingHom.instRingHomClassRingHom.{max u2 u4, max u2 u1} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3))))))) (MvPolynomial.bind₂.{u2, u4, u1} σ R T _inst_1 _inst_3 (RingHom.comp.{u4, max u2 u3, max u2 u1} R (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3))) (MvPolynomial.bind₂.{u2, u3, u1} σ S T _inst_2 _inst_3 g) f)) φ)
+  forall {σ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} {T : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u1} T] (f : RingHom.{u4, max u3 u2} R (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (g : RingHom.{u3, max u1 u2} S (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3)))) (φ : MvPolynomial.{u2, u4} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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(Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u2 u4, max u2 u3} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))))))) (MvPolynomial.bind₂.{u2, u4, u3} σ R S _inst_1 _inst_2 f) φ)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), max (succ u2) (succ u1)} (RingHom.{max u3 u2, max u1 u2} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3)))) (MvPolynomial.{u2, u3} σ S _inst_2) (fun (_x : MvPolynomial.{u2, u3} σ S _inst_2) => (fun 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(Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3))) (RingHom.instRingHomClassRingHom.{max u2 u4, max u2 u1} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3))))))) (MvPolynomial.bind₂.{u2, u4, u1} σ R T _inst_1 _inst_3 (RingHom.comp.{u4, max u2 u3, max u2 u1} R (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3))) (MvPolynomial.bind₂.{u2, u3, u1} σ S T _inst_2 _inst_3 g) f)) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_bind₂ MvPolynomial.bind₂_bind₂ₓ'. -/
 theorem bind₂_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPolynomial σ T)
     (φ : MvPolynomial σ R) : (bind₂ g) (bind₂ f φ) = bind₂ ((bind₂ g).comp f) φ :=
@@ -413,7 +413,7 @@ theorem rename_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ →
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} {T : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u4} T] (f : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (g : RingHom.{u3, u4} S T (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u1) (succ u4)} (MvPolynomial.{u1, u4} σ T _inst_3) (coeFn.{max (succ (max u1 u3)) (succ (max u1 u4)), max (succ (max u1 u3)) (succ (max u1 u4))} (RingHom.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (fun (_x : RingHom.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) => (MvPolynomial.{u1, u3} σ S _inst_2) -> (MvPolynomial.{u1, u4} σ T _inst_3)) (RingHom.hasCoeToFun.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (MvPolynomial.map.{u3, u4, u1} S T σ _inst_2 _inst_3 g) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.bind₂.{u1, u2, u3} σ R S _inst_1 _inst_2 f) φ)) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u4)), max (succ (max u1 u2)) (succ (max u1 u4))} (RingHom.{max u1 u2, max u1 u4} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (fun (_x : RingHom.{max u1 u2, max u1 u4} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u4} σ T _inst_3)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u4} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (MvPolynomial.bind₂.{u1, u2, u4} σ R T _inst_1 _inst_3 (RingHom.comp.{u2, max u1 u3, max u1 u4} R (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3))) (MvPolynomial.map.{u3, u4, u1} S T σ _inst_2 _inst_3 g) f)) φ)
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} {T : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u1} T] (f : RingHom.{u4, max u3 u2} R (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (g : RingHom.{u3, u1} S T (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T (CommSemiring.toSemiring.{u1} T _inst_3))) (φ : MvPolynomial.{u2, u4} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u3} σ S _inst_2) => MvPolynomial.{u2, u1} σ T _inst_3) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), max (succ u2) (succ u3)} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (MvPolynomial.{u2, u4} σ R _inst_1) (fun (a : MvPolynomial.{u2, u4} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u4} σ R _inst_1) => MvPolynomial.{u2, u3} σ S _inst_2) a) (MulHomClass.toFunLike.{max (max u2 u4) u3, max u2 u4, max u2 u3} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u4) u3, max u2 u4, max u2 u3} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u4) u3, max u2 u4, max u2 u3} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u2 u4, max u2 u3} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))))))) (MvPolynomial.bind₂.{u2, u4, u3} σ R S _inst_1 _inst_2 f) φ)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), max (succ u1) (succ u2)} (RingHom.{max u3 u2, max u1 u2} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3)))) (MvPolynomial.{u2, u3} σ S _inst_2) (fun (_x : MvPolynomial.{u2, u3} σ S _inst_2) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u3} σ S _inst_2) => MvPolynomial.{u2, u1} σ T _inst_3) _x) (MulHomClass.toFunLike.{max (max u3 u1) u2, max u3 u2, max u1 u2} (RingHom.{max u3 u2, max u1 u2} 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T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3))) (RingHom.instRingHomClassRingHom.{max u2 u4, max u2 u1} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3))))))) (MvPolynomial.bind₂.{u2, u4, u1} σ R T _inst_1 _inst_3 (RingHom.comp.{u4, max u3 u2, max u1 u2} R (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3))) (MvPolynomial.map.{u3, u1, u2} S T σ _inst_2 _inst_3 g) f)) φ)
+  forall {σ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} {T : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u1} T] (f : RingHom.{u4, max u3 u2} R (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (g : RingHom.{u3, u1} S T (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T (CommSemiring.toSemiring.{u1} T _inst_3))) (φ : MvPolynomial.{u2, u4} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u3} σ S _inst_2) => MvPolynomial.{u2, u1} σ T _inst_3) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), max (succ u2) (succ u3)} 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_inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u2 u4, max u2 u3} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))))))) (MvPolynomial.bind₂.{u2, u4, u3} σ R S _inst_1 _inst_2 f) φ)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), max (succ u1) (succ u2)} (RingHom.{max u3 u2, max u1 u2} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3)))) (MvPolynomial.{u2, u3} σ S _inst_2) (fun (_x : MvPolynomial.{u2, u3} σ S _inst_2) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u3} σ S _inst_2) => MvPolynomial.{u2, u1} σ T _inst_3) _x) (MulHomClass.toFunLike.{max (max u3 u1) u2, max u3 u2, max u1 u2} (RingHom.{max u3 u2, max u1 u2} 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(CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u4) u3, max u2 u4, max u2 u3} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) 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(RingHomClass.toNonUnitalRingHomClass.{max (max u2 u4) u1, max u2 u4, max u2 u1} (RingHom.{max u4 u2, max u1 u2} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3)))) (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3))) (RingHom.instRingHomClassRingHom.{max u2 u4, max u2 u1} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3))))))) (MvPolynomial.bind₂.{u2, u4, u1} σ R T _inst_1 _inst_3 (RingHom.comp.{u4, max u3 u2, max u1 u2} R (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3))) (MvPolynomial.map.{u3, u1, u2} S T σ _inst_2 _inst_3 g) f)) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_bind₂ MvPolynomial.map_bind₂ₓ'. -/
 theorem map_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* T) (φ : MvPolynomial σ R) :
     map g (bind₂ f φ) = bind₂ ((map g).comp f) φ :=
@@ -451,7 +451,7 @@ theorem bind₁_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ →
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} {T : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u4} T] (f : RingHom.{u3, max u1 u4} S (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (g : RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u1) (succ u4)} (MvPolynomial.{u1, u4} σ T _inst_3) (coeFn.{max (succ (max u1 u3)) (succ (max u1 u4)), max (succ (max u1 u3)) (succ (max u1 u4))} (RingHom.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (fun (_x : RingHom.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) => (MvPolynomial.{u1, u3} σ S _inst_2) -> (MvPolynomial.{u1, u4} σ T 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 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} {S : Type.{u4}} {T : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u3} T] (f : RingHom.{u4, max u3 u2} S (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3)))) (g : RingHom.{u1, u4} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (φ : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u4} σ S _inst_2) => MvPolynomial.{u2, u3} σ T _inst_3) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u2), max (succ u1) (succ u2), max (succ u4) (succ u2)} 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(Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S σ _inst_2)))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u2, max u4 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S σ _inst_2))))))) (MvPolynomial.map.{u1, u4, u2} R S σ _inst_1 _inst_2 g) φ)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u1), max (succ u2) (succ u3)} (RingHom.{max u1 u2, max u3 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} 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(CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3)))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u3} σ T _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u1) u3, max u2 u1, max u2 u3} (RingHom.{max u1 u2, max u3 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3)))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3))) (RingHom.instRingHomClassRingHom.{max u2 u1, max u2 u3} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3))))))) (MvPolynomial.bind₂.{u2, u1, u3} σ R T _inst_1 _inst_3 (RingHom.comp.{u1, u4, max u2 u3} R S (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3))) f g)) φ)
+  forall {σ : Type.{u2}} {R : Type.{u1}} {S : Type.{u4}} {T : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u3} T] (f : RingHom.{u4, max u3 u2} S (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3)))) (g : RingHom.{u1, u4} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (φ : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u4} σ S _inst_2) => MvPolynomial.{u2, u3} σ T _inst_3) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u2), max (succ u1) (succ u2), max (succ u4) (succ u2)} 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(MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u1) u3, max u2 u1, max u2 u3} (RingHom.{max u1 u2, max u3 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3)))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u3} σ T _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u1) u3, max u2 u1, max u2 u3} (RingHom.{max u1 u2, max u3 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3)))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3))) (RingHom.instRingHomClassRingHom.{max u2 u1, max u2 u3} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3))))))) (MvPolynomial.bind₂.{u2, u1, u3} σ R T _inst_1 _inst_3 (RingHom.comp.{u1, u4, max u2 u3} R S (MvPolynomial.{u2, u3} σ T _inst_3) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3))) f g)) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_map MvPolynomial.bind₂_mapₓ'. -/
 theorem bind₂_map (f : S →+* MvPolynomial σ T) (g : R →+* S) (φ : MvPolynomial σ R) :
     bind₂ f (map g φ) = bind₂ (f.comp g) φ := by simp [bind₂]
@@ -474,7 +474,7 @@ theorem map_comp_C (f : R →+* S) : (map f).comp (C : R →+* MvPolynomial σ R
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u4} S] (f : RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (g : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{succ u4} S (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (fun (_x : RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) f (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 g) φ)) (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (RingHom.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (fun (_x : RingHom.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (MvPolynomial.eval₂Hom.{u3, u4, u1} R S σ _inst_1 _inst_2 (RingHom.comp.{u3, max u2 u3, u4} R (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) f (MvPolynomial.C.{u3, u2} R τ _inst_1)) (fun (i : σ) => coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (fun (_x : RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) f (g i))) φ)
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u4}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (g : σ -> (MvPolynomial.{u3, u4} τ R _inst_1)) (φ : MvPolynomial.{u1, u4} σ R _inst_1), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u3, u4} τ R _inst_1) => S) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u1) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u4, max u4 u1, max u4 u3} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u3, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) 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R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, max u3 u4} R (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))))) (Algebra.toModule.{u4, max u3 u4} R (MvPolynomial.{u3, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) 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(MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) (MvPolynomial.algebra.{u4, u4, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1))) (AlgHom.algHomClass.{u4, max u1 u4, max u3 u4} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u3, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) (MvPolynomial.algebra.{u4, u4, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u4} σ τ R _inst_1 g) φ)) (FunLike.coe.{max (max (succ u1) (succ u4)) 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(Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) f (MvPolynomial.C.{u4, u3} R τ _inst_1)) (fun (i : σ) => FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u4), succ u2} (RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) (fun (_x : MvPolynomial.{u3, u4} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u3, u4} τ R _inst_1) => S) _x) (MulHomClass.toFunLike.{max (max u3 u4) u2, max u3 u4, u2} (RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) S (NonUnitalNonAssocSemiring.toMul.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u3 u4) u2, max u3 u4, u2} (RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u3 u4) u2, max u3 u4, u2} (RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u3 u4, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f (g i))) φ)
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u4}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (g : σ -> (MvPolynomial.{u3, u4} τ R _inst_1)) (φ : MvPolynomial.{u1, u4} σ R _inst_1), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u4} τ R _inst_1) => S) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u1) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u4, max u4 u1, max u4 u3} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u3, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) 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R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, max u3 u4} R (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))))) (Algebra.toModule.{u4, max u3 u4} R (MvPolynomial.{u3, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) 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_inst_1) S (NonUnitalNonAssocSemiring.toMul.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u4) u2, max u1 u4, u2} (RingHom.{max u4 u1, u2} (MvPolynomial.{u1, u4} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u1, u4} 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(Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) f (MvPolynomial.C.{u4, u3} R τ _inst_1)) (fun (i : σ) => FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u4), succ u2} (RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) (fun (_x : MvPolynomial.{u3, u4} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u4} τ R _inst_1) => S) _x) (MulHomClass.toFunLike.{max (max u3 u4) u2, max u3 u4, u2} (RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) S (NonUnitalNonAssocSemiring.toMul.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u3 u4) u2, max u3 u4, u2} (RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u3 u4) u2, max u3 u4, u2} (RingHom.{max u4 u3, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u3 u4, u2} (MvPolynomial.{u3, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u3} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f (g i))) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.hom_bind₁ MvPolynomial.hom_bind₁ₓ'. -/
 -- mixing the two monad structures
 theorem hom_bind₁ (f : MvPolynomial τ R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
@@ -486,7 +486,7 @@ theorem hom_bind₁ (f : MvPolynomial τ R →+* S) (g : σ → MvPolynomial τ
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u4} S] (f : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (g : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u2) (succ u4)} (MvPolynomial.{u2, u4} τ S _inst_2) (coeFn.{max (succ (max u2 u3)) (succ (max u2 u4)), max (succ (max u2 u3)) (succ (max u2 u4))} (RingHom.{max u2 u3, max u2 u4} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u4} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)))) (fun (_x : RingHom.{max u2 u3, max u2 u4} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u4} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u2, u4} τ S _inst_2)) (RingHom.hasCoeToFun.{max u2 u3, max u2 u4} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u4} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)))) (MvPolynomial.map.{u3, u4, u2} R S τ _inst_1 _inst_2 f) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 g) φ)) (coeFn.{max (succ (max u1 u4)) (succ (max u2 u4)), max (succ (max u1 u4)) (succ (max u2 u4))} (AlgHom.{u4, max u1 u4, max u2 u4} S (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.{u2, u4} τ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) (MvPolynomial.algebra.{u4, u4, u2} S S τ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2))) (fun (_x : AlgHom.{u4, max u1 u4, max u2 u4} S (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.{u2, u4} τ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) (MvPolynomial.algebra.{u4, u4, u2} S S τ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2))) => (MvPolynomial.{u1, u4} σ S _inst_2) -> (MvPolynomial.{u2, u4} τ S _inst_2)) ([anonymous].{u4, max u1 u4, max u2 u4} S (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.{u2, u4} τ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) (MvPolynomial.algebra.{u4, u4, u2} S S τ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2))) (MvPolynomial.bind₁.{u1, u2, u4} σ τ S _inst_2 (fun (i : σ) => coeFn.{max (succ (max u2 u3)) (succ (max u2 u4)), max (succ (max u2 u3)) (succ (max u2 u4))} (RingHom.{max u2 u3, max u2 u4} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u4} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)))) (fun (_x : RingHom.{max u2 u3, max u2 u4} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u4} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u2, u4} τ S _inst_2)) (RingHom.hasCoeToFun.{max u2 u3, max u2 u4} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u4} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ S _inst_2) (MvPolynomial.commSemiring.{u4, u2} S τ _inst_2)))) (MvPolynomial.map.{u3, u4, u2} R S τ _inst_1 _inst_2 f) (g i))) (coeFn.{max (succ (max u1 u3)) (succ (max u1 u4)), max (succ (max u1 u3)) (succ (max u1 u4))} (RingHom.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u1, u4} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (MvPolynomial.map.{u3, u4, u1} R S σ _inst_1 _inst_2 f) φ))
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (g : σ -> (MvPolynomial.{u2, u4} τ R _inst_1)) (φ : MvPolynomial.{u1, u4} σ R _inst_1), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u4} τ R _inst_1) => MvPolynomial.{u2, u3} τ S _inst_2) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), max (succ u2) (succ u4)} (AlgHom.{u4, max u4 u1, max u4 u2} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1))) (MvPolynomial.{u1, u4} σ R _inst_1) (fun (a : MvPolynomial.{u1, u4} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u4} σ R _inst_1) => MvPolynomial.{u2, u4} τ R _inst_1) a) (SMulHomClass.toFunLike.{max (max u1 u2) u4, u4, max u1 u4, max u2 u4} (AlgHom.{u4, max u4 u1, max u4 u2} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1))) R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) (SMulZeroClass.toSMul.{u4, max u1 u4} R (MvPolynomial.{u1, u4} σ R _inst_1) (AddMonoid.toZero.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max u1 u4} R (MvPolynomial.{u1, u4} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max u1 u4} R (MvPolynomial.{u1, u4} σ R _inst_1) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) 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u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))))) (MvPolynomial.map.{u4, u3, u1} R S σ _inst_1 _inst_2 f) φ))
+  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (g : σ -> (MvPolynomial.{u2, u4} τ R _inst_1)) (φ : MvPolynomial.{u1, u4} σ R _inst_1), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u4} τ R _inst_1) => MvPolynomial.{u2, u3} τ S _inst_2) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), max (succ u2) (succ u4)} (AlgHom.{u4, max u4 u1, max u4 u2} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) 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(MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 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_inst_2))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} S (MvPolynomial.{u2, u3} τ S _inst_2) (MonoidWithZero.toMonoid.{u3} S (Semiring.toMonoidWithZero.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)))))) (Module.toDistribMulAction.{u3, max u2 u3} S (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{u3} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ S _inst_2) 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(MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) (MvPolynomial.algebra.{u3, u3, u2} S S τ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2))) (AlgHom.algHomClass.{u3, max u1 u3, max u2 u3} S (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u2, u3} τ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) (MvPolynomial.algebra.{u3, u3, u2} S S τ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2))))))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ S _inst_2 (fun (i : σ) => FunLike.coe.{max (max (succ u4) (succ 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(Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u4 u3) u2, max u4 u2, max u3 u2} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)))) (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.{u2, u3} τ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u4 u3) u2, max u4 u2, max u3 u2} (RingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2)))) (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2))) (RingHom.instRingHomClassRingHom.{max u4 u2, max u3 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.{u2, u3} τ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} τ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S τ _inst_2))))))) (MvPolynomial.map.{u4, u3, u2} R S τ _inst_1 _inst_2 f) (g i))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (succ u4) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u4 u1, max u3 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.{u1, u4} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u4} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u4} σ R _inst_1) => MvPolynomial.{u1, u3} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u4 u3) u1, max u4 u1, max u3 u1} (RingHom.{max u4 u1, max u3 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u4 u3) u1, max u4 u1, max u3 u1} (RingHom.{max u4 u1, max u3 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u4 u3) u1, max u4 u1, max u3 u1} (RingHom.{max u4 u1, max u3 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u4 u1, max u3 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))))) (MvPolynomial.map.{u4, u3, u1} R S σ _inst_1 _inst_2 f) φ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_bind₁ MvPolynomial.map_bind₁ₓ'. -/
 theorem map_bind₁ (f : R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     map f (bind₁ g φ) = bind₁ (fun i : σ => (map f) (g i)) (map f φ) :=
@@ -512,7 +512,7 @@ theorem eval₂Hom_comp_C (f : R →+* S) (g : σ → S) : (eval₂Hom f g).comp
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u4} S] (f : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (g : τ -> S) (h : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{succ u4} S (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (fun (_x : RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (MvPolynomial.eval₂Hom.{u3, u4, u2} R S τ _inst_1 _inst_2 f g) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 h) φ)) (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (RingHom.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (fun (_x : RingHom.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (MvPolynomial.eval₂Hom.{u3, u4, u1} R S σ _inst_1 _inst_2 f (fun (i : σ) => coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (fun (_x : RingHom.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u2 u3, u4} (MvPolynomial.{u2, u3} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (MvPolynomial.eval₂Hom.{u3, u4, u2} R S τ _inst_1 _inst_2 f g) (h i))) φ)
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (g : τ -> S) (h : σ -> (MvPolynomial.{u2, u4} τ R _inst_1)) (φ : MvPolynomial.{u1, u4} σ R _inst_1), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u4} τ R _inst_1) => S) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), max (succ u2) (succ u4)} (AlgHom.{u4, max u4 u1, max u4 u2} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) 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(MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u4) u3, max u2 u4, u3} (RingHom.{max u4 u2, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u2, u4} τ R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u4) u3, max u2 u4, u3} (RingHom.{max u4 u2, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u2 u4, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max 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+  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (g : τ -> S) (h : σ -> (MvPolynomial.{u2, u4} τ R _inst_1)) (φ : MvPolynomial.{u1, u4} σ R _inst_1), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u4} τ R _inst_1) => S) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), max (succ u2) (succ u4)} (AlgHom.{u4, max u4 u1, max u4 u2} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) 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_inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) 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_inst_1 (Algebra.id.{u4} R _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1))) R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} 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_inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) 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R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (Algebra.toModule.{u4, max u2 u4} R (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, max u1 u4, max u2 u4, max (max u1 u2) u4} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) (AlgHom.{u4, max u4 u1, max u4 u2} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1))) (AlgHom.algHomClass.{u4, max u1 u4, max u2 u4} R (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.{u2, u4} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)) (MvPolynomial.algebra.{u4, u4, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1)) (MvPolynomial.algebra.{u4, u4, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u4} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u2, u4} σ τ R _inst_1 h) φ)) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u1) (succ u4), succ u3} (RingHom.{max u4 u1, u3} (MvPolynomial.{u1, u4} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u4} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u4} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u4} σ R _inst_1) => S) _x) (MulHomClass.toFunLike.{max (max u1 u4) u3, max u1 u4, u3} (RingHom.{max u4 u1, u3} (MvPolynomial.{u1, u4} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u4} σ R _inst_1) S (NonUnitalNonAssocSemiring.toMul.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u4) u3, max u1 u4, u3} (RingHom.{max u4 u1, u3} (MvPolynomial.{u1, u4} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u4} σ R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u4) u3, max u1 u4, u3} (RingHom.{max u4 u1, u3} (MvPolynomial.{u1, u4} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u4} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ R _inst_1) 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(Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u2, u4} τ R _inst_1) (fun (_x : MvPolynomial.{u2, u4} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u4} τ R _inst_1) => S) _x) (MulHomClass.toFunLike.{max (max u2 u4) u3, max u2 u4, u3} (RingHom.{max u4 u2, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u2, u4} τ R _inst_1) S (NonUnitalNonAssocSemiring.toMul.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u4) u3, max u2 u4, u3} (RingHom.{max u4 u2, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u2, u4} τ R _inst_1) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u4) u3, max u2 u4, u3} (RingHom.{max u4 u2, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u2 u4, u3} (MvPolynomial.{u2, u4} τ R _inst_1) S (Semiring.toNonAssocSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u2, u4} τ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R τ _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (MvPolynomial.eval₂Hom.{u4, u3, u2} R S τ _inst_1 _inst_2 f g) (h i))) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_bind₁ MvPolynomial.eval₂Hom_bind₁ₓ'. -/
 theorem eval₂Hom_bind₁ (f : R →+* S) (g : τ → S) (h : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     eval₂Hom f g (bind₁ h φ) = eval₂Hom f (fun i => eval₂Hom f g (h i)) φ := by
@@ -557,7 +557,7 @@ theorem eval₂Hom_comp_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPo
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} {T : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u4} T] (f : RingHom.{u3, u4} S T (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) (g : σ -> T) (h : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u4} T (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (RingHom.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) (fun (_x : RingHom.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) => (MvPolynomial.{u1, u3} σ S _inst_2) -> T) (RingHom.hasCoeToFun.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) (MvPolynomial.eval₂Hom.{u3, u4, u1} S T σ _inst_2 _inst_3 f g) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.bind₂.{u1, u2, u3} σ R S _inst_1 _inst_2 h) φ)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (RingHom.{max u1 u2, u4} (MvPolynomial.{u1, u2} σ R _inst_1) T (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) (fun (_x : RingHom.{max u1 u2, u4} (MvPolynomial.{u1, u2} σ R _inst_1) T (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> T) (RingHom.hasCoeToFun.{max u1 u2, u4} (MvPolynomial.{u1, u2} σ R _inst_1) T (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) (MvPolynomial.eval₂Hom.{u2, u4, u1} R T σ _inst_1 _inst_3 (RingHom.comp.{u2, max u1 u3, u4} R (MvPolynomial.{u1, u3} σ S _inst_2) T (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3)) (MvPolynomial.eval₂Hom.{u3, u4, u1} S T σ _inst_2 _inst_3 f g) h) g) φ)
 but is expected to have type
-  forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u4}} {T : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u3} T] (f : RingHom.{u4, u3} S T (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3))) (g : σ -> T) (h : RingHom.{u2, max u4 u1} R (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u4} σ S _inst_2) => T) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u2), max (succ u1) (succ u4)} (RingHom.{max u2 u1, max u4 u1} 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_inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u2) u4, max u1 u2, max u1 u4} (RingHom.{max u2 u1, max u4 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u2) u4, max u1 u2, max u1 u4} (RingHom.{max u2 u1, max u4 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u2, max u1 u4} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))))))) (MvPolynomial.bind₂.{u1, u2, u4} σ R S _inst_1 _inst_2 h) φ)) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u1) (succ u4), succ u3} (RingHom.{max u4 u1, u3} (MvPolynomial.{u1, u4} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3))) (MvPolynomial.{u1, u4} σ S _inst_2) (fun (_x : MvPolynomial.{u1, u4} σ S _inst_2) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u4} σ S _inst_2) => T) _x) (MulHomClass.toFunLike.{max (max u1 u4) u3, max u1 u4, u3} (RingHom.{max u4 u1, u3} (MvPolynomial.{u1, u4} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3))) (MvPolynomial.{u1, u4} σ S _inst_2) T (NonUnitalNonAssocSemiring.toMul.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u4) u3, max u1 u4, u3} (RingHom.{max u4 u1, u3} (MvPolynomial.{u1, u4} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))) 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(Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3)) (RingHom.instRingHomClassRingHom.{max u1 u4, u3} (MvPolynomial.{u1, u4} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3)))))) (MvPolynomial.eval₂Hom.{u4, u3, u1} S T σ _inst_2 _inst_3 f g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u2), max (succ u1) (succ u4)} (RingHom.{max u2 u1, max u4 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 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(MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u2) u3, max u1 u2, u3} (RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) T (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3))) (MvPolynomial.{u1, u2} σ R _inst_1) T (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3)) (RingHom.instRingHomClassRingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} σ R _inst_1) T (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3)))))) (MvPolynomial.eval₂Hom.{u2, u3, u1} R T σ _inst_1 _inst_3 (RingHom.comp.{u2, max u1 u4, u3} R (MvPolynomial.{u1, u4} σ S _inst_2) T (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3)) (MvPolynomial.eval₂Hom.{u4, u3, u1} S T σ _inst_2 _inst_3 f g) h) g) φ)
+  forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u4}} {T : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u3} T] (f : RingHom.{u4, u3} S T (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3))) (g : σ -> T) (h : RingHom.{u2, max u4 u1} R (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u4} σ S _inst_2) => T) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u2), max (succ u1) (succ u4)} (RingHom.{max u2 u1, max u4 u1} 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(MvPolynomial.eval₂Hom.{u4, u3, u1} S T σ _inst_2 _inst_3 f g) h) g) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_bind₂ MvPolynomial.eval₂Hom_bind₂ₓ'. -/
 theorem eval₂Hom_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPolynomial σ S)
     (φ : MvPolynomial σ R) : eval₂Hom f g (bind₂ h φ) = eval₂Hom ((eval₂Hom f g).comp h) g φ :=
@@ -568,7 +568,7 @@ theorem eval₂Hom_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPolynom
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} {T : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u4} T] [_inst_4 : Algebra.{u3, u4} S T _inst_2 (CommSemiring.toSemiring.{u4} T _inst_3)] (f : σ -> T) (g : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u4} T (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (AlgHom.{u3, max u1 u3, u4} S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4) (fun (_x : AlgHom.{u3, max u1 u3, u4} S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4) => (MvPolynomial.{u1, u3} σ S _inst_2) -> T) ([anonymous].{u3, max u1 u3, u4} S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4) (MvPolynomial.aeval.{u3, u4, u1} S T σ _inst_2 _inst_3 _inst_4 f) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max 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_inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.bind₂.{u1, u2, u3} σ R S _inst_1 _inst_2 g) φ)) (coeFn.{max (succ (max u1 u2)) (succ u4), max (succ (max u1 u2)) (succ u4)} (RingHom.{max u1 u2, u4} (MvPolynomial.{u1, u2} σ R _inst_1) T (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) (fun (_x : RingHom.{max u1 u2, u4} (MvPolynomial.{u1, u2} σ R _inst_1) T (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> T) (RingHom.hasCoeToFun.{max u1 u2, u4} (MvPolynomial.{u1, u2} σ R _inst_1) T (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) (MvPolynomial.eval₂Hom.{u2, u4, u1} R T σ _inst_1 _inst_3 (RingHom.comp.{u2, max u1 u3, u4} R (MvPolynomial.{u1, u3} σ S _inst_2) T (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3)) ((fun (a : Sort.{max (succ (max u1 u3)) (succ u4)}) (b : Sort.{max (succ (max u1 u3)) (succ u4)}) [self : HasLiftT.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} a b] => self.0) (AlgHom.{u3, max u1 u3, u4} S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4) (RingHom.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) (HasLiftT.mk.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (AlgHom.{u3, max u1 u3, u4} S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4) (RingHom.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) (CoeTCₓ.coe.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (AlgHom.{u3, max u1 u3, u4} S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4) (RingHom.{max u1 u3, u4} (MvPolynomial.{u1, u3} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3))) (RingHom.hasCoeT.{max (max u1 u3) u4, max u1 u3, u4} (AlgHom.{u3, max u1 u3, u4} S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4) (MvPolynomial.{u1, u3} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T _inst_3)) (AlgHomClass.toRingHomClass.{max (max u1 u3) u4, u3, max u1 u3, u4} (AlgHom.{u3, max u1 u3, u4} S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4) S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4 (AlgHom.algHomClass.{u3, max u1 u3, u4} S (MvPolynomial.{u1, u3} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u4} T _inst_3) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) _inst_4))))) (MvPolynomial.aeval.{u3, u4, u1} S T σ _inst_2 _inst_3 _inst_4 f)) g) f) φ)
 but is expected to have type
-  forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u4}} {T : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u3} T] [_inst_4 : Algebra.{u4, u3} S T _inst_2 (CommSemiring.toSemiring.{u3} T _inst_3)] (f : σ -> T) (g : RingHom.{u2, max u4 u1} R (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u4} σ S _inst_2) => T) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u2), max (succ u1) (succ u4)} (RingHom.{max u2 u1, max u4 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) 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(MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u2) u4, max u1 u2, max u1 u4} (RingHom.{max u2 u1, max u4 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ 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(MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u2, max u1 u4} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 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(Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3)) (RingHomClass.toRingHom.{max (max u1 u4) u3, max u1 u4, u3} (AlgHom.{u4, max u4 u1, u3} S (MvPolynomial.{u1, u4} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u3} T _inst_3) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) _inst_4) (MvPolynomial.{u1, u4} σ S _inst_2) T (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))) (Semiring.toNonAssocSemiring.{u3} T (CommSemiring.toSemiring.{u3} T _inst_3)) (AlgHomClass.toRingHomClass.{max (max u1 u4) u3, u4, max u1 u4, u3} (AlgHom.{u4, max u4 u1, u3} S (MvPolynomial.{u1, u4} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u3} T _inst_3) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) _inst_4) S (MvPolynomial.{u1, u4} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u3} T _inst_3) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) _inst_4 (AlgHom.algHomClass.{u4, max u1 u4, u3} S (MvPolynomial.{u1, u4} σ S _inst_2) T _inst_2 (CommSemiring.toSemiring.{max u4 u1} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)) (CommSemiring.toSemiring.{u3} T _inst_3) (MvPolynomial.algebra.{u4, u4, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) _inst_4)) (MvPolynomial.aeval.{u4, u3, u1} S T σ _inst_2 _inst_3 _inst_4 f)) g) f) φ)
+  forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u4}} {T : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u3} T] [_inst_4 : Algebra.{u4, u3} S T _inst_2 (CommSemiring.toSemiring.{u3} T _inst_3)] (f : σ -> T) (g : RingHom.{u2, max u4 u1} R (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u4} σ S _inst_2) => T) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u2), max (succ u1) (succ u4)} (RingHom.{max u2 u1, max u4 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) 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(MvPolynomial.commSemiring.{u4, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u2) u4, max u1 u2, max u1 u4} (RingHom.{max u2 u1, max u4 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ S _inst_2) (MvPolynomial.commSemiring.{u4, u1} S σ _inst_2)))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ 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σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) _inst_4)) (MvPolynomial.aeval.{u4, u3, u1} S T σ _inst_2 _inst_3 _inst_4 f)) g) f) φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_bind₂ MvPolynomial.aeval_bind₂ₓ'. -/
 theorem aeval_bind₂ [Algebra S T] (f : σ → T) (g : R →+* MvPolynomial σ S) (φ : MvPolynomial σ R) :
     aeval f (bind₂ g φ) = eval₂Hom ((↑(aeval f : _ →ₐ[S] _) : _ →+* _).comp g) f φ :=
@@ -589,7 +589,7 @@ theorem eval₂Hom_C_left (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero) (r : R), Eq.{max (succ u2) (succ u3)} (MvPolynomial.{u2, u3} τ R _inst_1) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ 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 but is expected to have type
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+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (d : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (r : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) R (MvPolynomial.{u3, u2} τ R _inst_1) 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(MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (MvPolynomial.C.{u2, u3} R τ _inst_1) r) (Finset.prod.{max u3 u2, u1} (MvPolynomial.{u3, u2} τ R _inst_1) σ (CommSemiring.toCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => HPow.hPow.{max u3 u2, 0, max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) ((fun 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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_monomial MvPolynomial.bind₁_monomialₓ'. -/
 theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r : R) :
     bind₁ f (monomial d r) = C r * ∏ i in d.support, f i ^ d i := by
@@ -601,7 +601,7 @@ theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero) (r : R), Eq.{max (succ u1) (succ u3)} (MvPolynomial.{u1, u3} σ S _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_monomial MvPolynomial.bind₂_monomialₓ'. -/
 theorem bind₂_monomial (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) (r : R) :
     bind₂ f (monomial d r) = f r * monomial d 1 := by
@@ -613,7 +613,7 @@ theorem bind₂_monomial (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) (r
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero), Eq.{max (succ u1) (succ u3)} (MvPolynomial.{u1, u3} σ S _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.bind₂.{u1, u2, u3} σ R S _inst_1 _inst_2 f) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPolynomial.monomial.{u2, u1} R σ _inst_1 d) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))))) (coeFn.{max (succ u3) (succ (max u1 u3)), max (succ u3) (succ (max u1 u3))} (LinearMap.{u3, u3, u3, max u1 u3} S S (CommSemiring.toSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u3} S _inst_2) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) S (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (MvPolynomial.module.{u3, u3, u1} S S σ (CommSemiring.toSemiring.{u3} S _inst_2) _inst_2 (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (fun (_x : LinearMap.{u3, u3, u3, max u1 u3} S S (CommSemiring.toSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u3} S _inst_2) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) S (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (MvPolynomial.module.{u3, u3, u1} S S σ (CommSemiring.toSemiring.{u3} S _inst_2) _inst_2 (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) => S -> (MvPolynomial.{u1, u3} σ S _inst_2)) (LinearMap.hasCoeToFun.{u3, u3, u3, max u1 u3} S S S (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u3} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))) (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (MvPolynomial.module.{u3, u3, u1} S S σ (CommSemiring.toSemiring.{u3} S _inst_2) _inst_2 (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (MvPolynomial.monomial.{u3, u1} S σ _inst_2 d) (OfNat.ofNat.{u3} S 1 (OfNat.mk.{u3} S 1 (One.one.{u3} S (AddMonoidWithOne.toOne.{u3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))))))
 but is expected to have type
-  forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, max u2 u1} R (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (d : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (LinearMap.{u3, u3, u3, max u3 u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u3} σ R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u3, u3, u3, max u1 u3} R R R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MvPolynomial.monomial.{u3, u1} R σ _inst_1 d) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), max (succ u1) (succ u2)} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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(CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MvPolynomial.monomial.{u3, u1} R σ _inst_1 d) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), max (succ u1) (succ u2)} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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(CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 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u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u3, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.bind₂.{u1, u3, u2} σ R S _inst_1 _inst_2 f) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (LinearMap.{u3, u3, u3, max u3 u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u3} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u3, max u1 u3} R R R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MvPolynomial.monomial.{u3, u1} R σ _inst_1 d) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} S S (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (MvPolynomial.{u1, u2} σ S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (MvPolynomial.module.{u2, u2, u1} S S σ (CommSemiring.toSemiring.{u2} S _inst_2) _inst_2 (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => MvPolynomial.{u1, u2} σ S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u1 u2} S S S (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (MvPolynomial.module.{u2, u2, u1} S S σ (CommSemiring.toSemiring.{u2} S _inst_2) _inst_2 (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MvPolynomial.monomial.{u2, u1} S σ _inst_2 d) (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_monomial_one MvPolynomial.bind₂_monomial_oneₓ'. -/
 @[simp]
 theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) :

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

@@ -589,7 +589,7 @@ theorem eval₂Hom_C_left (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind
 lean 3 declaration is
   forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero) (r : R), Eq.{max (succ u2) (succ u3)} (MvPolynomial.{u2, u3} τ R _inst_1) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) (coeFn.{max (succ u3) (succ (max u1 u3)), max (succ u3) (succ (max u1 u3))} (LinearMap.{u3, u3, u3, max u1 u3} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (fun (_x : LinearMap.{u3, u3, u3, max u1 u3} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) => R -> (MvPolynomial.{u1, u3} σ R _inst_1)) (LinearMap.hasCoeToFun.{u3, u3, u3, max u1 u3} R R R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MvPolynomial.monomial.{u3, u1} R σ _inst_1 d) r)) (HMul.hMul.{max u2 u3, max u2 u3, max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (instHMul.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (Distrib.toHasMul.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) 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 but is expected to have type
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(MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (MvPolynomial.C.{u2, u3} R τ _inst_1) r) (Finset.prod.{max u3 u2, u1} (MvPolynomial.{u3, u2} τ R _inst_1) σ (CommSemiring.toCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => HPow.hPow.{max u3 u2, 0, max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) i) (MvPolynomial.{u3, u2} τ R _inst_1) (instHPow.{max u3 u2, 0} (MvPolynomial.{u3, u2} τ R _inst_1) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) i) (Monoid.Pow.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toMonoidWithZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (f i) (FunLike.coe.{succ u1, succ u1, 1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (_x : σ) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) _x) (Finsupp.funLike.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i))))
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (d : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (r : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} 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(CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPolynomial.monomial.{u2, u1} R σ _inst_1 d) r)) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (MvPolynomial.C.{u2, u3} R τ _inst_1) r) (Finset.prod.{max u3 u2, u1} (MvPolynomial.{u3, u2} τ R _inst_1) σ (CommSemiring.toCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => HPow.hPow.{max u3 u2, 0, max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) i) (MvPolynomial.{u3, u2} τ R _inst_1) (instHPow.{max u3 u2, 0} (MvPolynomial.{u3, u2} τ R _inst_1) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) i) (Monoid.Pow.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toMonoidWithZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (f i) (FunLike.coe.{succ u1, succ u1, 1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (_x : σ) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) _x) (Finsupp.funLike.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_monomial MvPolynomial.bind₁_monomialₓ'. -/
 theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r : R) :
     bind₁ f (monomial d r) = C r * ∏ i in d.support, f i ^ d i := by
@@ -601,7 +601,7 @@ theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero) (r : R), Eq.{max (succ u1) (succ u3)} (MvPolynomial.{u1, u3} σ S _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.bind₂.{u1, u2, u3} σ R S _inst_1 _inst_2 f) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPolynomial.monomial.{u2, u1} R σ _inst_1 d) r)) (HMul.hMul.{max u1 u3, max u1 u3, max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u3} σ S _inst_2) (instHMul.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (Distrib.toHasMul.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))))) (coeFn.{max (succ u2) (succ (max u1 u3)), max (succ u2) (succ (max u1 u3))} (RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R 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(MvPolynomial.monomial.{u3, u1} S σ _inst_2 d) (OfNat.ofNat.{u3} S 1 (OfNat.mk.{u3} S 1 (One.one.{u3} S (AddMonoidWithOne.toOne.{u3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))))))))))
 but is expected to have type
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(CommSemiring.toSemiring.{u2} S _inst_2))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (LinearMap.{u3, u3, u3, max u3 u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, 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=> (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => MvPolynomial.{u1, u2} σ S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u1 u2} S S S (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (MvPolynomial.module.{u2, u2, u1} S S σ (CommSemiring.toSemiring.{u2} S _inst_2) _inst_2 (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MvPolynomial.monomial.{u2, u1} S σ _inst_2 d) (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_monomial MvPolynomial.bind₂_monomialₓ'. -/
 theorem bind₂_monomial (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) (r : R) :
     bind₂ f (monomial d r) = f r * monomial d 1 := by
@@ -613,7 +613,7 @@ theorem bind₂_monomial (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) (r
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u2, max u1 u3} R (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero), Eq.{max (succ u1) (succ u3)} (MvPolynomial.{u1, u3} σ S _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 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 but is expected to have type
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(CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MvPolynomial.module.{u3, u3, u1} R R σ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_1 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MvPolynomial.monomial.{u3, u1} R σ _inst_1 d) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} S S (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (MvPolynomial.{u1, u2} σ S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (MvPolynomial.module.{u2, u2, u1} S S σ (CommSemiring.toSemiring.{u2} S _inst_2) _inst_2 (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => MvPolynomial.{u1, u2} σ S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u1 u2} S S S (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (MvPolynomial.module.{u2, u2, u1} S S σ (CommSemiring.toSemiring.{u2} S _inst_2) _inst_2 (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (MvPolynomial.monomial.{u2, u1} S σ _inst_2 d) (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_monomial_one MvPolynomial.bind₂_monomial_oneₓ'. -/
 @[simp]
 theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Robert Y. Lewis
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.monad
-! leanprover-community/mathlib commit d64d67d000b974f0d86a2be7918cf800be6271c8
+! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -622,15 +622,13 @@ theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ)
 
 section
 
-open Classical
-
 /- warning: mv_polynomial.vars_bind₁ -> MvPolynomial.vars_bind₁ is a dubious translation:
 lean 3 declaration is
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+  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] [_inst_4 : DecidableEq.{succ u2} τ] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} τ) (Finset.hasSubset.{u2} τ) (MvPolynomial.vars.{u3, u2} R τ _inst_1 (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ)) (Finset.biUnion.{u1, u2} σ τ (fun (a : τ) (b : τ) => _inst_4 a b) (MvPolynomial.vars.{u3, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u3, u2} R τ _inst_1 (f i)))
 but is expected to have type
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(MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ)) (Finset.biUnion.{u1, u3} σ τ (fun (a : τ) (b : τ) => Classical.propDecidable (Eq.{succ u3} τ a b)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u2, u3} R τ _inst_1 (f i)))
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (_inst_4 : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (f : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u3} (Finset.{u3} τ) (Finset.instHasSubsetFinset.{u3} τ) (MvPolynomial.vars.{u2, u3} R τ _inst_1 (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (a : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) a) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} 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(CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 _inst_4) f)) (Finset.biUnion.{u1, u3} σ τ (fun (a : τ) (b : τ) => Classical.propDecidable (Eq.{succ u3} τ a b)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 f) (fun (i : σ) => MvPolynomial.vars.{u2, u3} R τ _inst_1 (_inst_4 i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_bind₁ MvPolynomial.vars_bind₁ₓ'. -/
-theorem vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
+theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     (bind₁ f φ).vars ⊆ φ.vars.biUnion fun i => (f i).vars :=
   by
   calc
@@ -677,7 +675,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁ₓ'. -/
 theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
     (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by
-  simpa only [exists_prop, Finset.mem_biUnion, mem_support_iff, Ne.def] using vars_bind₁ f φ h
+  classical simpa only [exists_prop, Finset.mem_biUnion, mem_support_iff, Ne.def] using
+      vars_bind₁ f φ h
 #align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁
 
 #print MvPolynomial.monad /-

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -626,12 +626,12 @@ open Classical
 
 /- warning: mv_polynomial.vars_bind₁ -> MvPolynomial.vars_bind₁ is a dubious translation:
 lean 3 declaration is
-  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} τ) (Finset.hasSubset.{u2} τ) (MvPolynomial.vars.{u3, u2} R τ _inst_1 (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ)) (Finset.bunionᵢ.{u1, u2} σ τ (fun (a : τ) (b : τ) => Classical.propDecidable (Eq.{succ u2} τ a b)) (MvPolynomial.vars.{u3, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u3, u2} R τ _inst_1 (f i)))
+  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} τ) (Finset.hasSubset.{u2} τ) (MvPolynomial.vars.{u3, u2} R τ _inst_1 (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ)) (Finset.biUnion.{u1, u2} σ τ (fun (a : τ) (b : τ) => Classical.propDecidable (Eq.{succ u2} τ a b)) (MvPolynomial.vars.{u3, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u3, u2} R τ _inst_1 (f i)))
 but is expected to have type
-  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (φ : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u3} (Finset.{u3} τ) (Finset.instHasSubsetFinset.{u3} τ) (MvPolynomial.vars.{u2, u3} R τ _inst_1 (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 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(Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R 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(MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ)) (Finset.bunionᵢ.{u1, u3} σ τ (fun (a : τ) (b : τ) => Classical.propDecidable (Eq.{succ u3} τ a b)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u2, u3} R τ _inst_1 (f i)))
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (φ : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u3} (Finset.{u3} τ) (Finset.instHasSubsetFinset.{u3} τ) (MvPolynomial.vars.{u2, u3} R τ _inst_1 (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ)) (Finset.biUnion.{u1, u3} σ τ (fun (a : τ) (b : τ) => Classical.propDecidable (Eq.{succ u3} τ a b)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u2, u3} R τ _inst_1 (f i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_bind₁ MvPolynomial.vars_bind₁ₓ'. -/
 theorem vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
-    (bind₁ f φ).vars ⊆ φ.vars.bunionᵢ fun i => (f i).vars :=
+    (bind₁ f φ).vars ⊆ φ.vars.biUnion fun i => (f i).vars :=
   by
   calc
     (bind₁ f φ).vars = (φ.support.sum fun x : σ →₀ ℕ => (bind₁ f) (monomial x (coeff x φ))).vars :=
@@ -647,7 +647,7 @@ theorem vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
       _
     
   -- proof below
-  · apply Finset.bunionᵢ_mono
+  · apply Finset.biUnion_mono
     intro d hd
     calc
       (C (coeff d φ) * ∏ i : σ in d.support, f i ^ d i).vars ≤
@@ -658,11 +658,11 @@ theorem vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
       _ ≤ d.support.bUnion fun i : σ => (f i ^ d i).vars := (vars_prod _)
       _ ≤ d.support.bUnion fun i : σ => (f i).vars := _
       
-    apply Finset.bunionᵢ_mono
+    apply Finset.biUnion_mono
     intro i hi
     apply vars_pow
   · intro j
-    simp_rw [Finset.mem_bunionᵢ]
+    simp_rw [Finset.mem_biUnion]
     rintro ⟨d, hd, ⟨i, hi, hj⟩⟩
     exact ⟨i, (mem_vars _).mpr ⟨d, hd, hi⟩, hj⟩
 #align mv_polynomial.vars_bind₁ MvPolynomial.vars_bind₁
@@ -677,7 +677,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁ₓ'. -/
 theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
     (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by
-  simpa only [exists_prop, Finset.mem_bunionᵢ, mem_support_iff, Ne.def] using vars_bind₁ f φ h
+  simpa only [exists_prop, Finset.mem_biUnion, mem_support_iff, Ne.def] using vars_bind₁ f φ h
 #align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁
 
 #print MvPolynomial.monad /-

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Robert Y. Lewis
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.monad
-! leanprover-community/mathlib commit 5120cf49cb659e2499edd7e4d336a04efd598f2f
+! leanprover-community/mathlib commit d64d67d000b974f0d86a2be7918cf800be6271c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Data.MvPolynomial.Variables
 
 # Monad operations on `mv_polynomial`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines two monadic operations on `mv_polynomial`. Given `p : mv_polynomial σ R`,
 
 * `mv_polynomial.bind₁` and `mv_polynomial.join₁` operate on the variable type `σ`.

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

@@ -62,6 +62,7 @@ variable {σ : Type _} {τ : Type _}
 
 variable {R S T : Type _} [CommSemiring R] [CommSemiring S] [CommSemiring T]
 
+#print MvPolynomial.bind₁ /-
 /--
 `bind₁` is the "left hand side" bind operation on `mv_polynomial`, operating on the variable type.
 Given a polynomial `p : mv_polynomial σ R` and a map `f : σ → mv_polynomial τ R` taking variables
@@ -72,7 +73,9 @@ This operation is an algebra hom.
 def bind₁ (f : σ → MvPolynomial τ R) : MvPolynomial σ R →ₐ[R] MvPolynomial τ R :=
   aeval f
 #align mv_polynomial.bind₁ MvPolynomial.bind₁
+-/
 
+#print MvPolynomial.bind₂ /-
 /-- `bind₂` is the "right hand side" bind operation on `mv_polynomial`,
 operating on the coefficient type.
 Given a polynomial `p : mv_polynomial σ R` and
@@ -84,7 +87,9 @@ The variable type remains the same. This operation is a ring hom.
 def bind₂ (f : R →+* MvPolynomial σ S) : MvPolynomial σ R →+* MvPolynomial σ S :=
   eval₂Hom f X
 #align mv_polynomial.bind₂ MvPolynomial.bind₂
+-/
 
+#print MvPolynomial.join₁ /-
 /--
 `join₁` is the monadic join operation corresponding to `mv_polynomial.bind₁`. Given a polynomial `p`
 with coefficients in `R` whose variables are polynomials in `σ` with coefficients in `R`,
@@ -94,7 +99,9 @@ This operation is an algebra hom.
 def join₁ : MvPolynomial (MvPolynomial σ R) R →ₐ[R] MvPolynomial σ R :=
   aeval id
 #align mv_polynomial.join₁ MvPolynomial.join₁
+-/
 
+#print MvPolynomial.join₂ /-
 /--
 `join₂` is the monadic join operation corresponding to `mv_polynomial.bind₂`. Given a polynomial `p`
 with variables in `σ` whose coefficients are polynomials in `σ` with coefficients in `R`,
@@ -104,17 +111,36 @@ This operation is a ring hom.
 def join₂ : MvPolynomial σ (MvPolynomial σ R) →+* MvPolynomial σ R :=
   eval₂Hom (RingHom.id _) X
 #align mv_polynomial.join₂ MvPolynomial.join₂
+-/
 
+/- warning: mv_polynomial.aeval_eq_bind₁ -> MvPolynomial.aeval_eq_bind₁ is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)), Eq.{max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.aeval.{u3, max u2 u3, u1} R (MvPolynomial.{u2, u3} τ R _inst_1) σ _inst_1 (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) f) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f)
+but is expected to have type
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (AlgHom.{u2, max u2 u1, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.aeval.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} τ R _inst_1) σ _inst_1 (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) f) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_eq_bind₁ MvPolynomial.aeval_eq_bind₁ₓ'. -/
 @[simp]
 theorem aeval_eq_bind₁ (f : σ → MvPolynomial τ R) : aeval f = bind₁ f :=
   rfl
 #align mv_polynomial.aeval_eq_bind₁ MvPolynomial.aeval_eq_bind₁
 
+/- warning: mv_polynomial.eval₂_hom_C_eq_bind₁ -> MvPolynomial.eval₂Hom_C_eq_bind₁ is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_C_eq_bind₁ MvPolynomial.eval₂Hom_C_eq_bind₁ₓ'. -/
 @[simp]
-theorem eval₂Hom_c_eq_bind₁ (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind₁ f :=
+theorem eval₂Hom_C_eq_bind₁ (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind₁ f :=
   rfl
-#align mv_polynomial.eval₂_hom_C_eq_bind₁ MvPolynomial.eval₂Hom_c_eq_bind₁
-
+#align mv_polynomial.eval₂_hom_C_eq_bind₁ MvPolynomial.eval₂Hom_C_eq_bind₁
+
+/- warning: mv_polynomial.eval₂_hom_eq_bind₂ -> MvPolynomial.eval₂Hom_eq_bind₂ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_eq_bind₂ MvPolynomial.eval₂Hom_eq_bind₂ₓ'. -/
 @[simp]
 theorem eval₂Hom_eq_bind₂ (f : R →+* MvPolynomial σ S) : eval₂Hom f X = bind₂ f :=
   rfl
@@ -124,20 +150,38 @@ section
 
 variable (σ R)
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_id_eq_join₁ MvPolynomial.aeval_id_eq_join₁ₓ'. -/
 @[simp]
 theorem aeval_id_eq_join₁ : aeval id = @join₁ σ R _ :=
   rfl
 #align mv_polynomial.aeval_id_eq_join₁ MvPolynomial.aeval_id_eq_join₁
 
-theorem eval₂Hom_c_id_eq_join₁ (φ : MvPolynomial (MvPolynomial σ R) R) :
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u2} σ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.join₁.{u1, u2} σ R _inst_1) φ)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_C_id_eq_join₁ MvPolynomial.eval₂Hom_C_id_eq_join₁ₓ'. -/
+theorem eval₂Hom_C_id_eq_join₁ (φ : MvPolynomial (MvPolynomial σ R) R) :
     eval₂Hom C id φ = join₁ φ :=
   rfl
-#align mv_polynomial.eval₂_hom_C_id_eq_join₁ MvPolynomial.eval₂Hom_c_id_eq_join₁
-
+#align mv_polynomial.eval₂_hom_C_id_eq_join₁ MvPolynomial.eval₂Hom_C_id_eq_join₁
+
+/- warning: mv_polynomial.eval₂_hom_id_X_eq_join₂ -> MvPolynomial.eval₂Hom_id_X_eq_join₂ is a dubious translation:
+lean 3 declaration is
+  forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommSemiring.{u2} R], Eq.{succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, max u1 u2} σ (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.commSemiring.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ R _inst_1) σ (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.eval₂Hom.{max u1 u2, max u1 u2, u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) σ (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1) (RingHom.id.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.X.{u2, u1} R σ _inst_1)) (MvPolynomial.join₂.{u1, u2} σ R _inst_1)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_id_X_eq_join₂ MvPolynomial.eval₂Hom_id_X_eq_join₂ₓ'. -/
 @[simp]
-theorem eval₂Hom_id_x_eq_join₂ : eval₂Hom (RingHom.id _) X = @join₂ σ R _ :=
+theorem eval₂Hom_id_X_eq_join₂ : eval₂Hom (RingHom.id _) X = @join₂ σ R _ :=
   rfl
-#align mv_polynomial.eval₂_hom_id_X_eq_join₂ MvPolynomial.eval₂Hom_id_x_eq_join₂
+#align mv_polynomial.eval₂_hom_id_X_eq_join₂ MvPolynomial.eval₂Hom_id_X_eq_join₂
 
 end
 
@@ -147,79 +191,169 @@ end
 attribute [-simp]
   aeval_eq_bind₁ eval₂_hom_C_eq_bind₁ eval₂_hom_eq_bind₂ aeval_id_eq_join₁ eval₂_hom_id_X_eq_join₂
 
+/- warning: mv_polynomial.bind₁_X_right -> MvPolynomial.bind₁_X_right 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 mv_polynomial.bind₁_X_right MvPolynomial.bind₁_X_rightₓ'. -/
 @[simp]
-theorem bind₁_x_right (f : σ → MvPolynomial τ R) (i : σ) : bind₁ f (X i) = f i :=
+theorem bind₁_X_right (f : σ → MvPolynomial τ R) (i : σ) : bind₁ f (X i) = f i :=
   aeval_X f i
-#align mv_polynomial.bind₁_X_right MvPolynomial.bind₁_x_right
-
+#align mv_polynomial.bind₁_X_right MvPolynomial.bind₁_X_right
+
+/- warning: mv_polynomial.bind₂_X_right -> MvPolynomial.bind₂_X_right is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_X_right MvPolynomial.bind₂_X_rightₓ'. -/
 @[simp]
-theorem bind₂_x_right (f : R →+* MvPolynomial σ S) (i : σ) : bind₂ f (X i) = X i :=
+theorem bind₂_X_right (f : R →+* MvPolynomial σ S) (i : σ) : bind₂ f (X i) = X i :=
   eval₂Hom_X' f X i
-#align mv_polynomial.bind₂_X_right MvPolynomial.bind₂_x_right
-
+#align mv_polynomial.bind₂_X_right MvPolynomial.bind₂_X_right
+
+/- warning: mv_polynomial.bind₁_X_left -> MvPolynomial.bind₁_X_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_X_left MvPolynomial.bind₁_X_leftₓ'. -/
 @[simp]
-theorem bind₁_x_left : bind₁ (X : σ → MvPolynomial σ R) = AlgHom.id R _ :=
+theorem bind₁_X_left : bind₁ (X : σ → MvPolynomial σ R) = AlgHom.id R _ :=
   by
   ext1 i
   simp
-#align mv_polynomial.bind₁_X_left MvPolynomial.bind₁_x_left
+#align mv_polynomial.bind₁_X_left MvPolynomial.bind₁_X_left
 
 variable (f : σ → MvPolynomial τ R)
 
+/- warning: mv_polynomial.bind₁_C_right -> MvPolynomial.bind₁_C_right is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_C_right MvPolynomial.bind₁_C_rightₓ'. -/
 @[simp]
-theorem bind₁_c_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (C x) = C x := by
+theorem bind₁_C_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (C x) = C x := by
   simp [bind₁, algebra_map_eq]
-#align mv_polynomial.bind₁_C_right MvPolynomial.bind₁_c_right
-
+#align mv_polynomial.bind₁_C_right MvPolynomial.bind₁_C_right
+
+/- warning: mv_polynomial.bind₂_C_right -> MvPolynomial.bind₂_C_right is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_C_right MvPolynomial.bind₂_C_rightₓ'. -/
 @[simp]
-theorem bind₂_c_right (f : R →+* MvPolynomial σ S) (r : R) : bind₂ f (C r) = f r :=
+theorem bind₂_C_right (f : R →+* MvPolynomial σ S) (r : R) : bind₂ f (C r) = f r :=
   eval₂Hom_C f X r
-#align mv_polynomial.bind₂_C_right MvPolynomial.bind₂_c_right
-
+#align mv_polynomial.bind₂_C_right MvPolynomial.bind₂_C_right
+
+/- warning: mv_polynomial.bind₂_C_left -> MvPolynomial.bind₂_C_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_C_left MvPolynomial.bind₂_C_leftₓ'. -/
 @[simp]
-theorem bind₂_c_left : bind₂ (C : R →+* MvPolynomial σ R) = RingHom.id _ := by ext : 2 <;> simp
-#align mv_polynomial.bind₂_C_left MvPolynomial.bind₂_c_left
-
+theorem bind₂_C_left : bind₂ (C : R →+* MvPolynomial σ R) = RingHom.id _ := by ext : 2 <;> simp
+#align mv_polynomial.bind₂_C_left MvPolynomial.bind₂_C_left
+
+/- warning: mv_polynomial.bind₂_comp_C -> MvPolynomial.bind₂_comp_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_comp_C MvPolynomial.bind₂_comp_Cₓ'. -/
 @[simp]
-theorem bind₂_comp_c (f : R →+* MvPolynomial σ S) : (bind₂ f).comp C = f :=
-  RingHom.ext <| bind₂_c_right _
-#align mv_polynomial.bind₂_comp_C MvPolynomial.bind₂_comp_c
-
+theorem bind₂_comp_C (f : R →+* MvPolynomial σ S) : (bind₂ f).comp C = f :=
+  RingHom.ext <| bind₂_C_right _
+#align mv_polynomial.bind₂_comp_C MvPolynomial.bind₂_comp_C
+
+/- warning: mv_polynomial.join₂_map -> MvPolynomial.join₂_map is a dubious translation:
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_inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, max u1 u3, max u1 u2} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u3, max u1 u2} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.bind₂.{u1, u3, u2} σ R S _inst_1 _inst_2 f) φ)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.join₂_map MvPolynomial.join₂_mapₓ'. -/
 @[simp]
 theorem join₂_map (f : R →+* MvPolynomial σ S) (φ : MvPolynomial σ R) :
     join₂ (map f φ) = bind₂ f φ := by simp only [join₂, bind₂, eval₂_hom_map_hom, RingHom.id_comp]
 #align mv_polynomial.join₂_map MvPolynomial.join₂_map
 
+/- warning: mv_polynomial.join₂_comp_map -> MvPolynomial.join₂_comp_map is a dubious translation:
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 @[simp]
 theorem join₂_comp_map (f : R →+* MvPolynomial σ S) : join₂.comp (map f) = bind₂ f :=
   RingHom.ext <| join₂_map _
 #align mv_polynomial.join₂_comp_map MvPolynomial.join₂_comp_map
 
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_inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{max u3 u2, u2} (MvPolynomial.{u3, u2} τ R _inst_1) R _inst_1) (MvPolynomial.commSemiring.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1))))))) 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_id_rename MvPolynomial.aeval_id_renameₓ'. -/
 theorem aeval_id_rename (f : σ → MvPolynomial τ R) (p : MvPolynomial σ R) :
     aeval id (rename f p) = aeval f p := by rw [aeval_rename, Function.comp.left_id]
 #align mv_polynomial.aeval_id_rename MvPolynomial.aeval_id_rename
 
+/- warning: mv_polynomial.join₁_rename -> MvPolynomial.join₁_rename is a dubious translation:
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+but is expected to have type
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 @[simp]
 theorem join₁_rename (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     join₁ (rename f φ) = bind₁ f φ :=
   aeval_id_rename _ _
 #align mv_polynomial.join₁_rename MvPolynomial.join₁_rename
 
+/- warning: mv_polynomial.bind₁_id -> MvPolynomial.bind₁_id is a dubious translation:
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 @[simp]
 theorem bind₁_id : bind₁ (@id (MvPolynomial σ R)) = join₁ :=
   rfl
 #align mv_polynomial.bind₁_id MvPolynomial.bind₁_id
 
+/- warning: mv_polynomial.bind₂_id -> MvPolynomial.bind₂_id is a dubious translation:
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 @[simp]
 theorem bind₂_id : bind₂ (RingHom.id (MvPolynomial σ R)) = join₂ :=
   rfl
 #align mv_polynomial.bind₂_id MvPolynomial.bind₂_id
 
+/- warning: mv_polynomial.bind₁_bind₁ -> MvPolynomial.bind₁_bind₁ is a dubious translation:
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(MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u2, u4, u3} τ υ R _inst_1 g) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ)) (coeFn.{max (succ (max u1 u3)) (succ (max u4 u3)), max (succ (max u1 u3)) (succ (max u4 u3))} (AlgHom.{u3, max u1 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u1 u3, max u4 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u4, u3} σ υ R _inst_1 (fun (i : σ) => coeFn.{max (succ (max u2 u3)) (succ (max u4 u3)), max (succ (max u2 u3)) (succ (max u4 u3))} 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(MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u4, u3} υ R _inst_1)) ([anonymous].{u3, max u2 u3, max u4 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u2, u4, u3} τ υ R _inst_1 g) (f i))) φ)
+but is expected to have type
+  forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {υ : Type.{u4}} (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (g : τ -> (MvPolynomial.{u4, u2} υ R _inst_1)) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u2) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u3, u2} τ R _inst_1) => MvPolynomial.{u4, u2} υ R _inst_1) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ 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R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u4, u2} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1))))) (Algebra.toModule.{u2, max u2 u4} R (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u2 u4, max (max u3 u2) u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u3, u4, u2} τ υ R _inst_1 g) (f i))) φ)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_bind₁ MvPolynomial.bind₁_bind₁ₓ'. -/
 theorem bind₁_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R)
     (φ : MvPolynomial σ R) : (bind₁ g) (bind₁ f φ) = bind₁ (fun i => bind₁ g (f i)) φ := by
   simp [bind₁, ← comp_aeval]
 #align mv_polynomial.bind₁_bind₁ MvPolynomial.bind₁_bind₁
 
+/- warning: mv_polynomial.bind₁_comp_bind₁ -> MvPolynomial.bind₁_comp_bind₁ is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_1 (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u2 u4, max (max u3 u2) u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u2 u4} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u4, u2} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u4 u2} (MvPolynomial.{u4, u2} υ R _inst_1) (MvPolynomial.commSemiring.{u2, u4} R υ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u3, u4, u2} τ υ R _inst_1 g) (f i)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_comp_bind₁ MvPolynomial.bind₁_comp_bind₁ₓ'. -/
 theorem bind₁_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R) :
     (bind₁ g).comp (bind₁ f) = bind₁ fun i => bind₁ g (f i) :=
   by
@@ -227,15 +361,33 @@ theorem bind₁_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : 
   apply bind₁_bind₁
 #align mv_polynomial.bind₁_comp_bind₁ MvPolynomial.bind₁_comp_bind₁
 
+/- warning: mv_polynomial.bind₂_comp_bind₂ -> MvPolynomial.bind₂_comp_bind₂ 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 mv_polynomial.bind₂_comp_bind₂ MvPolynomial.bind₂_comp_bind₂ₓ'. -/
 theorem bind₂_comp_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPolynomial σ T) :
     (bind₂ g).comp (bind₂ f) = bind₂ ((bind₂ g).comp f) := by ext : 2 <;> simp
 #align mv_polynomial.bind₂_comp_bind₂ MvPolynomial.bind₂_comp_bind₂
 
+/- warning: mv_polynomial.bind₂_bind₂ -> MvPolynomial.bind₂_bind₂ is a dubious translation:
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u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (fun (_x : RingHom.{max u1 u2, max u1 u4} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u4} σ T _inst_3)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u4} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R 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+but is expected to have type
+  forall {σ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} {T : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u1} T] (f : RingHom.{u4, max u3 u2} R (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (g : RingHom.{u3, max u1 u2} S (MvPolynomial.{u2, u1} σ T _inst_3) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ T _inst_3) (MvPolynomial.commSemiring.{u1, u2} T σ _inst_3)))) (φ : MvPolynomial.{u2, u4} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_bind₂ MvPolynomial.bind₂_bind₂ₓ'. -/
 theorem bind₂_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPolynomial σ T)
     (φ : MvPolynomial σ R) : (bind₂ g) (bind₂ f φ) = bind₂ ((bind₂ g).comp f) φ :=
   RingHom.congr_fun (bind₂_comp_bind₂ f g) φ
 #align mv_polynomial.bind₂_bind₂ MvPolynomial.bind₂_bind₂
 
+/- warning: mv_polynomial.rename_comp_bind₁ -> MvPolynomial.rename_comp_bind₁ 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 mv_polynomial.rename_comp_bind₁ MvPolynomial.rename_comp_bind₁ₓ'. -/
 theorem rename_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) :
     (rename g).comp (bind₁ f) = bind₁ fun i => rename g <| f i :=
   by
@@ -243,11 +395,23 @@ theorem rename_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ
   simp
 #align mv_polynomial.rename_comp_bind₁ MvPolynomial.rename_comp_bind₁
 
+/- warning: mv_polynomial.rename_bind₁ -> MvPolynomial.rename_bind₁ 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 mv_polynomial.rename_bind₁ MvPolynomial.rename_bind₁ₓ'. -/
 theorem rename_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) (φ : MvPolynomial σ R) :
     rename g (bind₁ f φ) = bind₁ (fun i => rename g <| f i) φ :=
   AlgHom.congr_fun (rename_comp_bind₁ f g) φ
 #align mv_polynomial.rename_bind₁ MvPolynomial.rename_bind₁
 
+/- warning: mv_polynomial.map_bind₂ -> MvPolynomial.map_bind₂ is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {σ : Type.{u2}} {R : Type.{u4}} {S : Type.{u3}} {T : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u1} T] (f : RingHom.{u4, max u3 u2} R (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2)))) (g : RingHom.{u3, u1} S T (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T (CommSemiring.toSemiring.{u1} T _inst_3))) (φ : MvPolynomial.{u2, u4} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u3} σ S _inst_2) => MvPolynomial.{u2, u1} σ T _inst_3) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u2) (succ u4), max (succ u2) (succ u3)} 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_inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u2 u4, max u2 u3} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.{u2, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ R _inst_1) (MvPolynomial.commSemiring.{u4, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u2} S σ _inst_2))))))) 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_bind₂ MvPolynomial.map_bind₂ₓ'. -/
 theorem map_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* T) (φ : MvPolynomial σ R) :
     map g (bind₂ f φ) = bind₂ ((map g).comp f) φ :=
   by
@@ -256,6 +420,12 @@ theorem map_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* T) (φ : MvPoly
   simp only [Function.comp_apply, map_X]
 #align mv_polynomial.map_bind₂ MvPolynomial.map_bind₂
 
+/- warning: mv_polynomial.bind₁_comp_rename -> MvPolynomial.bind₁_comp_rename is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_comp_rename MvPolynomial.bind₁_comp_renameₓ'. -/
 theorem bind₁_comp_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ → τ) :
     (bind₁ f).comp (rename g) = bind₁ (f ∘ g) :=
   by
@@ -263,28 +433,58 @@ theorem bind₁_comp_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ
   simp
 #align mv_polynomial.bind₁_comp_rename MvPolynomial.bind₁_comp_rename
 
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+but is expected to have type
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(CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)))))) 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υ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1))))) (Algebra.toModule.{u3, max u3 u4} R (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u2 u3) u4, u3, max u2 u3, max u3 u4} (AlgHom.{u3, max u3 u2, max u3 u4} R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u4, u3} υ R _inst_1) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))) (Algebra.toModule.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u3 u4} R (MvPolynomial.{u4, u3} υ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u4} 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R (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.{u4, u3} υ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u4 u3} (MvPolynomial.{u4, u3} υ R _inst_1) (MvPolynomial.commSemiring.{u3, u4} R υ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u4} R R υ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (MvPolynomial.bind₁.{u2, u4, u3} σ υ R _inst_1 (Function.comp.{succ u2, succ u1, max (succ u3) (succ u4)} σ τ (MvPolynomial.{u4, u3} υ R _inst_1) f g)) φ)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_rename MvPolynomial.bind₁_renameₓ'. -/
 theorem bind₁_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ → τ) (φ : MvPolynomial σ R) :
     bind₁ f (rename g φ) = bind₁ (f ∘ g) φ :=
   AlgHom.congr_fun (bind₁_comp_rename f g) φ
 #align mv_polynomial.bind₁_rename MvPolynomial.bind₁_rename
 
+/- warning: mv_polynomial.bind₂_map -> MvPolynomial.bind₂_map is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} {T : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : CommSemiring.{u4} T] (f : RingHom.{u3, max u1 u4} S (MvPolynomial.{u1, u4} σ T _inst_3) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (CommSemiring.toSemiring.{max u1 u4} (MvPolynomial.{u1, u4} σ T _inst_3) (MvPolynomial.commSemiring.{u4, u1} T σ _inst_3)))) (g : RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u1) (succ u4)} (MvPolynomial.{u1, u4} σ T _inst_3) (coeFn.{max (succ (max u1 u3)) (succ (max u1 u4)), max (succ (max u1 u3)) (succ (max u1 u4))} (RingHom.{max u1 u3, max u1 u4} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u4} σ T 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+but is expected to have type
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(MvPolynomial.{u2, u3} σ T _inst_3) (MvPolynomial.commSemiring.{u3, u2} T σ _inst_3))) f g)) φ)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₂_map MvPolynomial.bind₂_mapₓ'. -/
 theorem bind₂_map (f : S →+* MvPolynomial σ T) (g : R →+* S) (φ : MvPolynomial σ R) :
     bind₂ f (map g φ) = bind₂ (f.comp g) φ := by simp [bind₂]
 #align mv_polynomial.bind₂_map MvPolynomial.bind₂_map
 
+/- warning: mv_polynomial.map_comp_C -> MvPolynomial.map_comp_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_comp_C MvPolynomial.map_comp_Cₓ'. -/
 @[simp]
-theorem map_comp_c (f : R →+* S) : (map f).comp (C : R →+* MvPolynomial σ R) = C.comp f :=
+theorem map_comp_C (f : R →+* S) : (map f).comp (C : R →+* MvPolynomial σ R) = C.comp f :=
   by
   ext1
   apply map_C
-#align mv_polynomial.map_comp_C MvPolynomial.map_comp_c
-
+#align mv_polynomial.map_comp_C MvPolynomial.map_comp_C
+
+/- warning: mv_polynomial.hom_bind₁ -> MvPolynomial.hom_bind₁ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.hom_bind₁ MvPolynomial.hom_bind₁ₓ'. -/
 -- mixing the two monad structures
 theorem hom_bind₁ (f : MvPolynomial τ R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     f (bind₁ g φ) = eval₂Hom (f.comp C) (fun i => f (g i)) φ := by
   rw [bind₁, map_aeval, algebra_map_eq]
 #align mv_polynomial.hom_bind₁ MvPolynomial.hom_bind₁
 
+/- warning: mv_polynomial.map_bind₁ -> MvPolynomial.map_bind₁ is a dubious translation:
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u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))))))) (MvPolynomial.map.{u4, u3, u1} R S σ _inst_1 _inst_2 f) φ))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_bind₁ MvPolynomial.map_bind₁ₓ'. -/
 theorem map_bind₁ (f : R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     map f (bind₁ g φ) = bind₁ (fun i : σ => (map f) (g i)) (map f φ) :=
   by
@@ -292,23 +492,47 @@ theorem map_bind₁ (f : R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolyn
   rfl
 #align mv_polynomial.map_bind₁ MvPolynomial.map_bind₁
 
+/- warning: mv_polynomial.eval₂_hom_comp_C -> MvPolynomial.eval₂Hom_comp_C 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 mv_polynomial.eval₂_hom_comp_C MvPolynomial.eval₂Hom_comp_Cₓ'. -/
 @[simp]
-theorem eval₂Hom_comp_c (f : R →+* S) (g : σ → S) : (eval₂Hom f g).comp C = f :=
+theorem eval₂Hom_comp_C (f : R →+* S) (g : σ → S) : (eval₂Hom f g).comp C = f :=
   by
   ext1 r
   exact eval₂_C f g r
-#align mv_polynomial.eval₂_hom_comp_C MvPolynomial.eval₂Hom_comp_c
-
+#align mv_polynomial.eval₂_hom_comp_C MvPolynomial.eval₂Hom_comp_C
+
+/- warning: mv_polynomial.eval₂_hom_bind₁ -> MvPolynomial.eval₂Hom_bind₁ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_bind₁ MvPolynomial.eval₂Hom_bind₁ₓ'. -/
 theorem eval₂Hom_bind₁ (f : R →+* S) (g : τ → S) (h : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     eval₂Hom f g (bind₁ h φ) = eval₂Hom f (fun i => eval₂Hom f g (h i)) φ := by
   rw [hom_bind₁, eval₂_hom_comp_C]
 #align mv_polynomial.eval₂_hom_bind₁ MvPolynomial.eval₂Hom_bind₁
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_bind₁ MvPolynomial.aeval_bind₁ₓ'. -/
 theorem aeval_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     aeval f (bind₁ g φ) = aeval (fun i => aeval f (g i)) φ :=
   eval₂Hom_bind₁ _ _ _ _
 #align mv_polynomial.aeval_bind₁ MvPolynomial.aeval_bind₁
 
+/- warning: mv_polynomial.aeval_comp_bind₁ -> MvPolynomial.aeval_comp_bind₁ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_comp_bind₁ MvPolynomial.aeval_comp_bind₁ₓ'. -/
 theorem aeval_comp_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial τ R) :
     (aeval f).comp (bind₁ g) = aeval fun i => aeval f (g i) :=
   by
@@ -316,36 +540,78 @@ theorem aeval_comp_bind₁ [Algebra R S] (f : τ → S) (g : σ → MvPolynomial
   apply aeval_bind₁
 #align mv_polynomial.aeval_comp_bind₁ MvPolynomial.aeval_comp_bind₁
 
+/- warning: mv_polynomial.eval₂_hom_comp_bind₂ -> MvPolynomial.eval₂Hom_comp_bind₂ 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 mv_polynomial.eval₂_hom_comp_bind₂ MvPolynomial.eval₂Hom_comp_bind₂ₓ'. -/
 theorem eval₂Hom_comp_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPolynomial σ S) :
     (eval₂Hom f g).comp (bind₂ h) = eval₂Hom ((eval₂Hom f g).comp h) g := by ext : 2 <;> simp
 #align mv_polynomial.eval₂_hom_comp_bind₂ MvPolynomial.eval₂Hom_comp_bind₂
 
+/- warning: mv_polynomial.eval₂_hom_bind₂ -> MvPolynomial.eval₂Hom_bind₂ is a dubious translation:
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(MvPolynomial.eval₂Hom.{u4, u3, u1} S T σ _inst_2 _inst_3 f g) h) g) φ)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_bind₂ MvPolynomial.eval₂Hom_bind₂ₓ'. -/
 theorem eval₂Hom_bind₂ (f : S →+* T) (g : σ → T) (h : R →+* MvPolynomial σ S)
     (φ : MvPolynomial σ R) : eval₂Hom f g (bind₂ h φ) = eval₂Hom ((eval₂Hom f g).comp h) g φ :=
   RingHom.congr_fun (eval₂Hom_comp_bind₂ f g h) φ
 #align mv_polynomial.eval₂_hom_bind₂ MvPolynomial.eval₂Hom_bind₂
 
+/- warning: mv_polynomial.aeval_bind₂ -> MvPolynomial.aeval_bind₂ is a dubious translation:
+lean 3 declaration is
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σ _inst_2 _inst_2 (Algebra.id.{u4} S _inst_2)) _inst_4)) (MvPolynomial.aeval.{u4, u3, u1} S T σ _inst_2 _inst_3 _inst_4 f)) g) f) φ)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_bind₂ MvPolynomial.aeval_bind₂ₓ'. -/
 theorem aeval_bind₂ [Algebra S T] (f : σ → T) (g : R →+* MvPolynomial σ S) (φ : MvPolynomial σ R) :
     aeval f (bind₂ g φ) = eval₂Hom ((↑(aeval f : _ →ₐ[S] _) : _ →+* _).comp g) f φ :=
   eval₂Hom_bind₂ _ _ _ _
 #align mv_polynomial.aeval_bind₂ MvPolynomial.aeval_bind₂
 
-theorem eval₂Hom_c_left (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind₁ f :=
+/- warning: mv_polynomial.eval₂_hom_C_left -> MvPolynomial.eval₂Hom_C_left 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 mv_polynomial.eval₂_hom_C_left MvPolynomial.eval₂Hom_C_leftₓ'. -/
+theorem eval₂Hom_C_left (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind₁ f :=
   rfl
-#align mv_polynomial.eval₂_hom_C_left MvPolynomial.eval₂Hom_c_left
-
+#align mv_polynomial.eval₂_hom_C_left MvPolynomial.eval₂Hom_C_left
+
+/- warning: mv_polynomial.bind₁_monomial -> MvPolynomial.bind₁_monomial is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.bind₁_monomial MvPolynomial.bind₁_monomialₓ'. -/
 theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r : R) :
     bind₁ f (monomial d r) = C r * ∏ i in d.support, f i ^ d i := by
   simp only [monomial_eq, AlgHom.map_mul, bind₁_C_right, Finsupp.prod, AlgHom.map_prod,
     AlgHom.map_pow, bind₁_X_right]
 #align mv_polynomial.bind₁_monomial MvPolynomial.bind₁_monomial
 
+/- warning: mv_polynomial.bind₂_monomial -> MvPolynomial.bind₂_monomial 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 mv_polynomial.bind₂_monomial MvPolynomial.bind₂_monomialₓ'. -/
 theorem bind₂_monomial (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) (r : R) :
     bind₂ f (monomial d r) = f r * monomial d 1 := by
   simp only [monomial_eq, RingHom.map_mul, bind₂_C_right, Finsupp.prod, RingHom.map_prod,
     RingHom.map_pow, bind₂_X_right, C_1, one_mul]
 #align mv_polynomial.bind₂_monomial MvPolynomial.bind₂_monomial
 
+/- warning: mv_polynomial.bind₂_monomial_one -> MvPolynomial.bind₂_monomial_one 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 mv_polynomial.bind₂_monomial_one MvPolynomial.bind₂_monomial_oneₓ'. -/
 @[simp]
 theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ) :
     bind₂ f (monomial d 1) = monomial d 1 := by rw [bind₂_monomial, f.map_one, one_mul]
@@ -355,6 +621,12 @@ section
 
 open Classical
 
+/- warning: mv_polynomial.vars_bind₁ -> MvPolynomial.vars_bind₁ is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} τ) (Finset.hasSubset.{u2} τ) (MvPolynomial.vars.{u3, u2} R τ _inst_1 (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ)) (Finset.bunionᵢ.{u1, u2} σ τ (fun (a : τ) (b : τ) => Classical.propDecidable (Eq.{succ u2} τ a b)) (MvPolynomial.vars.{u3, u1} R σ _inst_1 φ) (fun (i : σ) => MvPolynomial.vars.{u3, u2} R τ _inst_1 (f i)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_bind₁ MvPolynomial.vars_bind₁ₓ'. -/
 theorem vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     (bind₁ f φ).vars ⊆ φ.vars.bunionᵢ fun i => (f i).vars :=
   by
@@ -394,29 +666,41 @@ theorem vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
 
 end
 
+/- warning: mv_polynomial.mem_vars_bind₁ -> MvPolynomial.mem_vars_bind₁ is a dubious translation:
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(CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u1 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f) φ))) -> (Exists.{succ u1} σ (fun (i : σ) => And (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ)) (Membership.mem.{u3, u3} τ (Finset.{u3} τ) (Finset.instMembershipFinset.{u3} τ) j (MvPolynomial.vars.{u2, u3} R τ _inst_1 (f i)))))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁ₓ'. -/
 theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
     (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by
   simpa only [exists_prop, Finset.mem_bunionᵢ, mem_support_iff, Ne.def] using vars_bind₁ f φ h
 #align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁
 
+#print MvPolynomial.monad /-
 instance monad : Monad fun σ => MvPolynomial σ R
     where
   map α β f p := rename f p
   pure _ := X
   bind _ _ p f := bind₁ f p
 #align mv_polynomial.monad MvPolynomial.monad
+-/
 
+#print MvPolynomial.lawfulFunctor /-
 instance lawfulFunctor : LawfulFunctor fun σ => MvPolynomial σ R
     where
   id_map := by intros <;> simp [(· <$> ·)]
   comp_map := by intros <;> simp [(· <$> ·)]
 #align mv_polynomial.is_lawful_functor MvPolynomial.lawfulFunctor
+-/
 
+#print MvPolynomial.lawfulMonad /-
 instance lawfulMonad : LawfulMonad fun σ => MvPolynomial σ R
     where
   pure_bind := by intros <;> simp [pure, bind]
   bind_assoc := by intros <;> simp [bind, ← bind₁_comp_bind₁]
 #align mv_polynomial.is_lawful_monad MvPolynomial.lawfulMonad
+-/
 
 /-
 Possible TODO for the future:

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

@@ -4,11 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Robert Y. Lewis
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.monad
-! leanprover-community/mathlib commit 9532aeba3ad43fb4dfc0ed02eea0b7a13d890813
+! leanprover-community/mathlib commit 5120cf49cb659e2499edd7e4d336a04efd598f2f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Data.MvPolynomial.Rename
+import Mathbin.Data.MvPolynomial.Variables
 
 /-!
 
@@ -350,6 +351,54 @@ theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ)
     bind₂ f (monomial d 1) = monomial d 1 := by rw [bind₂_monomial, f.map_one, one_mul]
 #align mv_polynomial.bind₂_monomial_one MvPolynomial.bind₂_monomial_one
 
+section
+
+open Classical
+
+theorem vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
+    (bind₁ f φ).vars ⊆ φ.vars.bunionᵢ fun i => (f i).vars :=
+  by
+  calc
+    (bind₁ f φ).vars = (φ.support.sum fun x : σ →₀ ℕ => (bind₁ f) (monomial x (coeff x φ))).vars :=
+      by rw [← AlgHom.map_sum, ← φ.as_sum]
+    _ ≤ φ.support.bUnion fun i : σ →₀ ℕ => ((bind₁ f) (monomial i (coeff i φ))).vars :=
+      (vars_sum_subset _ _)
+    _ = φ.support.bUnion fun d : σ →₀ ℕ => (C (coeff d φ) * ∏ i in d.support, f i ^ d i).vars := by
+      simp only [bind₁_monomial]
+    _ ≤ φ.support.bUnion fun d : σ →₀ ℕ => d.support.bUnion fun i => (f i).vars := _
+    -- proof below
+        _ ≤
+        φ.vars.bUnion fun i : σ => (f i).vars :=
+      _
+    
+  -- proof below
+  · apply Finset.bunionᵢ_mono
+    intro d hd
+    calc
+      (C (coeff d φ) * ∏ i : σ in d.support, f i ^ d i).vars ≤
+          (C (coeff d φ)).vars ∪ (∏ i : σ in d.support, f i ^ d i).vars :=
+        vars_mul _ _
+      _ ≤ (∏ i : σ in d.support, f i ^ d i).vars := by
+        simp only [Finset.empty_union, vars_C, Finset.le_iff_subset, Finset.Subset.refl]
+      _ ≤ d.support.bUnion fun i : σ => (f i ^ d i).vars := (vars_prod _)
+      _ ≤ d.support.bUnion fun i : σ => (f i).vars := _
+      
+    apply Finset.bunionᵢ_mono
+    intro i hi
+    apply vars_pow
+  · intro j
+    simp_rw [Finset.mem_bunionᵢ]
+    rintro ⟨d, hd, ⟨i, hi, hj⟩⟩
+    exact ⟨i, (mem_vars _).mpr ⟨d, hd, hi⟩, hj⟩
+#align mv_polynomial.vars_bind₁ MvPolynomial.vars_bind₁
+
+end
+
+theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
+    (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by
+  simpa only [exists_prop, Finset.mem_bunionᵢ, mem_support_iff, Ne.def] using vars_bind₁ f φ h
+#align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁
+
 instance monad : Monad fun σ => MvPolynomial σ R
     where
   map α β f p := rename f p

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

@@ -81,7 +81,7 @@ producing a new polynomial over `S`.
 The variable type remains the same. This operation is a ring hom.
 -/
 def bind₂ (f : R →+* MvPolynomial σ S) : MvPolynomial σ R →+* MvPolynomial σ S :=
-  eval₂Hom f x
+  eval₂Hom f X
 #align mv_polynomial.bind₂ MvPolynomial.bind₂
 
 /--
@@ -101,7 +101,7 @@ with variables in `σ` whose coefficients are polynomials in `σ` with coefficie
 This operation is a ring hom.
 -/
 def join₂ : MvPolynomial σ (MvPolynomial σ R) →+* MvPolynomial σ R :=
-  eval₂Hom (RingHom.id _) x
+  eval₂Hom (RingHom.id _) X
 #align mv_polynomial.join₂ MvPolynomial.join₂
 
 @[simp]
@@ -110,12 +110,12 @@ theorem aeval_eq_bind₁ (f : σ → MvPolynomial τ R) : aeval f = bind₁ f :=
 #align mv_polynomial.aeval_eq_bind₁ MvPolynomial.aeval_eq_bind₁
 
 @[simp]
-theorem eval₂Hom_c_eq_bind₁ (f : σ → MvPolynomial τ R) : eval₂Hom c f = bind₁ f :=
+theorem eval₂Hom_c_eq_bind₁ (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind₁ f :=
   rfl
 #align mv_polynomial.eval₂_hom_C_eq_bind₁ MvPolynomial.eval₂Hom_c_eq_bind₁
 
 @[simp]
-theorem eval₂Hom_eq_bind₂ (f : R →+* MvPolynomial σ S) : eval₂Hom f x = bind₂ f :=
+theorem eval₂Hom_eq_bind₂ (f : R →+* MvPolynomial σ S) : eval₂Hom f X = bind₂ f :=
   rfl
 #align mv_polynomial.eval₂_hom_eq_bind₂ MvPolynomial.eval₂Hom_eq_bind₂
 
@@ -129,12 +129,12 @@ theorem aeval_id_eq_join₁ : aeval id = @join₁ σ R _ :=
 #align mv_polynomial.aeval_id_eq_join₁ MvPolynomial.aeval_id_eq_join₁
 
 theorem eval₂Hom_c_id_eq_join₁ (φ : MvPolynomial (MvPolynomial σ R) R) :
-    eval₂Hom c id φ = join₁ φ :=
+    eval₂Hom C id φ = join₁ φ :=
   rfl
 #align mv_polynomial.eval₂_hom_C_id_eq_join₁ MvPolynomial.eval₂Hom_c_id_eq_join₁
 
 @[simp]
-theorem eval₂Hom_id_x_eq_join₂ : eval₂Hom (RingHom.id _) x = @join₂ σ R _ :=
+theorem eval₂Hom_id_x_eq_join₂ : eval₂Hom (RingHom.id _) X = @join₂ σ R _ :=
   rfl
 #align mv_polynomial.eval₂_hom_id_X_eq_join₂ MvPolynomial.eval₂Hom_id_x_eq_join₂
 
@@ -147,17 +147,17 @@ attribute [-simp]
   aeval_eq_bind₁ eval₂_hom_C_eq_bind₁ eval₂_hom_eq_bind₂ aeval_id_eq_join₁ eval₂_hom_id_X_eq_join₂
 
 @[simp]
-theorem bind₁_x_right (f : σ → MvPolynomial τ R) (i : σ) : bind₁ f (x i) = f i :=
-  aeval_x f i
+theorem bind₁_x_right (f : σ → MvPolynomial τ R) (i : σ) : bind₁ f (X i) = f i :=
+  aeval_X f i
 #align mv_polynomial.bind₁_X_right MvPolynomial.bind₁_x_right
 
 @[simp]
-theorem bind₂_x_right (f : R →+* MvPolynomial σ S) (i : σ) : bind₂ f (x i) = x i :=
-  eval₂Hom_X' f x i
+theorem bind₂_x_right (f : R →+* MvPolynomial σ S) (i : σ) : bind₂ f (X i) = X i :=
+  eval₂Hom_X' f X i
 #align mv_polynomial.bind₂_X_right MvPolynomial.bind₂_x_right
 
 @[simp]
-theorem bind₁_x_left : bind₁ (x : σ → MvPolynomial σ R) = AlgHom.id R _ :=
+theorem bind₁_x_left : bind₁ (X : σ → MvPolynomial σ R) = AlgHom.id R _ :=
   by
   ext1 i
   simp
@@ -166,21 +166,21 @@ theorem bind₁_x_left : bind₁ (x : σ → MvPolynomial σ R) = AlgHom.id R _
 variable (f : σ → MvPolynomial τ R)
 
 @[simp]
-theorem bind₁_c_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (c x) = c x := by
+theorem bind₁_c_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (C x) = C x := by
   simp [bind₁, algebra_map_eq]
 #align mv_polynomial.bind₁_C_right MvPolynomial.bind₁_c_right
 
 @[simp]
-theorem bind₂_c_right (f : R →+* MvPolynomial σ S) (r : R) : bind₂ f (c r) = f r :=
-  eval₂Hom_c f x r
+theorem bind₂_c_right (f : R →+* MvPolynomial σ S) (r : R) : bind₂ f (C r) = f r :=
+  eval₂Hom_C f X r
 #align mv_polynomial.bind₂_C_right MvPolynomial.bind₂_c_right
 
 @[simp]
-theorem bind₂_c_left : bind₂ (c : R →+* MvPolynomial σ R) = RingHom.id _ := by ext : 2 <;> simp
+theorem bind₂_c_left : bind₂ (C : R →+* MvPolynomial σ R) = RingHom.id _ := by ext : 2 <;> simp
 #align mv_polynomial.bind₂_C_left MvPolynomial.bind₂_c_left
 
 @[simp]
-theorem bind₂_comp_c (f : R →+* MvPolynomial σ S) : (bind₂ f).comp c = f :=
+theorem bind₂_comp_c (f : R →+* MvPolynomial σ S) : (bind₂ f).comp C = f :=
   RingHom.ext <| bind₂_c_right _
 #align mv_polynomial.bind₂_comp_C MvPolynomial.bind₂_comp_c
 
@@ -272,7 +272,7 @@ theorem bind₂_map (f : S →+* MvPolynomial σ T) (g : R →+* S) (φ : MvPoly
 #align mv_polynomial.bind₂_map MvPolynomial.bind₂_map
 
 @[simp]
-theorem map_comp_c (f : R →+* S) : (map f).comp (c : R →+* MvPolynomial σ R) = c.comp f :=
+theorem map_comp_c (f : R →+* S) : (map f).comp (C : R →+* MvPolynomial σ R) = C.comp f :=
   by
   ext1
   apply map_C
@@ -280,7 +280,7 @@ theorem map_comp_c (f : R →+* S) : (map f).comp (c : R →+* MvPolynomial σ R
 
 -- mixing the two monad structures
 theorem hom_bind₁ (f : MvPolynomial τ R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
-    f (bind₁ g φ) = eval₂Hom (f.comp c) (fun i => f (g i)) φ := by
+    f (bind₁ g φ) = eval₂Hom (f.comp C) (fun i => f (g i)) φ := by
   rw [bind₁, map_aeval, algebra_map_eq]
 #align mv_polynomial.hom_bind₁ MvPolynomial.hom_bind₁
 
@@ -292,7 +292,7 @@ theorem map_bind₁ (f : R →+* S) (g : σ → MvPolynomial τ R) (φ : MvPolyn
 #align mv_polynomial.map_bind₁ MvPolynomial.map_bind₁
 
 @[simp]
-theorem eval₂Hom_comp_c (f : R →+* S) (g : σ → S) : (eval₂Hom f g).comp c = f :=
+theorem eval₂Hom_comp_c (f : R →+* S) (g : σ → S) : (eval₂Hom f g).comp C = f :=
   by
   ext1 r
   exact eval₂_C f g r
@@ -329,12 +329,12 @@ theorem aeval_bind₂ [Algebra S T] (f : σ → T) (g : R →+* MvPolynomial σ
   eval₂Hom_bind₂ _ _ _ _
 #align mv_polynomial.aeval_bind₂ MvPolynomial.aeval_bind₂
 
-theorem eval₂Hom_c_left (f : σ → MvPolynomial τ R) : eval₂Hom c f = bind₁ f :=
+theorem eval₂Hom_c_left (f : σ → MvPolynomial τ R) : eval₂Hom C f = bind₁ f :=
   rfl
 #align mv_polynomial.eval₂_hom_C_left MvPolynomial.eval₂Hom_c_left
 
 theorem bind₁_monomial (f : σ → MvPolynomial τ R) (d : σ →₀ ℕ) (r : R) :
-    bind₁ f (monomial d r) = c r * ∏ i in d.support, f i ^ d i := by
+    bind₁ f (monomial d r) = C r * ∏ i in d.support, f i ^ d i := by
   simp only [monomial_eq, AlgHom.map_mul, bind₁_C_right, Finsupp.prod, AlgHom.map_prod,
     AlgHom.map_pow, bind₁_X_right]
 #align mv_polynomial.bind₁_monomial MvPolynomial.bind₁_monomial
@@ -353,7 +353,7 @@ theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ)
 instance monad : Monad fun σ => MvPolynomial σ R
     where
   map α β f p := rename f p
-  pure _ := x
+  pure _ := X
   bind _ _ p f := bind₁ f p
 #align mv_polynomial.monad MvPolynomial.monad
 

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

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

@@ -372,7 +372,7 @@ theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPol
         vars_mul _ _
       _ ≤ (∏ i : σ in d.support, f i ^ d i).vars := by
         simp only [Finset.empty_union, vars_C, Finset.le_iff_subset, Finset.Subset.refl]
-      _ ≤ d.support.biUnion fun i : σ => vars (f i ^ d i) := (vars_prod _)
+      _ ≤ d.support.biUnion fun i : σ => vars (f i ^ d i) := vars_prod _
       _ ≤ d.support.biUnion fun i : σ => (f i).vars := ?_
     apply Finset.biUnion_mono
     intro i _hi

Mostly automatic, with a few manual corrections.

@@ -42,7 +42,7 @@ whereas `MvPolynomial.map` is the "map" operation for the other pair.
 
 We add a `LawfulMonad` instance for the (`bind₁`, `join₁`) pair.
 The second pair cannot be instantiated as a `Monad`,
-since it is not a monad in `Type` but in `CommRing` (or rather `CommSemiRing`).
+since it is not a monad in `Type` but in `CommRingCat` (or rather `CommSemiRingCat`).
 
 -/
 

Polynomial and MvPolynomial are algebraic objects, hence should be under Algebra (or at least not under Data)

@@ -3,8 +3,8 @@ Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Robert Y. Lewis
 -/
-import Mathlib.Data.MvPolynomial.Rename
-import Mathlib.Data.MvPolynomial.Variables
+import Mathlib.Algebra.MvPolynomial.Rename
+import Mathlib.Algebra.MvPolynomial.Variables
 
 #align_import data.mv_polynomial.monad from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 

@@ -388,7 +388,7 @@ end
 theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
     (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by
   classical
-  simpa only [exists_prop, Finset.mem_biUnion, mem_support_iff, Ne.def] using vars_bind₁ f φ h
+  simpa only [exists_prop, Finset.mem_biUnion, mem_support_iff, Ne] using vars_bind₁ f φ h
 #align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁
 
 instance monad : Monad fun σ => MvPolynomial σ R

Generalizes algHom_C to work over polynomials of different variable types. Adds related lemma killCompl_C using this. Also removes simp tags from a few lemmas that are made redundant by this.

@@ -167,9 +167,7 @@ set_option linter.uppercaseLean3 false in
 
 variable (f : σ → MvPolynomial τ R)
 
-@[simp]
-theorem bind₁_C_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (C x) = C x := by
-  simp [bind₁, algebraMap_eq]
+theorem bind₁_C_right (f : σ → MvPolynomial τ R) (x) : bind₁ f (C x) = C x := algHom_C _ _
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.bind₁_C_right MvPolynomial.bind₁_C_right
 

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)

@@ -56,7 +56,6 @@ namespace MvPolynomial
 open Finsupp
 
 variable {σ : Type*} {τ : Type*}
-
 variable {R S T : Type*} [CommSemiring R] [CommSemiring S] [CommSemiring T]
 
 /--

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -404,7 +404,7 @@ instance monad : Monad fun σ => MvPolynomial σ R
 instance lawfulFunctor : LawfulFunctor fun σ => MvPolynomial σ R
     where
   map_const := by intros; rfl
-  -- porting note: I guess `map_const` no longer has a default implementation?
+  -- Porting note: I guess `map_const` no longer has a default implementation?
   id_map := by intros; simp [(· <$> ·)]
   comp_map := by intros; simp [(· <$> ·)]
 #align mv_polynomial.is_lawful_functor MvPolynomial.lawfulFunctor

• Merge Function.left_id and Function.comp.left_id into Function.id_comp.
• Merge Function.right_id and Function.comp.right_id into Function.comp_id.
• Merge Function.comp_const_right and Function.comp_const into Function.comp_const, use explicit arguments.
• Move Function.const_comp to Mathlib.Init.Function, use explicit arguments.

@@ -202,7 +202,7 @@ theorem join₂_comp_map (f : R →+* MvPolynomial σ S) : join₂.comp (map f)
 #align mv_polynomial.join₂_comp_map MvPolynomial.join₂_comp_map
 
 theorem aeval_id_rename (f : σ → MvPolynomial τ R) (p : MvPolynomial σ R) :
-    aeval id (rename f p) = aeval f p := by rw [aeval_rename, Function.comp.left_id]
+    aeval id (rename f p) = aeval f p := by rw [aeval_rename, Function.id_comp]
 #align mv_polynomial.aeval_id_rename MvPolynomial.aeval_id_rename
 
 @[simp]

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

This has nice performance benefits.

@@ -55,9 +55,9 @@ namespace MvPolynomial
 
 open Finsupp
 
-variable {σ : Type _} {τ : Type _}
+variable {σ : Type*} {τ : Type*}
 
-variable {R S T : Type _} [CommSemiring R] [CommSemiring S] [CommSemiring T]
+variable {R S T : Type*} [CommSemiring R] [CommSemiring S] [CommSemiring T]
 
 /--
 `bind₁` is the "left hand side" bind operation on `MvPolynomial`, operating on the variable type.
@@ -221,12 +221,12 @@ theorem bind₂_id : bind₂ (RingHom.id (MvPolynomial σ R)) = join₂ :=
   rfl
 #align mv_polynomial.bind₂_id MvPolynomial.bind₂_id
 
-theorem bind₁_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R)
+theorem bind₁_bind₁ {υ : Type*} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R)
     (φ : MvPolynomial σ R) : (bind₁ g) (bind₁ f φ) = bind₁ (fun i => bind₁ g (f i)) φ := by
   simp [bind₁, ← comp_aeval]
 #align mv_polynomial.bind₁_bind₁ MvPolynomial.bind₁_bind₁
 
-theorem bind₁_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R) :
+theorem bind₁_comp_bind₁ {υ : Type*} (f : σ → MvPolynomial τ R) (g : τ → MvPolynomial υ R) :
     (bind₁ g).comp (bind₁ f) = bind₁ fun i => bind₁ g (f i) := by
   ext1
   apply bind₁_bind₁
@@ -241,13 +241,13 @@ theorem bind₂_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* MvPolynomia
   RingHom.congr_fun (bind₂_comp_bind₂ f g) φ
 #align mv_polynomial.bind₂_bind₂ MvPolynomial.bind₂_bind₂
 
-theorem rename_comp_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) :
+theorem rename_comp_bind₁ {υ : Type*} (f : σ → MvPolynomial τ R) (g : τ → υ) :
     (rename g).comp (bind₁ f) = bind₁ fun i => rename g <| f i := by
   ext1 i
   simp
 #align mv_polynomial.rename_comp_bind₁ MvPolynomial.rename_comp_bind₁
 
-theorem rename_bind₁ {υ : Type _} (f : σ → MvPolynomial τ R) (g : τ → υ) (φ : MvPolynomial σ R) :
+theorem rename_bind₁ {υ : Type*} (f : σ → MvPolynomial τ R) (g : τ → υ) (φ : MvPolynomial σ R) :
     rename g (bind₁ f φ) = bind₁ (fun i => rename g <| f i) φ :=
   AlgHom.congr_fun (rename_comp_bind₁ f g) φ
 #align mv_polynomial.rename_bind₁ MvPolynomial.rename_bind₁
@@ -259,13 +259,13 @@ theorem map_bind₂ (f : R →+* MvPolynomial σ S) (g : S →+* T) (φ : MvPoly
   simp only [Function.comp_apply, map_X]
 #align mv_polynomial.map_bind₂ MvPolynomial.map_bind₂
 
-theorem bind₁_comp_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ → τ) :
+theorem bind₁_comp_rename {υ : Type*} (f : τ → MvPolynomial υ R) (g : σ → τ) :
     (bind₁ f).comp (rename g) = bind₁ (f ∘ g) := by
   ext1 i
   simp
 #align mv_polynomial.bind₁_comp_rename MvPolynomial.bind₁_comp_rename
 
-theorem bind₁_rename {υ : Type _} (f : τ → MvPolynomial υ R) (g : σ → τ) (φ : MvPolynomial σ R) :
+theorem bind₁_rename {υ : Type*} (f : τ → MvPolynomial υ R) (g : σ → τ) (φ : MvPolynomial σ R) :
     bind₁ f (rename g φ) = bind₁ (f ∘ g) φ :=
   AlgHom.congr_fun (bind₁_comp_rename f g) φ
 #align mv_polynomial.bind₁_rename MvPolynomial.bind₁_rename

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Robert Y. Lewis
-
-! This file was ported from Lean 3 source module data.mv_polynomial.monad
-! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.MvPolynomial.Rename
 import Mathlib.Data.MvPolynomial.Variables
 
+#align_import data.mv_polynomial.monad from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
+
 /-!
 
 # Monad operations on `MvPolynomial`

Part 2 of #5001

@@ -43,7 +43,7 @@ whereas `MvPolynomial.map` is the "map" operation for the other pair.
 
 ## Implementation notes
 
-We add an `LawfulMonad` instance for the (`bind₁`, `join₁`) pair.
+We add a `LawfulMonad` instance for the (`bind₁`, `join₁`) pair.
 The second pair cannot be instantiated as a `Monad`,
 since it is not a monad in `Type` but in `CommRing` (or rather `CommSemiRing`).
 

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -428,14 +428,14 @@ Possible TODO for the future:
 Enable the following definitions, and write a lot of supporting lemmas.
 
 def bind (f : R →+* mv_polynomial τ S) (g : σ → mv_polynomial τ S) :
-  mv_polynomial σ R →+* mv_polynomial τ S :=
-eval₂_hom f g
+    mv_polynomial σ R →+* mv_polynomial τ S :=
+  eval₂_hom f g
 
 def join (f : R →+* S) : mv_polynomial (mv_polynomial σ R) S →ₐ[S] mv_polynomial σ S :=
-aeval (map f)
+  aeval (map f)
 
 def ajoin [algebra R S] : mv_polynomial (mv_polynomial σ R) S →ₐ[S] mv_polynomial σ S :=
-join (algebra_map R S)
+  join (algebra_map R S)
 
 -/
 end MvPolynomial

I've been someone sloppy about forward-porting the exact mathport here; a lot of the classical additions result in the whole proof being indented, which IMO just adds noise to the diff.

What's important is that:

• open Classical is removed from all the same files
• [DecidableEq _] is added in the same position to all the same lemmas. In theory mathport will detect if we mess this up, so it's not essential to catch this in review. The linter will tell us if it is added unnecessarily, and the build will fail if is not added someewhere it is needed; so only the argument order is at risk of being wrong.
• The new foo_def lemmas are all added in variables.lean

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Robert Y. Lewis
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.monad
-! leanprover-community/mathlib commit 5120cf49cb659e2499edd7e4d336a04efd598f2f
+! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -357,9 +357,7 @@ theorem bind₂_monomial_one (f : R →+* MvPolynomial σ S) (d : σ →₀ ℕ)
 
 section
 
-open Classical
-
-theorem vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
+theorem vars_bind₁ [DecidableEq τ] (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     (bind₁ f φ).vars ⊆ φ.vars.biUnion fun i => (f i).vars := by
   calc
     (bind₁ f φ).vars = (φ.support.sum fun x : σ →₀ ℕ => (bind₁ f) (monomial x (coeff x φ))).vars :=

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -360,19 +360,19 @@ section
 open Classical
 
 theorem vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
-    (bind₁ f φ).vars ⊆ φ.vars.bunionᵢ fun i => (f i).vars := by
+    (bind₁ f φ).vars ⊆ φ.vars.biUnion fun i => (f i).vars := by
   calc
     (bind₁ f φ).vars = (φ.support.sum fun x : σ →₀ ℕ => (bind₁ f) (monomial x (coeff x φ))).vars :=
       by rw [← AlgHom.map_sum, ← φ.as_sum]
-    _ ≤ φ.support.bunionᵢ fun i : σ →₀ ℕ => ((bind₁ f) (monomial i (coeff i φ))).vars :=
+    _ ≤ φ.support.biUnion fun i : σ →₀ ℕ => ((bind₁ f) (monomial i (coeff i φ))).vars :=
       (vars_sum_subset _ _)
-    _ = φ.support.bunionᵢ fun d : σ →₀ ℕ => vars (C (coeff d φ) * ∏ i in d.support, f i ^ d i) := by
+    _ = φ.support.biUnion fun d : σ →₀ ℕ => vars (C (coeff d φ) * ∏ i in d.support, f i ^ d i) := by
       simp only [bind₁_monomial]
-    _ ≤ φ.support.bunionᵢ fun d : σ →₀ ℕ => d.support.bunionᵢ fun i => vars (f i) := ?_
+    _ ≤ φ.support.biUnion fun d : σ →₀ ℕ => d.support.biUnion fun i => vars (f i) := ?_
     -- proof below
-    _ ≤ φ.vars.bunionᵢ fun i : σ => vars (f i) := ?_
+    _ ≤ φ.vars.biUnion fun i : σ => vars (f i) := ?_
     -- proof below
-  · apply Finset.bunionᵢ_mono
+  · apply Finset.biUnion_mono
     intro d _hd
     calc
       vars (C (coeff d φ) * ∏ i : σ in d.support, f i ^ d i) ≤
@@ -380,13 +380,13 @@ theorem vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
         vars_mul _ _
       _ ≤ (∏ i : σ in d.support, f i ^ d i).vars := by
         simp only [Finset.empty_union, vars_C, Finset.le_iff_subset, Finset.Subset.refl]
-      _ ≤ d.support.bunionᵢ fun i : σ => vars (f i ^ d i) := (vars_prod _)
-      _ ≤ d.support.bunionᵢ fun i : σ => (f i).vars := ?_
-    apply Finset.bunionᵢ_mono
+      _ ≤ d.support.biUnion fun i : σ => vars (f i ^ d i) := (vars_prod _)
+      _ ≤ d.support.biUnion fun i : σ => (f i).vars := ?_
+    apply Finset.biUnion_mono
     intro i _hi
     apply vars_pow
   · intro j
-    simp_rw [Finset.mem_bunionᵢ]
+    simp_rw [Finset.mem_biUnion]
     rintro ⟨d, hd, ⟨i, hi, hj⟩⟩
     exact ⟨i, (mem_vars _).mpr ⟨d, hd, hi⟩, hj⟩
 #align mv_polynomial.vars_bind₁ MvPolynomial.vars_bind₁
@@ -396,7 +396,7 @@ end
 theorem mem_vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) {j : τ}
     (h : j ∈ (bind₁ f φ).vars) : ∃ i : σ, i ∈ φ.vars ∧ j ∈ (f i).vars := by
   classical
-  simpa only [exists_prop, Finset.mem_bunionᵢ, mem_support_iff, Ne.def] using vars_bind₁ f φ h
+  simpa only [exists_prop, Finset.mem_biUnion, mem_support_iff, Ne.def] using vars_bind₁ f φ h
 #align mv_polynomial.mem_vars_bind₁ MvPolynomial.mem_vars_bind₁
 
 instance monad : Monad fun σ => MvPolynomial σ R

• depends on: #2861
• depends on: #2886

Co-authored-by: Johan Commelin <johan@commelin.net>