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

@@ -935,7 +935,7 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
     (hp : ∀ i ∈ p.vars, g i = 0) : eval₂Hom f g p = f (constantCoeff p) :=
   by
   conv_lhs => rw [p.as_sum]
-  simp only [RingHom.map_sum, eval₂_hom_monomial]
+  simp only [map_sum, eval₂_hom_monomial]
   by_cases h0 : constant_coeff p = 0
   on_goal 1 =>
     rw [h0, f.map_zero, Finset.sum_eq_zero]
@@ -976,7 +976,7 @@ theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p
   rintro rfl h rfl
   rename' p₁ => p, f₁ => f
   rw [p.as_sum]
-  simp only [RingHom.map_sum, eval₂_hom_monomial]
+  simp only [map_sum, eval₂_hom_monomial]
   apply Finset.sum_congr rfl
   intro d hd
   congr 1

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

@@ -3,8 +3,8 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 -/
-import Algebra.BigOperators.Order
-import Data.MvPolynomial.Rename
+import Algebra.Order.BigOperators.Group.Finset
+import Algebra.MvPolynomial.Rename
 
 #align_import data.mv_polynomial.variables from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 

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

@@ -204,7 +204,7 @@ theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R
 theorem degrees_pow (p : MvPolynomial σ R) : ∀ n : ℕ, (p ^ n).degrees ≤ n • p.degrees
   | 0 => by rw [pow_zero, degrees_one]; exact Multiset.zero_le _
   | n + 1 => by
-    rw [pow_succ, add_smul, add_comm, one_smul]
+    rw [pow_succ', add_smul, add_comm, one_smul]
     exact le_trans (degrees_mul _ _) (add_le_add_left (degrees_pow n) _)
 #align mv_polynomial.degrees_pow MvPolynomial.degrees_pow
 -/
@@ -429,7 +429,7 @@ theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars
   simp_rw [vars_def]
   induction' n with n ih
   · simp
-  · rw [pow_succ]
+  · rw [pow_succ']
     apply Finset.Subset.trans (vars_mul _ _)
     exact Finset.union_subset (Finset.Subset.refl _) ih
 #align mv_polynomial.vars_pow MvPolynomial.vars_pow
@@ -814,7 +814,7 @@ theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree
   by
   induction' n with n ih
   · simp only [Nat.zero_eq, MulZeroClass.zero_mul, pow_zero, total_degree_one]
-  rw [pow_succ]
+  rw [pow_succ']
   calc
     total_degree (a * a ^ n) ≤ a.total_degree + (a ^ n).totalDegree := total_degree_mul _ _
     _ ≤ a.total_degree + n * a.total_degree := (add_le_add_left ih _)

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

@@ -104,7 +104,7 @@ theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) 
   classical
   refine' Finset.sup_le fun t h => _
   have := Finsupp.support_single_subset h
-  rw [Finset.mem_singleton] at this 
+  rw [Finset.mem_singleton] at this
   rw [this]
 #align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomial
 -/
@@ -157,7 +157,7 @@ theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
   simp_rw [degrees_def]
   refine' Finset.sup_le fun b hb => _
   have := Finsupp.support_add hb
-  rw [Finset.mem_union] at this 
+  rw [Finset.mem_union] at this
   cases this
   · exact le_sup_of_le_left (Finset.le_sup this)
   · exact le_sup_of_le_right (Finset.le_sup this)
@@ -181,7 +181,7 @@ theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees +
   classical
   refine' Finset.sup_le fun b hb => _
   have := support_mul p q hb
-  simp only [Finset.mem_biUnion, Finset.mem_singleton] at this 
+  simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
   rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
   rw [Finsupp.toMultiset_add]
   exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
@@ -222,7 +222,7 @@ theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degre
   classical
   apply Finset.sup_le
   intro d hd
-  rw [Multiset.disjoint_iff_ne] at h 
+  rw [Multiset.disjoint_iff_ne] at h
   rw [Multiset.le_iff_count]
   intro i
   rw [degrees, Multiset.count_finset_sup]
@@ -232,10 +232,10 @@ theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degre
   · refine' @Finset.le_sup _ _ _ _ (p + q).support _ d _
     rw [mem_support_iff, coeff_add]
     suffices q.coeff d = 0 by rwa [this, add_zero, coeff, ← Finsupp.mem_support_iff]
-    rw [← Finsupp.support_eq_empty, ← Ne.def, ← Finset.nonempty_iff_ne_empty] at h0 
+    rw [← Finsupp.support_eq_empty, ← Ne.def, ← Finset.nonempty_iff_ne_empty] at h0
     obtain ⟨j, hj⟩ := h0
     contrapose! h
-    rw [mem_support_iff] at hd 
+    rw [mem_support_iff] at hd
     refine' ⟨j, _, j, _, rfl⟩
     all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
 #align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_add
@@ -271,12 +271,12 @@ theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
   rw [mem_degrees, Multiset.mem_map]
   rintro ⟨d, hd, hi⟩
   obtain ⟨x, rfl, hx⟩ := coeff_rename_ne_zero _ _ _ hd
-  simp only [map_domain, Finsupp.mem_support_iff] at hi 
-  rw [sum_apply, Finsupp.sum] at hi 
+  simp only [map_domain, Finsupp.mem_support_iff] at hi
+  rw [sum_apply, Finsupp.sum] at hi
   contrapose! hi
   rw [Finset.sum_eq_zero]
   intro j hj
-  simp only [exists_prop, mem_degrees] at hi 
+  simp only [exists_prop, mem_degrees] at hi
   specialize hi j ⟨x, hx, hj⟩
   rw [single_apply, if_neg hi]
 #align mv_polynomial.degrees_rename MvPolynomial.degrees_rename
@@ -360,7 +360,7 @@ theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ
     {v : σ} (h : v ∉ vars f) : x v = 0 :=
   by
   letI := Classical.decEq σ
-  rw [vars_def, Multiset.mem_toFinset] at h 
+  rw [vars_def, Multiset.mem_toFinset] at h
   rw [← Finsupp.not_mem_support_iff]
   contrapose! h
   rw [degrees_def]
@@ -368,7 +368,7 @@ theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ
   rw [Finset.sup_insert]
   simp only [Multiset.mem_union, Multiset.sup_eq_union]
   left
-  rwa [← to_finset_to_multiset, Multiset.mem_toFinset] at h 
+  rwa [← to_finset_to_multiset, Multiset.mem_toFinset] at h
 #align mv_polynomial.mem_support_not_mem_vars_zero MvPolynomial.mem_support_not_mem_vars_zero
 -/
 
@@ -401,11 +401,11 @@ theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars 
   intro i
   simp only [mem_vars, Finset.mem_union]
   rintro ⟨d, hd, hi⟩
-  rw [mem_support_iff, coeff_mul] at hd 
+  rw [mem_support_iff, coeff_mul] at hd
   contrapose! hd; cases hd
   rw [Finset.sum_eq_zero]
   rintro ⟨d₁, d₂⟩ H
-  rw [Finsupp.mem_antidiagonal] at H 
+  rw [Finsupp.mem_antidiagonal] at H
   subst H
   obtain H | H : i ∈ d₁.support ∨ i ∈ d₂.support := by
     simpa only [Finset.mem_union] using Finsupp.support_add hi
@@ -497,11 +497,11 @@ theorem vars_sum_of_disjoint [DecidableEq σ] (h : Pairwise <| (Disjoint on fun
   · simp
   · intro a s has hsum
     rw [Finset.biUnion_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
-    unfold Pairwise on_fun at h 
+    unfold Pairwise on_fun at h
     rw [hsum]
     simp only [Finset.disjoint_iff_ne] at h ⊢
     intro v hv v2 hv2
-    rw [Finset.mem_biUnion] at hv2 
+    rw [Finset.mem_biUnion] at hv2
     rcases hv2 with ⟨i, his, hi⟩
     refine' h _ _ hv _ hi
     rintro rfl
@@ -711,7 +711,7 @@ theorem totalDegree_C (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
   Nat.eq_zero_of_le_zero <|
     Finset.sup_le fun n hn => by
       have := Finsupp.support_single_subset hn
-      rw [Finset.mem_singleton] at this 
+      rw [Finset.mem_singleton] at this
       subst this
       exact le_rfl
 #align mv_polynomial.total_degree_C MvPolynomial.totalDegree_C
@@ -747,7 +747,7 @@ theorem totalDegree_add (a b : MvPolynomial σ R) :
   Finset.sup_le fun n hn => by
     classical
     have := Finsupp.support_add hn
-    rw [Finset.mem_union] at this 
+    rw [Finset.mem_union] at this
     cases this
     · exact le_max_of_le_left (Finset.le_sup this)
     · exact le_max_of_le_right (Finset.le_sup this)
@@ -793,7 +793,7 @@ theorem totalDegree_mul (a b : MvPolynomial σ R) :
   Finset.sup_le fun n hn => by
     classical
     have := AddMonoidAlgebra.support_mul a b hn
-    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this 
+    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
     rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
     rw [Finsupp.sum_add_index']
     · exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
@@ -853,7 +853,7 @@ theorem totalDegree_multiset_prod (s : Multiset (MvPolynomial σ R)) :
     s.Prod.totalDegree ≤ (s.map MvPolynomial.totalDegree).Sum :=
   by
   refine' Quotient.inductionOn s fun l => _
-  rw [Multiset.quot_mk_to_coe, Multiset.coe_prod, Multiset.coe_map, Multiset.coe_sum]
+  rw [Multiset.quot_mk_to_coe, Multiset.prod_coe, Multiset.map_coe, Multiset.sum_coe]
   exact total_degree_list_prod l
 #align mv_polynomial.total_degree_multiset_prod MvPolynomial.totalDegree_multiset_prod
 -/
@@ -897,8 +897,8 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
 theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ ℕ}
     (h : f.totalDegree < ∑ i in d.support, d i) : coeff d f = 0 := by
   classical
-  rw [total_degree, Finset.sup_lt_iff] at h 
-  · specialize h d; rw [mem_support_iff] at h 
+  rw [total_degree, Finset.sup_lt_iff] at h
+  · specialize h d; rw [mem_support_iff] at h
     refine' not_not.mp (mt h _); exact lt_irrefl _
   · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_lt
@@ -909,10 +909,10 @@ theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     (rename f p).totalDegree ≤ p.totalDegree :=
   Finset.sup_le fun b => by
     intro h
-    rw [rename_eq] at h 
+    rw [rename_eq] at h
     classical
     have h' := Finsupp.mapDomain_support h
-    rw [Finset.mem_image] at h' 
+    rw [Finset.mem_image] at h'
     rcases h' with ⟨s, hs, rfl⟩
     rw [Finsupp.sum_mapDomain_index]
     exact le_trans le_rfl (Finset.le_sup hs)
@@ -948,14 +948,14 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
   repeat'
     obtain ⟨i, hi⟩ : d.support.nonempty :=
       by
-      rw [constant_coeff_eq, coeff, ← Finsupp.not_mem_support_iff] at h0 
+      rw [constant_coeff_eq, coeff, ← Finsupp.not_mem_support_iff] at h0
       rw [Finset.nonempty_iff_ne_empty, Ne.def, Finsupp.support_eq_empty]
       rintro rfl; contradiction
     rw [Finsupp.prod, Finset.prod_eq_zero hi, MulZeroClass.mul_zero]
     rw [hp, zero_pow (Nat.pos_of_ne_zero <| finsupp.mem_support_iff.mp hi)]
     rw [mem_vars]
     exact ⟨d, hd, hi⟩
-  · rw [constant_coeff_eq, coeff, ← Ne.def, ← Finsupp.mem_support_iff] at h0 
+  · rw [constant_coeff_eq, coeff, ← Ne.def, ← Finsupp.mem_support_iff] at h0
     intro; contradiction
 #align mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars
 -/

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

@@ -102,12 +102,19 @@ theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
 #print MvPolynomial.degrees_monomial /-
 theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ s.toMultiset := by
   classical
+  refine' Finset.sup_le fun t h => _
+  have := Finsupp.support_single_subset h
+  rw [Finset.mem_singleton] at this 
+  rw [this]
 #align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomial
 -/
 
 #print MvPolynomial.degrees_monomial_eq /-
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
-    degrees (monomial s a) = s.toMultiset := by classical
+    degrees (monomial s a) = s.toMultiset := by
+  classical
+  refine' le_antisymm (degrees_monomial s a) <| Finset.le_sup <| _
+  rw [support_monomial, if_neg ha, Finset.mem_singleton]
 #align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eq
 -/
 
@@ -145,25 +152,51 @@ theorem degrees_one : degrees (1 : MvPolynomial σ R) = 0 :=
 
 #print MvPolynomial.degrees_add /-
 theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
-    (p + q).degrees ≤ p.degrees ⊔ q.degrees := by classical
+    (p + q).degrees ≤ p.degrees ⊔ q.degrees := by
+  classical
+  simp_rw [degrees_def]
+  refine' Finset.sup_le fun b hb => _
+  have := Finsupp.support_add hb
+  rw [Finset.mem_union] at this 
+  cases this
+  · exact le_sup_of_le_left (Finset.le_sup this)
+  · exact le_sup_of_le_right (Finset.le_sup this)
 #align mv_polynomial.degrees_add MvPolynomial.degrees_add
 -/
 
 #print MvPolynomial.degrees_sum /-
 theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → MvPolynomial σ R) :
-    (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by classical
+    (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by
+  classical
+  refine' s.induction _ _
+  · simp only [Finset.sum_empty, Finset.sup_empty, degrees_zero]; exact le_rfl
+  · intro i s his ih
+    rw [Finset.sup_insert, Finset.sum_insert his]
+    exact le_trans (degrees_add _ _) (sup_le_sup_left ih _)
 #align mv_polynomial.degrees_sum MvPolynomial.degrees_sum
 -/
 
 #print MvPolynomial.degrees_mul /-
 theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees := by
   classical
+  refine' Finset.sup_le fun b hb => _
+  have := support_mul p q hb
+  simp only [Finset.mem_biUnion, Finset.mem_singleton] at this 
+  rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
+  rw [Finsupp.toMultiset_add]
+  exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
 #align mv_polynomial.degrees_mul MvPolynomial.degrees_mul
 -/
 
 #print MvPolynomial.degrees_prod /-
 theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
-    (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees := by classical
+    (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees := by
+  classical
+  refine' s.induction _ _
+  · simp only [Finset.prod_empty, Finset.sum_empty, degrees_one]
+  · intro i s his ih
+    rw [Finset.prod_insert his, Finset.sum_insert his]
+    exact le_trans (degrees_mul _ _) (add_le_add_left ih _)
 #align mv_polynomial.degrees_prod MvPolynomial.degrees_prod
 -/
 
@@ -185,7 +218,26 @@ theorem mem_degrees {p : MvPolynomial σ R} {i : σ} :
 
 #print MvPolynomial.le_degrees_add /-
 theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degrees) :
-    p.degrees ≤ (p + q).degrees := by classical
+    p.degrees ≤ (p + q).degrees := by
+  classical
+  apply Finset.sup_le
+  intro d hd
+  rw [Multiset.disjoint_iff_ne] at h 
+  rw [Multiset.le_iff_count]
+  intro i
+  rw [degrees, Multiset.count_finset_sup]
+  simp only [Finsupp.count_toMultiset]
+  by_cases h0 : d = 0
+  · simp only [h0, zero_le, Finsupp.zero_apply]
+  · refine' @Finset.le_sup _ _ _ _ (p + q).support _ d _
+    rw [mem_support_iff, coeff_add]
+    suffices q.coeff d = 0 by rwa [this, add_zero, coeff, ← Finsupp.mem_support_iff]
+    rw [← Finsupp.support_eq_empty, ← Ne.def, ← Finset.nonempty_iff_ne_empty] at h0 
+    obtain ⟨j, hj⟩ := h0
+    contrapose! h
+    rw [mem_support_iff] at hd 
+    refine' ⟨j, _, j, _, rfl⟩
+    all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
 #align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_add
 -/
 
@@ -213,7 +265,20 @@ theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
 
 #print MvPolynomial.degrees_rename /-
 theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
-    (rename f φ).degrees ⊆ φ.degrees.map f := by classical
+    (rename f φ).degrees ⊆ φ.degrees.map f := by
+  classical
+  intro i
+  rw [mem_degrees, Multiset.mem_map]
+  rintro ⟨d, hd, hi⟩
+  obtain ⟨x, rfl, hx⟩ := coeff_rename_ne_zero _ _ _ hd
+  simp only [map_domain, Finsupp.mem_support_iff] at hi 
+  rw [sum_apply, Finsupp.sum] at hi 
+  contrapose! hi
+  rw [Finset.sum_eq_zero]
+  intro j hj
+  simp only [exists_prop, mem_degrees] at hi 
+  specialize hi j ⟨x, hx, hj⟩
+  rw [single_apply, if_neg hi]
 #align mv_polynomial.degrees_rename MvPolynomial.degrees_rename
 -/
 
@@ -226,7 +291,12 @@ theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R
 
 #print MvPolynomial.degrees_rename_of_injective /-
 theorem degrees_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f) :
-    degrees (rename f p) = (degrees p).map f := by classical
+    degrees (rename f p) = (degrees p).map f := by
+  classical
+  simp only [degrees, Multiset.map_finset_sup p.support Finsupp.toMultiset f h,
+    support_rename_of_injective h, Finset.sup_image]
+  refine' Finset.sup_congr rfl fun x hx => _
+  exact (Finsupp.toMultiset_map _ _).symm
 #align mv_polynomial.degrees_rename_of_injective MvPolynomial.degrees_rename_of_injective
 -/
 
@@ -253,19 +323,22 @@ theorem vars_def [DecidableEq σ] (p : MvPolynomial σ R) : p.vars = p.degrees.t
 
 #print MvPolynomial.vars_0 /-
 @[simp]
-theorem vars_0 : (0 : MvPolynomial σ R).vars = ∅ := by classical
+theorem vars_0 : (0 : MvPolynomial σ R).vars = ∅ := by
+  classical rw [vars_def, degrees_zero, Multiset.toFinset_zero]
 #align mv_polynomial.vars_0 MvPolynomial.vars_0
 -/
 
 #print MvPolynomial.vars_monomial /-
 @[simp]
-theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by classical
+theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by
+  classical rw [vars_def, degrees_monomial_eq _ _ h, Finsupp.toFinset_toMultiset]
 #align mv_polynomial.vars_monomial MvPolynomial.vars_monomial
 -/
 
 #print MvPolynomial.vars_C /-
 @[simp]
-theorem vars_C : (C r : MvPolynomial σ R).vars = ∅ := by classical
+theorem vars_C : (C r : MvPolynomial σ R).vars = ∅ := by
+  classical rw [vars_def, degrees_C, Multiset.toFinset_zero]
 #align mv_polynomial.vars_C MvPolynomial.vars_C
 -/
 
@@ -351,7 +424,14 @@ theorem vars_one : (1 : MvPolynomial σ R).vars = ∅ :=
 -/
 
 #print MvPolynomial.vars_pow /-
-theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars := by classical
+theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars := by
+  classical
+  simp_rw [vars_def]
+  induction' n with n ih
+  · simp
+  · rw [pow_succ]
+    apply Finset.Subset.trans (vars_mul _ _)
+    exact Finset.union_subset (Finset.Subset.refl _) ih
 #align mv_polynomial.vars_pow MvPolynomial.vars_pow
 -/
 
@@ -360,7 +440,14 @@ theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars
 are a subset of the union of the sets of variables of each polynomial.
 -/
 theorem vars_prod {ι : Type _} [DecidableEq σ] {s : Finset ι} (f : ι → MvPolynomial σ R) :
-    (∏ i in s, f i).vars ⊆ s.biUnion fun i => (f i).vars := by classical
+    (∏ i in s, f i).vars ⊆ s.biUnion fun i => (f i).vars := by
+  classical
+  apply s.induction_on
+  · simp
+  · intro a s hs hsub
+    simp only [hs, Finset.biUnion_insert, Finset.prod_insert, not_false_iff]
+    apply Finset.Subset.trans (vars_mul _ _)
+    exact Finset.union_subset_union (Finset.Subset.refl _) hsub
 #align mv_polynomial.vars_prod MvPolynomial.vars_prod
 -/
 
@@ -390,13 +477,35 @@ variable {ι : Type _} (t : Finset ι) (φ : ι → MvPolynomial σ R)
 
 #print MvPolynomial.vars_sum_subset /-
 theorem vars_sum_subset [DecidableEq σ] :
-    (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by classical
+    (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by
+  classical
+  apply t.induction_on
+  · simp
+  · intro a s has hsum
+    rw [Finset.biUnion_insert, Finset.sum_insert has]
+    refine'
+      Finset.Subset.trans (vars_add_subset _ _) (Finset.union_subset_union (Finset.Subset.refl _) _)
+    assumption
 #align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subset
 -/
 
 #print MvPolynomial.vars_sum_of_disjoint /-
 theorem vars_sum_of_disjoint [DecidableEq σ] (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
-    (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars := by classical
+    (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars := by
+  classical
+  apply t.induction_on
+  · simp
+  · intro a s has hsum
+    rw [Finset.biUnion_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
+    unfold Pairwise on_fun at h 
+    rw [hsum]
+    simp only [Finset.disjoint_iff_ne] at h ⊢
+    intro v hv v2 hv2
+    rw [Finset.mem_biUnion] at hv2 
+    rcases hv2 with ⟨i, his, hi⟩
+    refine' h _ _ hv _ hi
+    rintro rfl
+    contradiction
 #align mv_polynomial.vars_sum_of_disjoint MvPolynomial.vars_sum_of_disjoint
 -/
 
@@ -459,7 +568,12 @@ theorem degreeOf_def [DecidableEq σ] (n : σ) (p : MvPolynomial σ R) :
 
 #print MvPolynomial.degreeOf_eq_sup /-
 theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
-    degreeOf n f = f.support.sup fun m => m n := by classical
+    degreeOf n f = f.support.sup fun m => m n := by
+  classical
+  rw [degree_of_def, degrees_def, Multiset.count_finset_sup]
+  congr
+  ext
+  simp
 #align mv_polynomial.degree_of_eq_sup MvPolynomial.degreeOf_eq_sup
 -/
 
@@ -496,7 +610,12 @@ theorem degreeOf_X [DecidableEq σ] (i j : σ) [Nontrivial R] :
 
 #print MvPolynomial.degreeOf_add_le /-
 theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
-    degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) := by classical
+    degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) := by
+  classical
+  repeat' rw [degree_of_def]
+  apply (Multiset.count_le_of_le n (degrees_add f g)).trans
+  dsimp
+  rw [Multiset.count_union]
 #align mv_polynomial.degree_of_add_le MvPolynomial.degreeOf_add_le
 -/
 
@@ -511,26 +630,46 @@ theorem monomial_le_degreeOf (i : σ) {f : MvPolynomial σ R} {m : σ →₀ ℕ
 #print MvPolynomial.degreeOf_mul_le /-
 -- TODO we can prove equality here if R is a domain
 theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
-    degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g := by classical
+    degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g := by
+  classical
+  repeat' rw [degree_of_def]
+  convert Multiset.count_le_of_le i (degrees_mul f g)
+  rw [Multiset.count_add]
 #align mv_polynomial.degree_of_mul_le MvPolynomial.degreeOf_mul_le
 -/
 
 #print MvPolynomial.degreeOf_mul_X_ne /-
 theorem degreeOf_mul_X_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
-    degreeOf i (f * X j) = degreeOf i f := by classical
+    degreeOf i (f * X j) = degreeOf i f := by
+  classical
+  repeat' rw [degree_of_eq_sup i]
+  rw [support_mul_X]
+  simp only [Finset.sup_map]
+  congr
+  ext
+  simp only [single, Nat.one_ne_zero, add_right_eq_self, addRightEmbedding_apply, coe_mk,
+    Pi.add_apply, comp_app, ite_eq_right_iff, Finsupp.coe_add, Pi.single_eq_of_ne h]
 #align mv_polynomial.degree_of_mul_X_ne MvPolynomial.degreeOf_mul_X_ne
 -/
 
 #print MvPolynomial.degreeOf_mul_X_eq /-
 -- TODO in the following we have equality iff f ≠ 0
 theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
-    degreeOf j (f * X j) ≤ degreeOf j f + 1 := by classical
+    degreeOf j (f * X j) ≤ degreeOf j f + 1 := by
+  classical
+  repeat' rw [degree_of_def]
+  apply (Multiset.count_le_of_le j (degrees_mul f (X j))).trans
+  simp only [Multiset.count_add, add_le_add_iff_left]
+  convert Multiset.count_le_of_le j (degrees_X' j)
+  rw [Multiset.count_singleton_self]
 #align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eq
 -/
 
 #print MvPolynomial.degreeOf_rename_of_injective /-
 theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
-    (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by classical
+    (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by
+  classical simp only [degree_of_def, degrees_rename_of_injective h,
+    Multiset.count_map_eq_count' f p.degrees h]
 #align mv_polynomial.degree_of_rename_of_injective MvPolynomial.degreeOf_rename_of_injective
 -/
 
@@ -561,6 +700,8 @@ theorem totalDegree_eq (p : MvPolynomial σ R) :
 #print MvPolynomial.totalDegree_le_degrees_card /-
 theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) : p.totalDegree ≤ p.degrees.card := by
   classical
+  rw [total_degree_eq]
+  exact Finset.sup_le fun s hs => Multiset.card_le_card <| Finset.le_sup hs
 #align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
 -/
 
@@ -603,13 +744,39 @@ theorem totalDegree_X {R} [CommSemiring R] [Nontrivial R] (s : σ) :
 #print MvPolynomial.totalDegree_add /-
 theorem totalDegree_add (a b : MvPolynomial σ R) :
     (a + b).totalDegree ≤ max a.totalDegree b.totalDegree :=
-  Finset.sup_le fun n hn => by classical
+  Finset.sup_le fun n hn => by
+    classical
+    have := Finsupp.support_add hn
+    rw [Finset.mem_union] at this 
+    cases this
+    · exact le_max_of_le_left (Finset.le_sup this)
+    · exact le_max_of_le_right (Finset.le_sup this)
 #align mv_polynomial.total_degree_add MvPolynomial.totalDegree_add
 -/
 
 #print MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt /-
 theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
-    (h : q.totalDegree < p.totalDegree) : (p + q).totalDegree = p.totalDegree := by classical
+    (h : q.totalDegree < p.totalDegree) : (p + q).totalDegree = p.totalDegree := by
+  classical
+  apply le_antisymm
+  · rw [← max_eq_left_of_lt h]
+    exact total_degree_add p q
+  by_cases hp : p = 0
+  · simp [hp]
+  obtain ⟨b, hb₁, hb₂⟩ :=
+    p.support.exists_mem_eq_sup (finsupp.support_nonempty_iff.mpr hp) fun m : σ →₀ ℕ =>
+      m.to_multiset.card
+  have hb : ¬b ∈ q.support := by
+    contrapose! h
+    rw [total_degree_eq p, hb₂, total_degree_eq]
+    apply Finset.le_sup h
+  have hbb : b ∈ (p + q).support :=
+    by
+    apply support_sdiff_support_subset_support_add
+    rw [Finset.mem_sdiff]
+    exact ⟨hb₁, hb⟩
+  rw [total_degree_eq, hb₂, total_degree_eq]
+  exact Finset.le_sup hbb
 #align mv_polynomial.total_degree_add_eq_left_of_total_degree_lt MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt
 -/
 
@@ -623,7 +790,15 @@ theorem totalDegree_add_eq_right_of_totalDegree_lt {p q : MvPolynomial σ R}
 #print MvPolynomial.totalDegree_mul /-
 theorem totalDegree_mul (a b : MvPolynomial σ R) :
     (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
-  Finset.sup_le fun n hn => by classical
+  Finset.sup_le fun n hn => by
+    classical
+    have := AddMonoidAlgebra.support_mul a b hn
+    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this 
+    rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
+    rw [Finsupp.sum_add_index']
+    · exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
+    · intro a; rfl
+    · intro a b₁ b₂; rfl
 #align mv_polynomial.total_degree_mul MvPolynomial.totalDegree_mul
 -/
 
@@ -650,7 +825,8 @@ theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree
 #print MvPolynomial.totalDegree_monomial /-
 @[simp]
 theorem totalDegree_monomial (s : σ →₀ ℕ) {c : R} (hc : c ≠ 0) :
-    (monomial s c : MvPolynomial σ R).totalDegree = s.Sum fun _ e => e := by classical
+    (monomial s c : MvPolynomial σ R).totalDegree = s.Sum fun _ e => e := by
+  classical simp [total_degree, support_monomial, if_neg hc]
 #align mv_polynomial.total_degree_monomial MvPolynomial.totalDegree_monomial
 -/
 
@@ -719,7 +895,12 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
 
 #print MvPolynomial.coeff_eq_zero_of_totalDegree_lt /-
 theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ ℕ}
-    (h : f.totalDegree < ∑ i in d.support, d i) : coeff d f = 0 := by classical
+    (h : f.totalDegree < ∑ i in d.support, d i) : coeff d f = 0 := by
+  classical
+  rw [total_degree, Finset.sup_lt_iff] at h 
+  · specialize h d; rw [mem_support_iff] at h 
+    refine' not_not.mp (mt h _); exact lt_irrefl _
+  · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_lt
 -/
 
@@ -730,6 +911,13 @@ theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     intro h
     rw [rename_eq] at h 
     classical
+    have h' := Finsupp.mapDomain_support h
+    rw [Finset.mem_image] at h' 
+    rcases h' with ⟨s, hs, rfl⟩
+    rw [Finsupp.sum_mapDomain_index]
+    exact le_trans le_rfl (Finset.le_sup hs)
+    exact fun _ => rfl
+    exact fun _ _ _ => rfl
 #align mv_polynomial.total_degree_rename_le MvPolynomial.totalDegree_rename_le
 -/
 
@@ -841,7 +1029,8 @@ theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
 
 #print MvPolynomial.mem_vars_rename /-
 theorem mem_vars_rename (f : σ → τ) (φ : MvPolynomial σ R) {j : τ} (h : j ∈ (rename f φ).vars) :
-    ∃ i : σ, i ∈ φ.vars ∧ f i = j := by classical
+    ∃ i : σ, i ∈ φ.vars ∧ f i = j := by
+  classical simpa only [exists_prop, Finset.mem_image] using vars_rename f φ h
 #align mv_polynomial.mem_vars_rename MvPolynomial.mem_vars_rename
 -/
 

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

@@ -102,19 +102,12 @@ theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
 #print MvPolynomial.degrees_monomial /-
 theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ s.toMultiset := by
   classical
-  refine' Finset.sup_le fun t h => _
-  have := Finsupp.support_single_subset h
-  rw [Finset.mem_singleton] at this 
-  rw [this]
 #align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomial
 -/
 
 #print MvPolynomial.degrees_monomial_eq /-
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
-    degrees (monomial s a) = s.toMultiset := by
-  classical
-  refine' le_antisymm (degrees_monomial s a) <| Finset.le_sup <| _
-  rw [support_monomial, if_neg ha, Finset.mem_singleton]
+    degrees (monomial s a) = s.toMultiset := by classical
 #align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eq
 -/
 
@@ -152,51 +145,25 @@ theorem degrees_one : degrees (1 : MvPolynomial σ R) = 0 :=
 
 #print MvPolynomial.degrees_add /-
 theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
-    (p + q).degrees ≤ p.degrees ⊔ q.degrees := by
-  classical
-  simp_rw [degrees_def]
-  refine' Finset.sup_le fun b hb => _
-  have := Finsupp.support_add hb
-  rw [Finset.mem_union] at this 
-  cases this
-  · exact le_sup_of_le_left (Finset.le_sup this)
-  · exact le_sup_of_le_right (Finset.le_sup this)
+    (p + q).degrees ≤ p.degrees ⊔ q.degrees := by classical
 #align mv_polynomial.degrees_add MvPolynomial.degrees_add
 -/
 
 #print MvPolynomial.degrees_sum /-
 theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → MvPolynomial σ R) :
-    (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by
-  classical
-  refine' s.induction _ _
-  · simp only [Finset.sum_empty, Finset.sup_empty, degrees_zero]; exact le_rfl
-  · intro i s his ih
-    rw [Finset.sup_insert, Finset.sum_insert his]
-    exact le_trans (degrees_add _ _) (sup_le_sup_left ih _)
+    (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by classical
 #align mv_polynomial.degrees_sum MvPolynomial.degrees_sum
 -/
 
 #print MvPolynomial.degrees_mul /-
 theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees := by
   classical
-  refine' Finset.sup_le fun b hb => _
-  have := support_mul p q hb
-  simp only [Finset.mem_biUnion, Finset.mem_singleton] at this 
-  rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
-  rw [Finsupp.toMultiset_add]
-  exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
 #align mv_polynomial.degrees_mul MvPolynomial.degrees_mul
 -/
 
 #print MvPolynomial.degrees_prod /-
 theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
-    (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees := by
-  classical
-  refine' s.induction _ _
-  · simp only [Finset.prod_empty, Finset.sum_empty, degrees_one]
-  · intro i s his ih
-    rw [Finset.prod_insert his, Finset.sum_insert his]
-    exact le_trans (degrees_mul _ _) (add_le_add_left ih _)
+    (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees := by classical
 #align mv_polynomial.degrees_prod MvPolynomial.degrees_prod
 -/
 
@@ -218,26 +185,7 @@ theorem mem_degrees {p : MvPolynomial σ R} {i : σ} :
 
 #print MvPolynomial.le_degrees_add /-
 theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degrees) :
-    p.degrees ≤ (p + q).degrees := by
-  classical
-  apply Finset.sup_le
-  intro d hd
-  rw [Multiset.disjoint_iff_ne] at h 
-  rw [Multiset.le_iff_count]
-  intro i
-  rw [degrees, Multiset.count_finset_sup]
-  simp only [Finsupp.count_toMultiset]
-  by_cases h0 : d = 0
-  · simp only [h0, zero_le, Finsupp.zero_apply]
-  · refine' @Finset.le_sup _ _ _ _ (p + q).support _ d _
-    rw [mem_support_iff, coeff_add]
-    suffices q.coeff d = 0 by rwa [this, add_zero, coeff, ← Finsupp.mem_support_iff]
-    rw [← Finsupp.support_eq_empty, ← Ne.def, ← Finset.nonempty_iff_ne_empty] at h0 
-    obtain ⟨j, hj⟩ := h0
-    contrapose! h
-    rw [mem_support_iff] at hd 
-    refine' ⟨j, _, j, _, rfl⟩
-    all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
+    p.degrees ≤ (p + q).degrees := by classical
 #align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_add
 -/
 
@@ -265,20 +213,7 @@ theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
 
 #print MvPolynomial.degrees_rename /-
 theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
-    (rename f φ).degrees ⊆ φ.degrees.map f := by
-  classical
-  intro i
-  rw [mem_degrees, Multiset.mem_map]
-  rintro ⟨d, hd, hi⟩
-  obtain ⟨x, rfl, hx⟩ := coeff_rename_ne_zero _ _ _ hd
-  simp only [map_domain, Finsupp.mem_support_iff] at hi 
-  rw [sum_apply, Finsupp.sum] at hi 
-  contrapose! hi
-  rw [Finset.sum_eq_zero]
-  intro j hj
-  simp only [exists_prop, mem_degrees] at hi 
-  specialize hi j ⟨x, hx, hj⟩
-  rw [single_apply, if_neg hi]
+    (rename f φ).degrees ⊆ φ.degrees.map f := by classical
 #align mv_polynomial.degrees_rename MvPolynomial.degrees_rename
 -/
 
@@ -291,12 +226,7 @@ theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R
 
 #print MvPolynomial.degrees_rename_of_injective /-
 theorem degrees_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f) :
-    degrees (rename f p) = (degrees p).map f := by
-  classical
-  simp only [degrees, Multiset.map_finset_sup p.support Finsupp.toMultiset f h,
-    support_rename_of_injective h, Finset.sup_image]
-  refine' Finset.sup_congr rfl fun x hx => _
-  exact (Finsupp.toMultiset_map _ _).symm
+    degrees (rename f p) = (degrees p).map f := by classical
 #align mv_polynomial.degrees_rename_of_injective MvPolynomial.degrees_rename_of_injective
 -/
 
@@ -323,22 +253,19 @@ theorem vars_def [DecidableEq σ] (p : MvPolynomial σ R) : p.vars = p.degrees.t
 
 #print MvPolynomial.vars_0 /-
 @[simp]
-theorem vars_0 : (0 : MvPolynomial σ R).vars = ∅ := by
-  classical rw [vars_def, degrees_zero, Multiset.toFinset_zero]
+theorem vars_0 : (0 : MvPolynomial σ R).vars = ∅ := by classical
 #align mv_polynomial.vars_0 MvPolynomial.vars_0
 -/
 
 #print MvPolynomial.vars_monomial /-
 @[simp]
-theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by
-  classical rw [vars_def, degrees_monomial_eq _ _ h, Finsupp.toFinset_toMultiset]
+theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by classical
 #align mv_polynomial.vars_monomial MvPolynomial.vars_monomial
 -/
 
 #print MvPolynomial.vars_C /-
 @[simp]
-theorem vars_C : (C r : MvPolynomial σ R).vars = ∅ := by
-  classical rw [vars_def, degrees_C, Multiset.toFinset_zero]
+theorem vars_C : (C r : MvPolynomial σ R).vars = ∅ := by classical
 #align mv_polynomial.vars_C MvPolynomial.vars_C
 -/
 
@@ -424,14 +351,7 @@ theorem vars_one : (1 : MvPolynomial σ R).vars = ∅ :=
 -/
 
 #print MvPolynomial.vars_pow /-
-theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars := by
-  classical
-  simp_rw [vars_def]
-  induction' n with n ih
-  · simp
-  · rw [pow_succ]
-    apply Finset.Subset.trans (vars_mul _ _)
-    exact Finset.union_subset (Finset.Subset.refl _) ih
+theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars := by classical
 #align mv_polynomial.vars_pow MvPolynomial.vars_pow
 -/
 
@@ -440,14 +360,7 @@ theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars
 are a subset of the union of the sets of variables of each polynomial.
 -/
 theorem vars_prod {ι : Type _} [DecidableEq σ] {s : Finset ι} (f : ι → MvPolynomial σ R) :
-    (∏ i in s, f i).vars ⊆ s.biUnion fun i => (f i).vars := by
-  classical
-  apply s.induction_on
-  · simp
-  · intro a s hs hsub
-    simp only [hs, Finset.biUnion_insert, Finset.prod_insert, not_false_iff]
-    apply Finset.Subset.trans (vars_mul _ _)
-    exact Finset.union_subset_union (Finset.Subset.refl _) hsub
+    (∏ i in s, f i).vars ⊆ s.biUnion fun i => (f i).vars := by classical
 #align mv_polynomial.vars_prod MvPolynomial.vars_prod
 -/
 
@@ -477,35 +390,13 @@ variable {ι : Type _} (t : Finset ι) (φ : ι → MvPolynomial σ R)
 
 #print MvPolynomial.vars_sum_subset /-
 theorem vars_sum_subset [DecidableEq σ] :
-    (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by
-  classical
-  apply t.induction_on
-  · simp
-  · intro a s has hsum
-    rw [Finset.biUnion_insert, Finset.sum_insert has]
-    refine'
-      Finset.Subset.trans (vars_add_subset _ _) (Finset.union_subset_union (Finset.Subset.refl _) _)
-    assumption
+    (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by classical
 #align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subset
 -/
 
 #print MvPolynomial.vars_sum_of_disjoint /-
 theorem vars_sum_of_disjoint [DecidableEq σ] (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
-    (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars := by
-  classical
-  apply t.induction_on
-  · simp
-  · intro a s has hsum
-    rw [Finset.biUnion_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
-    unfold Pairwise on_fun at h 
-    rw [hsum]
-    simp only [Finset.disjoint_iff_ne] at h ⊢
-    intro v hv v2 hv2
-    rw [Finset.mem_biUnion] at hv2 
-    rcases hv2 with ⟨i, his, hi⟩
-    refine' h _ _ hv _ hi
-    rintro rfl
-    contradiction
+    (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars := by classical
 #align mv_polynomial.vars_sum_of_disjoint MvPolynomial.vars_sum_of_disjoint
 -/
 
@@ -568,12 +459,7 @@ theorem degreeOf_def [DecidableEq σ] (n : σ) (p : MvPolynomial σ R) :
 
 #print MvPolynomial.degreeOf_eq_sup /-
 theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
-    degreeOf n f = f.support.sup fun m => m n := by
-  classical
-  rw [degree_of_def, degrees_def, Multiset.count_finset_sup]
-  congr
-  ext
-  simp
+    degreeOf n f = f.support.sup fun m => m n := by classical
 #align mv_polynomial.degree_of_eq_sup MvPolynomial.degreeOf_eq_sup
 -/
 
@@ -610,12 +496,7 @@ theorem degreeOf_X [DecidableEq σ] (i j : σ) [Nontrivial R] :
 
 #print MvPolynomial.degreeOf_add_le /-
 theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
-    degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) := by
-  classical
-  repeat' rw [degree_of_def]
-  apply (Multiset.count_le_of_le n (degrees_add f g)).trans
-  dsimp
-  rw [Multiset.count_union]
+    degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) := by classical
 #align mv_polynomial.degree_of_add_le MvPolynomial.degreeOf_add_le
 -/
 
@@ -630,46 +511,26 @@ theorem monomial_le_degreeOf (i : σ) {f : MvPolynomial σ R} {m : σ →₀ ℕ
 #print MvPolynomial.degreeOf_mul_le /-
 -- TODO we can prove equality here if R is a domain
 theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
-    degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g := by
-  classical
-  repeat' rw [degree_of_def]
-  convert Multiset.count_le_of_le i (degrees_mul f g)
-  rw [Multiset.count_add]
+    degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g := by classical
 #align mv_polynomial.degree_of_mul_le MvPolynomial.degreeOf_mul_le
 -/
 
 #print MvPolynomial.degreeOf_mul_X_ne /-
 theorem degreeOf_mul_X_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
-    degreeOf i (f * X j) = degreeOf i f := by
-  classical
-  repeat' rw [degree_of_eq_sup i]
-  rw [support_mul_X]
-  simp only [Finset.sup_map]
-  congr
-  ext
-  simp only [single, Nat.one_ne_zero, add_right_eq_self, addRightEmbedding_apply, coe_mk,
-    Pi.add_apply, comp_app, ite_eq_right_iff, Finsupp.coe_add, Pi.single_eq_of_ne h]
+    degreeOf i (f * X j) = degreeOf i f := by classical
 #align mv_polynomial.degree_of_mul_X_ne MvPolynomial.degreeOf_mul_X_ne
 -/
 
 #print MvPolynomial.degreeOf_mul_X_eq /-
 -- TODO in the following we have equality iff f ≠ 0
 theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
-    degreeOf j (f * X j) ≤ degreeOf j f + 1 := by
-  classical
-  repeat' rw [degree_of_def]
-  apply (Multiset.count_le_of_le j (degrees_mul f (X j))).trans
-  simp only [Multiset.count_add, add_le_add_iff_left]
-  convert Multiset.count_le_of_le j (degrees_X' j)
-  rw [Multiset.count_singleton_self]
+    degreeOf j (f * X j) ≤ degreeOf j f + 1 := by classical
 #align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eq
 -/
 
 #print MvPolynomial.degreeOf_rename_of_injective /-
 theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
-    (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by
-  classical simp only [degree_of_def, degrees_rename_of_injective h,
-    Multiset.count_map_eq_count' f p.degrees h]
+    (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by classical
 #align mv_polynomial.degree_of_rename_of_injective MvPolynomial.degreeOf_rename_of_injective
 -/
 
@@ -700,8 +561,6 @@ theorem totalDegree_eq (p : MvPolynomial σ R) :
 #print MvPolynomial.totalDegree_le_degrees_card /-
 theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) : p.totalDegree ≤ p.degrees.card := by
   classical
-  rw [total_degree_eq]
-  exact Finset.sup_le fun s hs => Multiset.card_le_card <| Finset.le_sup hs
 #align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
 -/
 
@@ -744,39 +603,13 @@ theorem totalDegree_X {R} [CommSemiring R] [Nontrivial R] (s : σ) :
 #print MvPolynomial.totalDegree_add /-
 theorem totalDegree_add (a b : MvPolynomial σ R) :
     (a + b).totalDegree ≤ max a.totalDegree b.totalDegree :=
-  Finset.sup_le fun n hn => by
-    classical
-    have := Finsupp.support_add hn
-    rw [Finset.mem_union] at this 
-    cases this
-    · exact le_max_of_le_left (Finset.le_sup this)
-    · exact le_max_of_le_right (Finset.le_sup this)
+  Finset.sup_le fun n hn => by classical
 #align mv_polynomial.total_degree_add MvPolynomial.totalDegree_add
 -/
 
 #print MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt /-
 theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
-    (h : q.totalDegree < p.totalDegree) : (p + q).totalDegree = p.totalDegree := by
-  classical
-  apply le_antisymm
-  · rw [← max_eq_left_of_lt h]
-    exact total_degree_add p q
-  by_cases hp : p = 0
-  · simp [hp]
-  obtain ⟨b, hb₁, hb₂⟩ :=
-    p.support.exists_mem_eq_sup (finsupp.support_nonempty_iff.mpr hp) fun m : σ →₀ ℕ =>
-      m.to_multiset.card
-  have hb : ¬b ∈ q.support := by
-    contrapose! h
-    rw [total_degree_eq p, hb₂, total_degree_eq]
-    apply Finset.le_sup h
-  have hbb : b ∈ (p + q).support :=
-    by
-    apply support_sdiff_support_subset_support_add
-    rw [Finset.mem_sdiff]
-    exact ⟨hb₁, hb⟩
-  rw [total_degree_eq, hb₂, total_degree_eq]
-  exact Finset.le_sup hbb
+    (h : q.totalDegree < p.totalDegree) : (p + q).totalDegree = p.totalDegree := by classical
 #align mv_polynomial.total_degree_add_eq_left_of_total_degree_lt MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt
 -/
 
@@ -790,15 +623,7 @@ theorem totalDegree_add_eq_right_of_totalDegree_lt {p q : MvPolynomial σ R}
 #print MvPolynomial.totalDegree_mul /-
 theorem totalDegree_mul (a b : MvPolynomial σ R) :
     (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
-  Finset.sup_le fun n hn => by
-    classical
-    have := AddMonoidAlgebra.support_mul a b hn
-    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this 
-    rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
-    rw [Finsupp.sum_add_index']
-    · exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
-    · intro a; rfl
-    · intro a b₁ b₂; rfl
+  Finset.sup_le fun n hn => by classical
 #align mv_polynomial.total_degree_mul MvPolynomial.totalDegree_mul
 -/
 
@@ -825,8 +650,7 @@ theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree
 #print MvPolynomial.totalDegree_monomial /-
 @[simp]
 theorem totalDegree_monomial (s : σ →₀ ℕ) {c : R} (hc : c ≠ 0) :
-    (monomial s c : MvPolynomial σ R).totalDegree = s.Sum fun _ e => e := by
-  classical simp [total_degree, support_monomial, if_neg hc]
+    (monomial s c : MvPolynomial σ R).totalDegree = s.Sum fun _ e => e := by classical
 #align mv_polynomial.total_degree_monomial MvPolynomial.totalDegree_monomial
 -/
 
@@ -895,12 +719,7 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
 
 #print MvPolynomial.coeff_eq_zero_of_totalDegree_lt /-
 theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ ℕ}
-    (h : f.totalDegree < ∑ i in d.support, d i) : coeff d f = 0 := by
-  classical
-  rw [total_degree, Finset.sup_lt_iff] at h 
-  · specialize h d; rw [mem_support_iff] at h 
-    refine' not_not.mp (mt h _); exact lt_irrefl _
-  · exact lt_of_le_of_lt (Nat.zero_le _) h
+    (h : f.totalDegree < ∑ i in d.support, d i) : coeff d f = 0 := by classical
 #align mv_polynomial.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_lt
 -/
 
@@ -911,13 +730,6 @@ theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     intro h
     rw [rename_eq] at h 
     classical
-    have h' := Finsupp.mapDomain_support h
-    rw [Finset.mem_image] at h' 
-    rcases h' with ⟨s, hs, rfl⟩
-    rw [Finsupp.sum_mapDomain_index]
-    exact le_trans le_rfl (Finset.le_sup hs)
-    exact fun _ => rfl
-    exact fun _ _ _ => rfl
 #align mv_polynomial.total_degree_rename_le MvPolynomial.totalDegree_rename_le
 -/
 
@@ -1029,8 +841,7 @@ theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
 
 #print MvPolynomial.mem_vars_rename /-
 theorem mem_vars_rename (f : σ → τ) (φ : MvPolynomial σ R) {j : τ} (h : j ∈ (rename f φ).vars) :
-    ∃ i : σ, i ∈ φ.vars ∧ f i = j := by
-  classical simpa only [exists_prop, Finset.mem_image] using vars_rename f φ h
+    ∃ i : σ, i ∈ φ.vars ∧ f i = j := by classical
 #align mv_polynomial.mem_vars_rename MvPolynomial.mem_vars_rename
 -/
 

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

@@ -701,7 +701,7 @@ theorem totalDegree_eq (p : MvPolynomial σ R) :
 theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) : p.totalDegree ≤ p.degrees.card := by
   classical
   rw [total_degree_eq]
-  exact Finset.sup_le fun s hs => Multiset.card_le_of_le <| Finset.le_sup hs
+  exact Finset.sup_le fun s hs => Multiset.card_le_card <| Finset.le_sup hs
 #align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 -/
-import Mathbin.Algebra.BigOperators.Order
-import Mathbin.Data.MvPolynomial.Rename
+import Algebra.BigOperators.Order
+import Data.MvPolynomial.Rename
 
 #align_import data.mv_polynomial.variables from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-
-! This file was ported from Lean 3 source module data.mv_polynomial.variables
-! 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.Algebra.BigOperators.Order
 import Mathbin.Data.MvPolynomial.Rename
 
+#align_import data.mv_polynomial.variables from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
+
 /-!
 # Degrees and variables of polynomials
 

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

@@ -96,10 +96,13 @@ def degrees (p : MvPolynomial σ R) : Multiset σ :=
 #align mv_polynomial.degrees MvPolynomial.degrees
 -/
 
+#print MvPolynomial.degrees_def /-
 theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
     p.degrees = p.support.sup fun s : σ →₀ ℕ => s.toMultiset := by convert rfl
 #align mv_polynomial.degrees_def MvPolynomial.degrees_def
+-/
 
+#print MvPolynomial.degrees_monomial /-
 theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ s.toMultiset := by
   classical
   refine' Finset.sup_le fun t h => _
@@ -107,36 +110,50 @@ theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) 
   rw [Finset.mem_singleton] at this 
   rw [this]
 #align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomial
+-/
 
+#print MvPolynomial.degrees_monomial_eq /-
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
     degrees (monomial s a) = s.toMultiset := by
   classical
   refine' le_antisymm (degrees_monomial s a) <| Finset.le_sup <| _
   rw [support_monomial, if_neg ha, Finset.mem_singleton]
 #align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eq
+-/
 
+#print MvPolynomial.degrees_C /-
 theorem degrees_C (a : R) : degrees (C a : MvPolynomial σ R) = 0 :=
   Multiset.le_zero.1 <| degrees_monomial _ _
 #align mv_polynomial.degrees_C MvPolynomial.degrees_C
+-/
 
+#print MvPolynomial.degrees_X' /-
 theorem degrees_X' (n : σ) : degrees (X n : MvPolynomial σ R) ≤ {n} :=
   le_trans (degrees_monomial _ _) <| le_of_eq <| toMultiset_single _ _
 #align mv_polynomial.degrees_X' MvPolynomial.degrees_X'
+-/
 
+#print MvPolynomial.degrees_X /-
 @[simp]
 theorem degrees_X [Nontrivial R] (n : σ) : degrees (X n : MvPolynomial σ R) = {n} :=
   (degrees_monomial_eq _ (1 : R) one_ne_zero).trans (toMultiset_single _ _)
 #align mv_polynomial.degrees_X MvPolynomial.degrees_X
+-/
 
+#print MvPolynomial.degrees_zero /-
 @[simp]
 theorem degrees_zero : degrees (0 : MvPolynomial σ R) = 0 := by rw [← C_0]; exact degrees_C 0
 #align mv_polynomial.degrees_zero MvPolynomial.degrees_zero
+-/
 
+#print MvPolynomial.degrees_one /-
 @[simp]
 theorem degrees_one : degrees (1 : MvPolynomial σ R) = 0 :=
   degrees_C 1
 #align mv_polynomial.degrees_one MvPolynomial.degrees_one
+-/
 
+#print MvPolynomial.degrees_add /-
 theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
     (p + q).degrees ≤ p.degrees ⊔ q.degrees := by
   classical
@@ -148,7 +165,9 @@ theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
   · exact le_sup_of_le_left (Finset.le_sup this)
   · exact le_sup_of_le_right (Finset.le_sup this)
 #align mv_polynomial.degrees_add MvPolynomial.degrees_add
+-/
 
+#print MvPolynomial.degrees_sum /-
 theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by
   classical
@@ -158,7 +177,9 @@ theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → M
     rw [Finset.sup_insert, Finset.sum_insert his]
     exact le_trans (degrees_add _ _) (sup_le_sup_left ih _)
 #align mv_polynomial.degrees_sum MvPolynomial.degrees_sum
+-/
 
+#print MvPolynomial.degrees_mul /-
 theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees := by
   classical
   refine' Finset.sup_le fun b hb => _
@@ -168,7 +189,9 @@ theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees +
   rw [Finsupp.toMultiset_add]
   exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
 #align mv_polynomial.degrees_mul MvPolynomial.degrees_mul
+-/
 
+#print MvPolynomial.degrees_prod /-
 theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees := by
   classical
@@ -178,19 +201,25 @@ theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R
     rw [Finset.prod_insert his, Finset.sum_insert his]
     exact le_trans (degrees_mul _ _) (add_le_add_left ih _)
 #align mv_polynomial.degrees_prod MvPolynomial.degrees_prod
+-/
 
+#print MvPolynomial.degrees_pow /-
 theorem degrees_pow (p : MvPolynomial σ R) : ∀ n : ℕ, (p ^ n).degrees ≤ n • p.degrees
   | 0 => by rw [pow_zero, degrees_one]; exact Multiset.zero_le _
   | n + 1 => by
     rw [pow_succ, add_smul, add_comm, one_smul]
     exact le_trans (degrees_mul _ _) (add_le_add_left (degrees_pow n) _)
 #align mv_polynomial.degrees_pow MvPolynomial.degrees_pow
+-/
 
+#print MvPolynomial.mem_degrees /-
 theorem mem_degrees {p : MvPolynomial σ R} {i : σ} :
     i ∈ p.degrees ↔ ∃ d, p.coeff d ≠ 0 ∧ i ∈ d.support := by
   simp only [degrees, Multiset.mem_sup, ← mem_support_iff, Finsupp.mem_toMultiset, exists_prop]
 #align mv_polynomial.mem_degrees MvPolynomial.mem_degrees
+-/
 
+#print MvPolynomial.le_degrees_add /-
 theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degrees) :
     p.degrees ≤ (p + q).degrees := by
   classical
@@ -213,7 +242,9 @@ theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degre
     refine' ⟨j, _, j, _, rfl⟩
     all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
 #align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_add
+-/
 
+#print MvPolynomial.degrees_add_of_disjoint /-
 theorem degrees_add_of_disjoint [DecidableEq σ] {p q : MvPolynomial σ R}
     (h : Multiset.Disjoint p.degrees q.degrees) : (p + q).degrees = p.degrees ∪ q.degrees :=
   by
@@ -223,7 +254,9 @@ theorem degrees_add_of_disjoint [DecidableEq σ] {p q : MvPolynomial σ R}
     · apply le_degrees_add h
     · rw [add_comm]; apply le_degrees_add h.symm
 #align mv_polynomial.degrees_add_of_disjoint MvPolynomial.degrees_add_of_disjoint
+-/
 
+#print MvPolynomial.degrees_map /-
 theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
     (map f p).degrees ⊆ p.degrees := by
   dsimp only [degrees]
@@ -231,7 +264,9 @@ theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
   apply Finset.sup_mono
   apply MvPolynomial.support_map_subset
 #align mv_polynomial.degrees_map MvPolynomial.degrees_map
+-/
 
+#print MvPolynomial.degrees_rename /-
 theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).degrees ⊆ φ.degrees.map f := by
   classical
@@ -248,12 +283,16 @@ theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
   specialize hi j ⟨x, hx, hj⟩
   rw [single_apply, if_neg hi]
 #align mv_polynomial.degrees_rename MvPolynomial.degrees_rename
+-/
 
+#print MvPolynomial.degrees_map_of_injective /-
 theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R →+* S}
     (hf : Injective f) : (map f p).degrees = p.degrees := by
   simp only [degrees, MvPolynomial.support_map_of_injective _ hf]
 #align mv_polynomial.degrees_map_of_injective MvPolynomial.degrees_map_of_injective
+-/
 
+#print MvPolynomial.degrees_rename_of_injective /-
 theorem degrees_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f) :
     degrees (rename f p) = (degrees p).map f := by
   classical
@@ -262,6 +301,7 @@ theorem degrees_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h :
   refine' Finset.sup_congr rfl fun x hx => _
   exact (Finsupp.toMultiset_map _ _).symm
 #align mv_polynomial.degrees_rename_of_injective MvPolynomial.degrees_rename_of_injective
+-/
 
 end Degrees
 
@@ -278,34 +318,47 @@ def vars (p : MvPolynomial σ R) : Finset σ :=
 #align mv_polynomial.vars MvPolynomial.vars
 -/
 
+#print MvPolynomial.vars_def /-
 theorem vars_def [DecidableEq σ] (p : MvPolynomial σ R) : p.vars = p.degrees.toFinset := by
   convert rfl
 #align mv_polynomial.vars_def MvPolynomial.vars_def
+-/
 
+#print MvPolynomial.vars_0 /-
 @[simp]
 theorem vars_0 : (0 : MvPolynomial σ R).vars = ∅ := by
   classical rw [vars_def, degrees_zero, Multiset.toFinset_zero]
 #align mv_polynomial.vars_0 MvPolynomial.vars_0
+-/
 
+#print MvPolynomial.vars_monomial /-
 @[simp]
 theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by
   classical rw [vars_def, degrees_monomial_eq _ _ h, Finsupp.toFinset_toMultiset]
 #align mv_polynomial.vars_monomial MvPolynomial.vars_monomial
+-/
 
+#print MvPolynomial.vars_C /-
 @[simp]
 theorem vars_C : (C r : MvPolynomial σ R).vars = ∅ := by
   classical rw [vars_def, degrees_C, Multiset.toFinset_zero]
 #align mv_polynomial.vars_C MvPolynomial.vars_C
+-/
 
+#print MvPolynomial.vars_X /-
 @[simp]
 theorem vars_X [Nontrivial R] : (X n : MvPolynomial σ R).vars = {n} := by
   rw [X, vars_monomial (one_ne_zero' R), Finsupp.support_single_ne_zero _ (one_ne_zero' ℕ)]
 #align mv_polynomial.vars_X MvPolynomial.vars_X
+-/
 
+#print MvPolynomial.mem_vars /-
 theorem mem_vars (i : σ) : i ∈ p.vars ↔ ∃ (d : σ →₀ ℕ) (H : d ∈ p.support), i ∈ d.support := by
   simp only [vars, Multiset.mem_toFinset, mem_degrees, mem_support_iff, exists_prop]
 #align mv_polynomial.mem_vars MvPolynomial.mem_vars
+-/
 
+#print MvPolynomial.mem_support_not_mem_vars_zero /-
 theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ} (H : x ∈ f.support)
     {v : σ} (h : v ∉ vars f) : x v = 0 :=
   by
@@ -320,14 +373,18 @@ theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ
   left
   rwa [← to_finset_to_multiset, Multiset.mem_toFinset] at h 
 #align mv_polynomial.mem_support_not_mem_vars_zero MvPolynomial.mem_support_not_mem_vars_zero
+-/
 
+#print MvPolynomial.vars_add_subset /-
 theorem vars_add_subset [DecidableEq σ] (p q : MvPolynomial σ R) : (p + q).vars ⊆ p.vars ∪ q.vars :=
   by
   intro x hx
   simp only [vars, Finset.mem_union, Multiset.mem_toFinset] at hx ⊢
   simpa using Multiset.mem_of_le (degrees_add _ _) hx
 #align mv_polynomial.vars_add_subset MvPolynomial.vars_add_subset
+-/
 
+#print MvPolynomial.vars_add_of_disjoint /-
 theorem vars_add_of_disjoint [DecidableEq σ] (h : Disjoint p.vars q.vars) :
     (p + q).vars = p.vars ∪ q.vars :=
   by
@@ -337,9 +394,11 @@ theorem vars_add_of_disjoint [DecidableEq σ] (h : Disjoint p.vars q.vars) :
   rw [degrees_add_of_disjoint h, Multiset.toFinset_union]
   exact hx
 #align mv_polynomial.vars_add_of_disjoint MvPolynomial.vars_add_of_disjoint
+-/
 
 section Mul
 
+#print MvPolynomial.vars_mul /-
 theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars ⊆ φ.vars ∪ ψ.vars :=
   by
   intro i
@@ -358,12 +417,16 @@ theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars 
   · suffices coeff d₂ ψ = 0 by simp [this]
     rw [coeff, ← Finsupp.not_mem_support_iff]; intro; solve_by_elim
 #align mv_polynomial.vars_mul MvPolynomial.vars_mul
+-/
 
+#print MvPolynomial.vars_one /-
 @[simp]
 theorem vars_one : (1 : MvPolynomial σ R).vars = ∅ :=
   vars_C
 #align mv_polynomial.vars_one MvPolynomial.vars_one
+-/
 
+#print MvPolynomial.vars_pow /-
 theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars := by
   classical
   simp_rw [vars_def]
@@ -373,7 +436,9 @@ theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars
     apply Finset.Subset.trans (vars_mul _ _)
     exact Finset.union_subset (Finset.Subset.refl _) ih
 #align mv_polynomial.vars_pow MvPolynomial.vars_pow
+-/
 
+#print MvPolynomial.vars_prod /-
 /-- The variables of the product of a family of polynomials
 are a subset of the union of the sets of variables of each polynomial.
 -/
@@ -387,11 +452,13 @@ theorem vars_prod {ι : Type _} [DecidableEq σ] {s : Finset ι} (f : ι → MvP
     apply Finset.Subset.trans (vars_mul _ _)
     exact Finset.union_subset_union (Finset.Subset.refl _) hsub
 #align mv_polynomial.vars_prod MvPolynomial.vars_prod
+-/
 
 section IsDomain
 
 variable {A : Type _} [CommRing A] [IsDomain A]
 
+#print MvPolynomial.vars_C_mul /-
 theorem vars_C_mul (a : A) (ha : a ≠ 0) (φ : MvPolynomial σ A) : (C a * φ).vars = φ.vars :=
   by
   ext1 i
@@ -401,6 +468,7 @@ theorem vars_C_mul (a : A) (ha : a ≠ 0) (φ : MvPolynomial σ A) : (C a * φ).
   apply and_congr _ Iff.rfl
   rw [coeff_C_mul, mul_ne_zero_iff, eq_true ha, true_and_iff]
 #align mv_polynomial.vars_C_mul MvPolynomial.vars_C_mul
+-/
 
 end IsDomain
 
@@ -410,6 +478,7 @@ section Sum
 
 variable {ι : Type _} (t : Finset ι) (φ : ι → MvPolynomial σ R)
 
+#print MvPolynomial.vars_sum_subset /-
 theorem vars_sum_subset [DecidableEq σ] :
     (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by
   classical
@@ -421,7 +490,9 @@ theorem vars_sum_subset [DecidableEq σ] :
       Finset.Subset.trans (vars_add_subset _ _) (Finset.union_subset_union (Finset.Subset.refl _) _)
     assumption
 #align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subset
+-/
 
+#print MvPolynomial.vars_sum_of_disjoint /-
 theorem vars_sum_of_disjoint [DecidableEq σ] (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
     (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars := by
   classical
@@ -439,6 +510,7 @@ theorem vars_sum_of_disjoint [DecidableEq σ] (h : Pairwise <| (Disjoint on fun
     rintro rfl
     contradiction
 #align mv_polynomial.vars_sum_of_disjoint MvPolynomial.vars_sum_of_disjoint
+-/
 
 end Sum
 
@@ -448,23 +520,31 @@ variable [CommSemiring S] (f : R →+* S)
 
 variable (p)
 
+#print MvPolynomial.vars_map /-
 theorem vars_map : (map f p).vars ⊆ p.vars := by simp [vars, degrees_map]
 #align mv_polynomial.vars_map MvPolynomial.vars_map
+-/
 
 variable {f}
 
+#print MvPolynomial.vars_map_of_injective /-
 theorem vars_map_of_injective (hf : Injective f) : (map f p).vars = p.vars := by
   simp [vars, degrees_map_of_injective _ hf]
 #align mv_polynomial.vars_map_of_injective MvPolynomial.vars_map_of_injective
+-/
 
+#print MvPolynomial.vars_monomial_single /-
 theorem vars_monomial_single (i : σ) {e : ℕ} {r : R} (he : e ≠ 0) (hr : r ≠ 0) :
     (monomial (Finsupp.single i e) r).vars = {i} := by
   rw [vars_monomial hr, Finsupp.support_single_ne_zero _ he]
 #align mv_polynomial.vars_monomial_single MvPolynomial.vars_monomial_single
+-/
 
+#print MvPolynomial.vars_eq_support_biUnion_support /-
 theorem vars_eq_support_biUnion_support [DecidableEq σ] :
     p.vars = p.support.biUnion Finsupp.support := by ext i; rw [mem_vars, Finset.mem_biUnion]
 #align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_biUnion_support
+-/
 
 end Map
 
@@ -483,10 +563,13 @@ def degreeOf (n : σ) (p : MvPolynomial σ R) : ℕ :=
 #align mv_polynomial.degree_of MvPolynomial.degreeOf
 -/
 
+#print MvPolynomial.degreeOf_def /-
 theorem degreeOf_def [DecidableEq σ] (n : σ) (p : MvPolynomial σ R) :
     p.degreeOf n = p.degrees.count n := by convert rfl
 #align mv_polynomial.degree_of_def MvPolynomial.degreeOf_def
+-/
 
+#print MvPolynomial.degreeOf_eq_sup /-
 theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
     degreeOf n f = f.support.sup fun m => m n := by
   classical
@@ -495,22 +578,30 @@ theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
   ext
   simp
 #align mv_polynomial.degree_of_eq_sup MvPolynomial.degreeOf_eq_sup
+-/
 
+#print MvPolynomial.degreeOf_lt_iff /-
 theorem degreeOf_lt_iff {n : σ} {f : MvPolynomial σ R} {d : ℕ} (h : 0 < d) :
     degreeOf n f < d ↔ ∀ m : σ →₀ ℕ, m ∈ f.support → m n < d := by
   rwa [degree_of_eq_sup n f, Finset.sup_lt_iff]
 #align mv_polynomial.degree_of_lt_iff MvPolynomial.degreeOf_lt_iff
+-/
 
+#print MvPolynomial.degreeOf_zero /-
 @[simp]
 theorem degreeOf_zero (n : σ) : degreeOf n (0 : MvPolynomial σ R) = 0 := by
   simp only [degree_of, degrees_zero, Multiset.count_zero]
 #align mv_polynomial.degree_of_zero MvPolynomial.degreeOf_zero
+-/
 
+#print MvPolynomial.degreeOf_C /-
 @[simp]
 theorem degreeOf_C (a : R) (x : σ) : degreeOf x (C a : MvPolynomial σ R) = 0 := by
   simp [degree_of, degrees_C]
 #align mv_polynomial.degree_of_C MvPolynomial.degreeOf_C
+-/
 
+#print MvPolynomial.degreeOf_X /-
 theorem degreeOf_X [DecidableEq σ] (i j : σ) [Nontrivial R] :
     degreeOf i (X j : MvPolynomial σ R) = if i = j then 1 else 0 :=
   by
@@ -518,7 +609,9 @@ theorem degreeOf_X [DecidableEq σ] (i j : σ) [Nontrivial R] :
   · simp only [c, if_true, eq_self_iff_true, degree_of, degrees_X, Multiset.count_singleton]
   simp [c, if_false, degree_of, degrees_X]
 #align mv_polynomial.degree_of_X MvPolynomial.degreeOf_X
+-/
 
+#print MvPolynomial.degreeOf_add_le /-
 theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
     degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) := by
   classical
@@ -527,13 +620,17 @@ theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
   dsimp
   rw [Multiset.count_union]
 #align mv_polynomial.degree_of_add_le MvPolynomial.degreeOf_add_le
+-/
 
+#print MvPolynomial.monomial_le_degreeOf /-
 theorem monomial_le_degreeOf (i : σ) {f : MvPolynomial σ R} {m : σ →₀ ℕ} (h_m : m ∈ f.support) :
     m i ≤ degreeOf i f := by
   rw [degree_of_eq_sup i]
   apply Finset.le_sup h_m
 #align mv_polynomial.monomial_le_degree_of MvPolynomial.monomial_le_degreeOf
+-/
 
+#print MvPolynomial.degreeOf_mul_le /-
 -- TODO we can prove equality here if R is a domain
 theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
     degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g := by
@@ -542,7 +639,9 @@ theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
   convert Multiset.count_le_of_le i (degrees_mul f g)
   rw [Multiset.count_add]
 #align mv_polynomial.degree_of_mul_le MvPolynomial.degreeOf_mul_le
+-/
 
+#print MvPolynomial.degreeOf_mul_X_ne /-
 theorem degreeOf_mul_X_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
     degreeOf i (f * X j) = degreeOf i f := by
   classical
@@ -554,7 +653,9 @@ theorem degreeOf_mul_X_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
   simp only [single, Nat.one_ne_zero, add_right_eq_self, addRightEmbedding_apply, coe_mk,
     Pi.add_apply, comp_app, ite_eq_right_iff, Finsupp.coe_add, Pi.single_eq_of_ne h]
 #align mv_polynomial.degree_of_mul_X_ne MvPolynomial.degreeOf_mul_X_ne
+-/
 
+#print MvPolynomial.degreeOf_mul_X_eq /-
 -- TODO in the following we have equality iff f ≠ 0
 theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
     degreeOf j (f * X j) ≤ degreeOf j f + 1 := by
@@ -565,12 +666,15 @@ theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
   convert Multiset.count_le_of_le j (degrees_X' j)
   rw [Multiset.count_singleton_self]
 #align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eq
+-/
 
+#print MvPolynomial.degreeOf_rename_of_injective /-
 theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
     (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by
   classical simp only [degree_of_def, degrees_rename_of_injective h,
     Multiset.count_map_eq_count' f p.degrees h]
 #align mv_polynomial.degree_of_rename_of_injective MvPolynomial.degreeOf_rename_of_injective
+-/
 
 end DegreeOf
 
@@ -586,6 +690,7 @@ def totalDegree (p : MvPolynomial σ R) : ℕ :=
 #align mv_polynomial.total_degree MvPolynomial.totalDegree
 -/
 
+#print MvPolynomial.totalDegree_eq /-
 theorem totalDegree_eq (p : MvPolynomial σ R) :
     p.totalDegree = p.support.sup fun m => m.toMultiset.card :=
   by
@@ -593,13 +698,17 @@ theorem totalDegree_eq (p : MvPolynomial σ R) :
   congr; funext m
   exact (Finsupp.card_toMultiset _).symm
 #align mv_polynomial.total_degree_eq MvPolynomial.totalDegree_eq
+-/
 
+#print MvPolynomial.totalDegree_le_degrees_card /-
 theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) : p.totalDegree ≤ p.degrees.card := by
   classical
   rw [total_degree_eq]
   exact Finset.sup_le fun s hs => Multiset.card_le_of_le <| Finset.le_sup hs
 #align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
+-/
 
+#print MvPolynomial.totalDegree_C /-
 @[simp]
 theorem totalDegree_C (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
   Nat.eq_zero_of_le_zero <|
@@ -609,16 +718,21 @@ theorem totalDegree_C (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
       subst this
       exact le_rfl
 #align mv_polynomial.total_degree_C MvPolynomial.totalDegree_C
+-/
 
+#print MvPolynomial.totalDegree_zero /-
 @[simp]
 theorem totalDegree_zero : (0 : MvPolynomial σ R).totalDegree = 0 := by
   rw [← C_0] <;> exact total_degree_C (0 : R)
 #align mv_polynomial.total_degree_zero MvPolynomial.totalDegree_zero
+-/
 
+#print MvPolynomial.totalDegree_one /-
 @[simp]
 theorem totalDegree_one : (1 : MvPolynomial σ R).totalDegree = 0 :=
   totalDegree_C (1 : R)
 #align mv_polynomial.total_degree_one MvPolynomial.totalDegree_one
+-/
 
 #print MvPolynomial.totalDegree_X /-
 @[simp]
@@ -630,6 +744,7 @@ theorem totalDegree_X {R} [CommSemiring R] [Nontrivial R] (s : σ) :
 #align mv_polynomial.total_degree_X MvPolynomial.totalDegree_X
 -/
 
+#print MvPolynomial.totalDegree_add /-
 theorem totalDegree_add (a b : MvPolynomial σ R) :
     (a + b).totalDegree ≤ max a.totalDegree b.totalDegree :=
   Finset.sup_le fun n hn => by
@@ -640,7 +755,9 @@ theorem totalDegree_add (a b : MvPolynomial σ R) :
     · exact le_max_of_le_left (Finset.le_sup this)
     · exact le_max_of_le_right (Finset.le_sup this)
 #align mv_polynomial.total_degree_add MvPolynomial.totalDegree_add
+-/
 
+#print MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt /-
 theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
     (h : q.totalDegree < p.totalDegree) : (p + q).totalDegree = p.totalDegree := by
   classical
@@ -664,12 +781,16 @@ theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
   rw [total_degree_eq, hb₂, total_degree_eq]
   exact Finset.le_sup hbb
 #align mv_polynomial.total_degree_add_eq_left_of_total_degree_lt MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt
+-/
 
+#print MvPolynomial.totalDegree_add_eq_right_of_totalDegree_lt /-
 theorem totalDegree_add_eq_right_of_totalDegree_lt {p q : MvPolynomial σ R}
     (h : q.totalDegree < p.totalDegree) : (q + p).totalDegree = p.totalDegree := by
   rw [add_comm, total_degree_add_eq_left_of_total_degree_lt h]
 #align mv_polynomial.total_degree_add_eq_right_of_total_degree_lt MvPolynomial.totalDegree_add_eq_right_of_totalDegree_lt
+-/
 
+#print MvPolynomial.totalDegree_mul /-
 theorem totalDegree_mul (a b : MvPolynomial σ R) :
     (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
   Finset.sup_le fun n hn => by
@@ -682,12 +803,16 @@ theorem totalDegree_mul (a b : MvPolynomial σ R) :
     · intro a; rfl
     · intro a b₁ b₂; rfl
 #align mv_polynomial.total_degree_mul MvPolynomial.totalDegree_mul
+-/
 
+#print MvPolynomial.totalDegree_smul_le /-
 theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f : MvPolynomial σ S) :
     (a • f).totalDegree ≤ f.totalDegree :=
   Finset.sup_mono support_smul
 #align mv_polynomial.total_degree_smul_le MvPolynomial.totalDegree_smul_le
+-/
 
+#print MvPolynomial.totalDegree_pow /-
 theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree ≤ n * a.totalDegree :=
   by
   induction' n with n ih
@@ -698,19 +823,25 @@ theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree
     _ ≤ a.total_degree + n * a.total_degree := (add_le_add_left ih _)
     _ = (n + 1) * a.total_degree := by rw [add_mul, one_mul, add_comm]
 #align mv_polynomial.total_degree_pow MvPolynomial.totalDegree_pow
+-/
 
+#print MvPolynomial.totalDegree_monomial /-
 @[simp]
 theorem totalDegree_monomial (s : σ →₀ ℕ) {c : R} (hc : c ≠ 0) :
     (monomial s c : MvPolynomial σ R).totalDegree = s.Sum fun _ e => e := by
   classical simp [total_degree, support_monomial, if_neg hc]
 #align mv_polynomial.total_degree_monomial MvPolynomial.totalDegree_monomial
+-/
 
+#print MvPolynomial.totalDegree_X_pow /-
 @[simp]
 theorem totalDegree_X_pow [Nontrivial R] (s : σ) (n : ℕ) :
     (X s ^ n : MvPolynomial σ R).totalDegree = n := by simp [X_pow_eq_monomial, one_ne_zero]
 #align mv_polynomial.total_degree_X_pow MvPolynomial.totalDegree_X_pow
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print MvPolynomial.totalDegree_list_prod /-
 theorem totalDegree_list_prod :
     ∀ s : List (MvPolynomial σ R), s.Prod.totalDegree ≤ (s.map MvPolynomial.totalDegree).Sum
   | [] => by rw [@List.prod_nil (MvPolynomial σ R) _, total_degree_one] <;> rfl
@@ -718,7 +849,9 @@ theorem totalDegree_list_prod :
     rw [@List.prod_cons (MvPolynomial σ R) _, List.map, List.sum_cons]
     exact le_trans (total_degree_mul _ _) (add_le_add_left (total_degree_list_prod ps) _)
 #align mv_polynomial.total_degree_list_prod MvPolynomial.totalDegree_list_prod
+-/
 
+#print MvPolynomial.totalDegree_multiset_prod /-
 theorem totalDegree_multiset_prod (s : Multiset (MvPolynomial σ R)) :
     s.Prod.totalDegree ≤ (s.map MvPolynomial.totalDegree).Sum :=
   by
@@ -726,7 +859,9 @@ theorem totalDegree_multiset_prod (s : Multiset (MvPolynomial σ R)) :
   rw [Multiset.quot_mk_to_coe, Multiset.coe_prod, Multiset.coe_map, Multiset.coe_sum]
   exact total_degree_list_prod l
 #align mv_polynomial.total_degree_multiset_prod MvPolynomial.totalDegree_multiset_prod
+-/
 
+#print MvPolynomial.totalDegree_finset_prod /-
 theorem totalDegree_finset_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (s.Prod f).totalDegree ≤ ∑ i in s, (f i).totalDegree :=
   by
@@ -734,7 +869,9 @@ theorem totalDegree_finset_prod {ι : Type _} (s : Finset ι) (f : ι → MvPoly
   rw [Multiset.map_map]
   rfl
 #align mv_polynomial.total_degree_finset_prod MvPolynomial.totalDegree_finset_prod
+-/
 
+#print MvPolynomial.totalDegree_finset_sum /-
 theorem totalDegree_finset_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (s.Sum f).totalDegree ≤ Finset.sup s fun i => (f i).totalDegree :=
   by
@@ -743,7 +880,9 @@ theorem totalDegree_finset_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolyn
   · rw [Finset.sum_cons, Finset.sup_cons, sup_eq_max]
     exact (MvPolynomial.totalDegree_add _ _).trans (max_le_max le_rfl hind)
 #align mv_polynomial.total_degree_finset_sum MvPolynomial.totalDegree_finset_sum
+-/
 
+#print MvPolynomial.exists_degree_lt /-
 theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
     (h : f.totalDegree < n * Fintype.card σ) {d : σ →₀ ℕ} (hd : d ∈ f.support) : ∃ i, d i < n :=
   by
@@ -755,7 +894,9 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
     _ ≤ d.sum fun i e => e := by rw [Finsupp.sum_fintype]; intros; rfl
     _ ≤ f.total_degree := Finset.le_sup hd
 #align mv_polynomial.exists_degree_lt MvPolynomial.exists_degree_lt
+-/
 
+#print MvPolynomial.coeff_eq_zero_of_totalDegree_lt /-
 theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ ℕ}
     (h : f.totalDegree < ∑ i in d.support, d i) : coeff d f = 0 := by
   classical
@@ -764,7 +905,9 @@ theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ 
     refine' not_not.mp (mt h _); exact lt_irrefl _
   · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_lt
+-/
 
+#print MvPolynomial.totalDegree_rename_le /-
 theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     (rename f p).totalDegree ≤ p.totalDegree :=
   Finset.sup_le fun b => by
@@ -779,6 +922,7 @@ theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     exact fun _ => rfl
     exact fun _ _ _ => rfl
 #align mv_polynomial.total_degree_rename_le MvPolynomial.totalDegree_rename_le
+-/
 
 end TotalDegree
 
@@ -789,6 +933,7 @@ section EvalVars
 
 variable [CommSemiring S]
 
+#print MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars /-
 theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p : MvPolynomial σ R}
     (hp : ∀ i ∈ p.vars, g i = 0) : eval₂Hom f g p = f (constantCoeff p) :=
   by
@@ -816,12 +961,16 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
   · rw [constant_coeff_eq, coeff, ← Ne.def, ← Finsupp.mem_support_iff] at h0 
     intro; contradiction
 #align mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars
+-/
 
+#print MvPolynomial.aeval_eq_constantCoeff_of_vars /-
 theorem aeval_eq_constantCoeff_of_vars [Algebra R S] {g : σ → S} {p : MvPolynomial σ R}
     (hp : ∀ i ∈ p.vars, g i = 0) : aeval g p = algebraMap _ _ (constantCoeff p) :=
   eval₂Hom_eq_constantCoeff_of_vars _ hp
 #align mv_polynomial.aeval_eq_constant_coeff_of_vars MvPolynomial.aeval_eq_constantCoeff_of_vars
+-/
 
+#print MvPolynomial.eval₂Hom_congr' /-
 theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p₂ : MvPolynomial σ R} :
     f₁ = f₂ →
       (∀ i, i ∈ p₁.vars → i ∈ p₂.vars → g₁ i = g₂ i) →
@@ -840,7 +989,9 @@ theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p
   have : i ∈ p.vars := by rw [mem_vars]; exact ⟨d, hd, hi⟩
   rw [h i this this]
 #align mv_polynomial.eval₂_hom_congr' MvPolynomial.eval₂Hom_congr'
+-/
 
+#print MvPolynomial.hom_congr_vars /-
 /-- If `f₁` and `f₂` are ring homs out of the polynomial ring and `p₁` and `p₂` are polynomials,
   then `f₁ p₁ = f₂ p₂` if `p₁ = p₂` and `f₁` and `f₂` are equal on `R` and on the variables
   of `p₁`.  -/
@@ -852,7 +1003,9 @@ theorem hom_congr_vars {f₁ f₂ : MvPolynomial σ R →+* S} {p₁ p₂ : MvPo
     _ = eval₂Hom (f₂.comp C) (f₂ ∘ X) p₂ := (eval₂Hom_congr' hC hv hp)
     _ = f₂ p₂ := RingHom.congr_fun (by ext <;> simp) _
 #align mv_polynomial.hom_congr_vars MvPolynomial.hom_congr_vars
+-/
 
+#print MvPolynomial.exists_rename_eq_of_vars_subset_range /-
 theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ → σ) (hfi : Injective f)
     (hf : ↑p.vars ⊆ Set.range f) : ∃ q : MvPolynomial τ R, rename f q = p :=
   ⟨aeval (fun i : σ => Option.elim' 0 X <| partialInv f i) p,
@@ -866,18 +1019,23 @@ theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ 
       simp [partial_inv_left hfi]
     · rfl⟩
 #align mv_polynomial.exists_rename_eq_of_vars_subset_range MvPolynomial.exists_rename_eq_of_vars_subset_range
+-/
 
+#print MvPolynomial.vars_rename /-
 theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).vars ⊆ φ.vars.image f := by
   intro i hi
   simp only [vars, exists_prop, Multiset.mem_toFinset, Finset.mem_image] at hi ⊢
   simpa only [Multiset.mem_map] using degrees_rename _ _ hi
 #align mv_polynomial.vars_rename MvPolynomial.vars_rename
+-/
 
+#print MvPolynomial.mem_vars_rename /-
 theorem mem_vars_rename (f : σ → τ) (φ : MvPolynomial σ R) {j : τ} (h : j ∈ (rename f φ).vars) :
     ∃ i : σ, i ∈ φ.vars ∧ f i = j := by
   classical simpa only [exists_prop, Finset.mem_image] using vars_rename f φ h
 #align mv_polynomial.mem_vars_rename MvPolynomial.mem_vars_rename
+-/
 
 end EvalVars
 

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

@@ -697,7 +697,6 @@ theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree
     total_degree (a * a ^ n) ≤ a.total_degree + (a ^ n).totalDegree := total_degree_mul _ _
     _ ≤ a.total_degree + n * a.total_degree := (add_le_add_left ih _)
     _ = (n + 1) * a.total_degree := by rw [add_mul, one_mul, add_comm]
-    
 #align mv_polynomial.total_degree_pow MvPolynomial.totalDegree_pow
 
 @[simp]
@@ -755,7 +754,6 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
     _ ≤ ∑ s, d s := (Finset.sum_le_sum fun s _ => h s)
     _ ≤ d.sum fun i e => e := by rw [Finsupp.sum_fintype]; intros; rfl
     _ ≤ f.total_degree := Finset.le_sup hd
-    
 #align mv_polynomial.exists_degree_lt MvPolynomial.exists_degree_lt
 
 theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ ℕ}
@@ -853,7 +851,6 @@ theorem hom_congr_vars {f₁ f₂ : MvPolynomial σ R →+* S} {p₁ p₂ : MvPo
     f₁ p₁ = eval₂Hom (f₁.comp C) (f₁ ∘ X) p₁ := RingHom.congr_fun (by ext <;> simp) _
     _ = eval₂Hom (f₂.comp C) (f₂ ∘ X) p₂ := (eval₂Hom_congr' hC hv hp)
     _ = f₂ p₂ := RingHom.congr_fun (by ext <;> simp) _
-    
 #align mv_polynomial.hom_congr_vars MvPolynomial.hom_congr_vars
 
 theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ → σ) (hfi : Injective f)

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

@@ -102,17 +102,17 @@ theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
 
 theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ s.toMultiset := by
   classical
-    refine' Finset.sup_le fun t h => _
-    have := Finsupp.support_single_subset h
-    rw [Finset.mem_singleton] at this 
-    rw [this]
+  refine' Finset.sup_le fun t h => _
+  have := Finsupp.support_single_subset h
+  rw [Finset.mem_singleton] at this 
+  rw [this]
 #align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomial
 
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
     degrees (monomial s a) = s.toMultiset := by
   classical
-    refine' le_antisymm (degrees_monomial s a) <| Finset.le_sup <| _
-    rw [support_monomial, if_neg ha, Finset.mem_singleton]
+  refine' le_antisymm (degrees_monomial s a) <| Finset.le_sup <| _
+  rw [support_monomial, if_neg ha, Finset.mem_singleton]
 #align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eq
 
 theorem degrees_C (a : R) : degrees (C a : MvPolynomial σ R) = 0 :=
@@ -140,43 +140,43 @@ theorem degrees_one : degrees (1 : MvPolynomial σ R) = 0 :=
 theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
     (p + q).degrees ≤ p.degrees ⊔ q.degrees := by
   classical
-    simp_rw [degrees_def]
-    refine' Finset.sup_le fun b hb => _
-    have := Finsupp.support_add hb
-    rw [Finset.mem_union] at this 
-    cases this
-    · exact le_sup_of_le_left (Finset.le_sup this)
-    · exact le_sup_of_le_right (Finset.le_sup this)
+  simp_rw [degrees_def]
+  refine' Finset.sup_le fun b hb => _
+  have := Finsupp.support_add hb
+  rw [Finset.mem_union] at this 
+  cases this
+  · exact le_sup_of_le_left (Finset.le_sup this)
+  · exact le_sup_of_le_right (Finset.le_sup this)
 #align mv_polynomial.degrees_add MvPolynomial.degrees_add
 
 theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by
   classical
-    refine' s.induction _ _
-    · simp only [Finset.sum_empty, Finset.sup_empty, degrees_zero]; exact le_rfl
-    · intro i s his ih
-      rw [Finset.sup_insert, Finset.sum_insert his]
-      exact le_trans (degrees_add _ _) (sup_le_sup_left ih _)
+  refine' s.induction _ _
+  · simp only [Finset.sum_empty, Finset.sup_empty, degrees_zero]; exact le_rfl
+  · intro i s his ih
+    rw [Finset.sup_insert, Finset.sum_insert his]
+    exact le_trans (degrees_add _ _) (sup_le_sup_left ih _)
 #align mv_polynomial.degrees_sum MvPolynomial.degrees_sum
 
 theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees := by
   classical
-    refine' Finset.sup_le fun b hb => _
-    have := support_mul p q hb
-    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this 
-    rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
-    rw [Finsupp.toMultiset_add]
-    exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
+  refine' Finset.sup_le fun b hb => _
+  have := support_mul p q hb
+  simp only [Finset.mem_biUnion, Finset.mem_singleton] at this 
+  rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
+  rw [Finsupp.toMultiset_add]
+  exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
 #align mv_polynomial.degrees_mul MvPolynomial.degrees_mul
 
 theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees := by
   classical
-    refine' s.induction _ _
-    · simp only [Finset.prod_empty, Finset.sum_empty, degrees_one]
-    · intro i s his ih
-      rw [Finset.prod_insert his, Finset.sum_insert his]
-      exact le_trans (degrees_mul _ _) (add_le_add_left ih _)
+  refine' s.induction _ _
+  · simp only [Finset.prod_empty, Finset.sum_empty, degrees_one]
+  · intro i s his ih
+    rw [Finset.prod_insert his, Finset.sum_insert his]
+    exact le_trans (degrees_mul _ _) (add_le_add_left ih _)
 #align mv_polynomial.degrees_prod MvPolynomial.degrees_prod
 
 theorem degrees_pow (p : MvPolynomial σ R) : ∀ n : ℕ, (p ^ n).degrees ≤ n • p.degrees
@@ -194,24 +194,24 @@ theorem mem_degrees {p : MvPolynomial σ R} {i : σ} :
 theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degrees) :
     p.degrees ≤ (p + q).degrees := by
   classical
-    apply Finset.sup_le
-    intro d hd
-    rw [Multiset.disjoint_iff_ne] at h 
-    rw [Multiset.le_iff_count]
-    intro i
-    rw [degrees, Multiset.count_finset_sup]
-    simp only [Finsupp.count_toMultiset]
-    by_cases h0 : d = 0
-    · simp only [h0, zero_le, Finsupp.zero_apply]
-    · refine' @Finset.le_sup _ _ _ _ (p + q).support _ d _
-      rw [mem_support_iff, coeff_add]
-      suffices q.coeff d = 0 by rwa [this, add_zero, coeff, ← Finsupp.mem_support_iff]
-      rw [← Finsupp.support_eq_empty, ← Ne.def, ← Finset.nonempty_iff_ne_empty] at h0 
-      obtain ⟨j, hj⟩ := h0
-      contrapose! h
-      rw [mem_support_iff] at hd 
-      refine' ⟨j, _, j, _, rfl⟩
-      all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
+  apply Finset.sup_le
+  intro d hd
+  rw [Multiset.disjoint_iff_ne] at h 
+  rw [Multiset.le_iff_count]
+  intro i
+  rw [degrees, Multiset.count_finset_sup]
+  simp only [Finsupp.count_toMultiset]
+  by_cases h0 : d = 0
+  · simp only [h0, zero_le, Finsupp.zero_apply]
+  · refine' @Finset.le_sup _ _ _ _ (p + q).support _ d _
+    rw [mem_support_iff, coeff_add]
+    suffices q.coeff d = 0 by rwa [this, add_zero, coeff, ← Finsupp.mem_support_iff]
+    rw [← Finsupp.support_eq_empty, ← Ne.def, ← Finset.nonempty_iff_ne_empty] at h0 
+    obtain ⟨j, hj⟩ := h0
+    contrapose! h
+    rw [mem_support_iff] at hd 
+    refine' ⟨j, _, j, _, rfl⟩
+    all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
 #align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_add
 
 theorem degrees_add_of_disjoint [DecidableEq σ] {p q : MvPolynomial σ R}
@@ -235,18 +235,18 @@ theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
 theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).degrees ⊆ φ.degrees.map f := by
   classical
-    intro i
-    rw [mem_degrees, Multiset.mem_map]
-    rintro ⟨d, hd, hi⟩
-    obtain ⟨x, rfl, hx⟩ := coeff_rename_ne_zero _ _ _ hd
-    simp only [map_domain, Finsupp.mem_support_iff] at hi 
-    rw [sum_apply, Finsupp.sum] at hi 
-    contrapose! hi
-    rw [Finset.sum_eq_zero]
-    intro j hj
-    simp only [exists_prop, mem_degrees] at hi 
-    specialize hi j ⟨x, hx, hj⟩
-    rw [single_apply, if_neg hi]
+  intro i
+  rw [mem_degrees, Multiset.mem_map]
+  rintro ⟨d, hd, hi⟩
+  obtain ⟨x, rfl, hx⟩ := coeff_rename_ne_zero _ _ _ hd
+  simp only [map_domain, Finsupp.mem_support_iff] at hi 
+  rw [sum_apply, Finsupp.sum] at hi 
+  contrapose! hi
+  rw [Finset.sum_eq_zero]
+  intro j hj
+  simp only [exists_prop, mem_degrees] at hi 
+  specialize hi j ⟨x, hx, hj⟩
+  rw [single_apply, if_neg hi]
 #align mv_polynomial.degrees_rename MvPolynomial.degrees_rename
 
 theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R →+* S}
@@ -257,10 +257,10 @@ theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R
 theorem degrees_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f) :
     degrees (rename f p) = (degrees p).map f := by
   classical
-    simp only [degrees, Multiset.map_finset_sup p.support Finsupp.toMultiset f h,
-      support_rename_of_injective h, Finset.sup_image]
-    refine' Finset.sup_congr rfl fun x hx => _
-    exact (Finsupp.toMultiset_map _ _).symm
+  simp only [degrees, Multiset.map_finset_sup p.support Finsupp.toMultiset f h,
+    support_rename_of_injective h, Finset.sup_image]
+  refine' Finset.sup_congr rfl fun x hx => _
+  exact (Finsupp.toMultiset_map _ _).symm
 #align mv_polynomial.degrees_rename_of_injective MvPolynomial.degrees_rename_of_injective
 
 end Degrees
@@ -366,12 +366,12 @@ theorem vars_one : (1 : MvPolynomial σ R).vars = ∅ :=
 
 theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars := by
   classical
-    simp_rw [vars_def]
-    induction' n with n ih
-    · simp
-    · rw [pow_succ]
-      apply Finset.Subset.trans (vars_mul _ _)
-      exact Finset.union_subset (Finset.Subset.refl _) ih
+  simp_rw [vars_def]
+  induction' n with n ih
+  · simp
+  · rw [pow_succ]
+    apply Finset.Subset.trans (vars_mul _ _)
+    exact Finset.union_subset (Finset.Subset.refl _) ih
 #align mv_polynomial.vars_pow MvPolynomial.vars_pow
 
 /-- The variables of the product of a family of polynomials
@@ -380,12 +380,12 @@ are a subset of the union of the sets of variables of each polynomial.
 theorem vars_prod {ι : Type _} [DecidableEq σ] {s : Finset ι} (f : ι → MvPolynomial σ R) :
     (∏ i in s, f i).vars ⊆ s.biUnion fun i => (f i).vars := by
   classical
-    apply s.induction_on
-    · simp
-    · intro a s hs hsub
-      simp only [hs, Finset.biUnion_insert, Finset.prod_insert, not_false_iff]
-      apply Finset.Subset.trans (vars_mul _ _)
-      exact Finset.union_subset_union (Finset.Subset.refl _) hsub
+  apply s.induction_on
+  · simp
+  · intro a s hs hsub
+    simp only [hs, Finset.biUnion_insert, Finset.prod_insert, not_false_iff]
+    apply Finset.Subset.trans (vars_mul _ _)
+    exact Finset.union_subset_union (Finset.Subset.refl _) hsub
 #align mv_polynomial.vars_prod MvPolynomial.vars_prod
 
 section IsDomain
@@ -413,32 +413,31 @@ variable {ι : Type _} (t : Finset ι) (φ : ι → MvPolynomial σ R)
 theorem vars_sum_subset [DecidableEq σ] :
     (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by
   classical
-    apply t.induction_on
-    · simp
-    · intro a s has hsum
-      rw [Finset.biUnion_insert, Finset.sum_insert has]
-      refine'
-        Finset.Subset.trans (vars_add_subset _ _)
-          (Finset.union_subset_union (Finset.Subset.refl _) _)
-      assumption
+  apply t.induction_on
+  · simp
+  · intro a s has hsum
+    rw [Finset.biUnion_insert, Finset.sum_insert has]
+    refine'
+      Finset.Subset.trans (vars_add_subset _ _) (Finset.union_subset_union (Finset.Subset.refl _) _)
+    assumption
 #align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subset
 
 theorem vars_sum_of_disjoint [DecidableEq σ] (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
     (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars := by
   classical
-    apply t.induction_on
-    · simp
-    · intro a s has hsum
-      rw [Finset.biUnion_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
-      unfold Pairwise on_fun at h 
-      rw [hsum]
-      simp only [Finset.disjoint_iff_ne] at h ⊢
-      intro v hv v2 hv2
-      rw [Finset.mem_biUnion] at hv2 
-      rcases hv2 with ⟨i, his, hi⟩
-      refine' h _ _ hv _ hi
-      rintro rfl
-      contradiction
+  apply t.induction_on
+  · simp
+  · intro a s has hsum
+    rw [Finset.biUnion_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
+    unfold Pairwise on_fun at h 
+    rw [hsum]
+    simp only [Finset.disjoint_iff_ne] at h ⊢
+    intro v hv v2 hv2
+    rw [Finset.mem_biUnion] at hv2 
+    rcases hv2 with ⟨i, his, hi⟩
+    refine' h _ _ hv _ hi
+    rintro rfl
+    contradiction
 #align mv_polynomial.vars_sum_of_disjoint MvPolynomial.vars_sum_of_disjoint
 
 end Sum
@@ -491,10 +490,10 @@ theorem degreeOf_def [DecidableEq σ] (n : σ) (p : MvPolynomial σ R) :
 theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
     degreeOf n f = f.support.sup fun m => m n := by
   classical
-    rw [degree_of_def, degrees_def, Multiset.count_finset_sup]
-    congr
-    ext
-    simp
+  rw [degree_of_def, degrees_def, Multiset.count_finset_sup]
+  congr
+  ext
+  simp
 #align mv_polynomial.degree_of_eq_sup MvPolynomial.degreeOf_eq_sup
 
 theorem degreeOf_lt_iff {n : σ} {f : MvPolynomial σ R} {d : ℕ} (h : 0 < d) :
@@ -523,10 +522,10 @@ theorem degreeOf_X [DecidableEq σ] (i j : σ) [Nontrivial R] :
 theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
     degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) := by
   classical
-    repeat' rw [degree_of_def]
-    apply (Multiset.count_le_of_le n (degrees_add f g)).trans
-    dsimp
-    rw [Multiset.count_union]
+  repeat' rw [degree_of_def]
+  apply (Multiset.count_le_of_le n (degrees_add f g)).trans
+  dsimp
+  rw [Multiset.count_union]
 #align mv_polynomial.degree_of_add_le MvPolynomial.degreeOf_add_le
 
 theorem monomial_le_degreeOf (i : σ) {f : MvPolynomial σ R} {m : σ →₀ ℕ} (h_m : m ∈ f.support) :
@@ -539,38 +538,38 @@ theorem monomial_le_degreeOf (i : σ) {f : MvPolynomial σ R} {m : σ →₀ ℕ
 theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
     degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g := by
   classical
-    repeat' rw [degree_of_def]
-    convert Multiset.count_le_of_le i (degrees_mul f g)
-    rw [Multiset.count_add]
+  repeat' rw [degree_of_def]
+  convert Multiset.count_le_of_le i (degrees_mul f g)
+  rw [Multiset.count_add]
 #align mv_polynomial.degree_of_mul_le MvPolynomial.degreeOf_mul_le
 
 theorem degreeOf_mul_X_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
     degreeOf i (f * X j) = degreeOf i f := by
   classical
-    repeat' rw [degree_of_eq_sup i]
-    rw [support_mul_X]
-    simp only [Finset.sup_map]
-    congr
-    ext
-    simp only [single, Nat.one_ne_zero, add_right_eq_self, addRightEmbedding_apply, coe_mk,
-      Pi.add_apply, comp_app, ite_eq_right_iff, Finsupp.coe_add, Pi.single_eq_of_ne h]
+  repeat' rw [degree_of_eq_sup i]
+  rw [support_mul_X]
+  simp only [Finset.sup_map]
+  congr
+  ext
+  simp only [single, Nat.one_ne_zero, add_right_eq_self, addRightEmbedding_apply, coe_mk,
+    Pi.add_apply, comp_app, ite_eq_right_iff, Finsupp.coe_add, Pi.single_eq_of_ne h]
 #align mv_polynomial.degree_of_mul_X_ne MvPolynomial.degreeOf_mul_X_ne
 
 -- TODO in the following we have equality iff f ≠ 0
 theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
     degreeOf j (f * X j) ≤ degreeOf j f + 1 := by
   classical
-    repeat' rw [degree_of_def]
-    apply (Multiset.count_le_of_le j (degrees_mul f (X j))).trans
-    simp only [Multiset.count_add, add_le_add_iff_left]
-    convert Multiset.count_le_of_le j (degrees_X' j)
-    rw [Multiset.count_singleton_self]
+  repeat' rw [degree_of_def]
+  apply (Multiset.count_le_of_le j (degrees_mul f (X j))).trans
+  simp only [Multiset.count_add, add_le_add_iff_left]
+  convert Multiset.count_le_of_le j (degrees_X' j)
+  rw [Multiset.count_singleton_self]
 #align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eq
 
 theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
     (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by
   classical simp only [degree_of_def, degrees_rename_of_injective h,
-      Multiset.count_map_eq_count' f p.degrees h]
+    Multiset.count_map_eq_count' f p.degrees h]
 #align mv_polynomial.degree_of_rename_of_injective MvPolynomial.degreeOf_rename_of_injective
 
 end DegreeOf
@@ -597,8 +596,8 @@ theorem totalDegree_eq (p : MvPolynomial σ R) :
 
 theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) : p.totalDegree ≤ p.degrees.card := by
   classical
-    rw [total_degree_eq]
-    exact Finset.sup_le fun s hs => Multiset.card_le_of_le <| Finset.le_sup hs
+  rw [total_degree_eq]
+  exact Finset.sup_le fun s hs => Multiset.card_le_of_le <| Finset.le_sup hs
 #align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
 
 @[simp]
@@ -635,35 +634,35 @@ theorem totalDegree_add (a b : MvPolynomial σ R) :
     (a + b).totalDegree ≤ max a.totalDegree b.totalDegree :=
   Finset.sup_le fun n hn => by
     classical
-      have := Finsupp.support_add hn
-      rw [Finset.mem_union] at this 
-      cases this
-      · exact le_max_of_le_left (Finset.le_sup this)
-      · exact le_max_of_le_right (Finset.le_sup this)
+    have := Finsupp.support_add hn
+    rw [Finset.mem_union] at this 
+    cases this
+    · exact le_max_of_le_left (Finset.le_sup this)
+    · exact le_max_of_le_right (Finset.le_sup this)
 #align mv_polynomial.total_degree_add MvPolynomial.totalDegree_add
 
 theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
     (h : q.totalDegree < p.totalDegree) : (p + q).totalDegree = p.totalDegree := by
   classical
-    apply le_antisymm
-    · rw [← max_eq_left_of_lt h]
-      exact total_degree_add p q
-    by_cases hp : p = 0
-    · simp [hp]
-    obtain ⟨b, hb₁, hb₂⟩ :=
-      p.support.exists_mem_eq_sup (finsupp.support_nonempty_iff.mpr hp) fun m : σ →₀ ℕ =>
-        m.to_multiset.card
-    have hb : ¬b ∈ q.support := by
-      contrapose! h
-      rw [total_degree_eq p, hb₂, total_degree_eq]
-      apply Finset.le_sup h
-    have hbb : b ∈ (p + q).support :=
-      by
-      apply support_sdiff_support_subset_support_add
-      rw [Finset.mem_sdiff]
-      exact ⟨hb₁, hb⟩
-    rw [total_degree_eq, hb₂, total_degree_eq]
-    exact Finset.le_sup hbb
+  apply le_antisymm
+  · rw [← max_eq_left_of_lt h]
+    exact total_degree_add p q
+  by_cases hp : p = 0
+  · simp [hp]
+  obtain ⟨b, hb₁, hb₂⟩ :=
+    p.support.exists_mem_eq_sup (finsupp.support_nonempty_iff.mpr hp) fun m : σ →₀ ℕ =>
+      m.to_multiset.card
+  have hb : ¬b ∈ q.support := by
+    contrapose! h
+    rw [total_degree_eq p, hb₂, total_degree_eq]
+    apply Finset.le_sup h
+  have hbb : b ∈ (p + q).support :=
+    by
+    apply support_sdiff_support_subset_support_add
+    rw [Finset.mem_sdiff]
+    exact ⟨hb₁, hb⟩
+  rw [total_degree_eq, hb₂, total_degree_eq]
+  exact Finset.le_sup hbb
 #align mv_polynomial.total_degree_add_eq_left_of_total_degree_lt MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt
 
 theorem totalDegree_add_eq_right_of_totalDegree_lt {p q : MvPolynomial σ R}
@@ -675,13 +674,13 @@ theorem totalDegree_mul (a b : MvPolynomial σ R) :
     (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
   Finset.sup_le fun n hn => by
     classical
-      have := AddMonoidAlgebra.support_mul a b hn
-      simp only [Finset.mem_biUnion, Finset.mem_singleton] at this 
-      rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
-      rw [Finsupp.sum_add_index']
-      · exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
-      · intro a; rfl
-      · intro a b₁ b₂; rfl
+    have := AddMonoidAlgebra.support_mul a b hn
+    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this 
+    rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
+    rw [Finsupp.sum_add_index']
+    · exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
+    · intro a; rfl
+    · intro a b₁ b₂; rfl
 #align mv_polynomial.total_degree_mul MvPolynomial.totalDegree_mul
 
 theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f : MvPolynomial σ S) :
@@ -762,10 +761,10 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
 theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ ℕ}
     (h : f.totalDegree < ∑ i in d.support, d i) : coeff d f = 0 := by
   classical
-    rw [total_degree, Finset.sup_lt_iff] at h 
-    · specialize h d; rw [mem_support_iff] at h 
-      refine' not_not.mp (mt h _); exact lt_irrefl _
-    · exact lt_of_le_of_lt (Nat.zero_le _) h
+  rw [total_degree, Finset.sup_lt_iff] at h 
+  · specialize h d; rw [mem_support_iff] at h 
+    refine' not_not.mp (mt h _); exact lt_irrefl _
+  · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_lt
 
 theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
@@ -774,13 +773,13 @@ theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     intro h
     rw [rename_eq] at h 
     classical
-      have h' := Finsupp.mapDomain_support h
-      rw [Finset.mem_image] at h' 
-      rcases h' with ⟨s, hs, rfl⟩
-      rw [Finsupp.sum_mapDomain_index]
-      exact le_trans le_rfl (Finset.le_sup hs)
-      exact fun _ => rfl
-      exact fun _ _ _ => rfl
+    have h' := Finsupp.mapDomain_support h
+    rw [Finset.mem_image] at h' 
+    rcases h' with ⟨s, hs, rfl⟩
+    rw [Finsupp.sum_mapDomain_index]
+    exact le_trans le_rfl (Finset.le_sup hs)
+    exact fun _ => rfl
+    exact fun _ _ _ => rfl
 #align mv_polynomial.total_degree_rename_le MvPolynomial.totalDegree_rename_le
 
 end TotalDegree

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

@@ -104,7 +104,7 @@ theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) 
   classical
     refine' Finset.sup_le fun t h => _
     have := Finsupp.support_single_subset h
-    rw [Finset.mem_singleton] at this
+    rw [Finset.mem_singleton] at this 
     rw [this]
 #align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomial
 
@@ -143,7 +143,7 @@ theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
     simp_rw [degrees_def]
     refine' Finset.sup_le fun b hb => _
     have := Finsupp.support_add hb
-    rw [Finset.mem_union] at this
+    rw [Finset.mem_union] at this 
     cases this
     · exact le_sup_of_le_left (Finset.le_sup this)
     · exact le_sup_of_le_right (Finset.le_sup this)
@@ -163,7 +163,7 @@ theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees +
   classical
     refine' Finset.sup_le fun b hb => _
     have := support_mul p q hb
-    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
+    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this 
     rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
     rw [Finsupp.toMultiset_add]
     exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
@@ -196,7 +196,7 @@ theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degre
   classical
     apply Finset.sup_le
     intro d hd
-    rw [Multiset.disjoint_iff_ne] at h
+    rw [Multiset.disjoint_iff_ne] at h 
     rw [Multiset.le_iff_count]
     intro i
     rw [degrees, Multiset.count_finset_sup]
@@ -206,10 +206,10 @@ theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degre
     · refine' @Finset.le_sup _ _ _ _ (p + q).support _ d _
       rw [mem_support_iff, coeff_add]
       suffices q.coeff d = 0 by rwa [this, add_zero, coeff, ← Finsupp.mem_support_iff]
-      rw [← Finsupp.support_eq_empty, ← Ne.def, ← Finset.nonempty_iff_ne_empty] at h0
+      rw [← Finsupp.support_eq_empty, ← Ne.def, ← Finset.nonempty_iff_ne_empty] at h0 
       obtain ⟨j, hj⟩ := h0
       contrapose! h
-      rw [mem_support_iff] at hd
+      rw [mem_support_iff] at hd 
       refine' ⟨j, _, j, _, rfl⟩
       all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
 #align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_add
@@ -239,12 +239,12 @@ theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
     rw [mem_degrees, Multiset.mem_map]
     rintro ⟨d, hd, hi⟩
     obtain ⟨x, rfl, hx⟩ := coeff_rename_ne_zero _ _ _ hd
-    simp only [map_domain, Finsupp.mem_support_iff] at hi
-    rw [sum_apply, Finsupp.sum] at hi
+    simp only [map_domain, Finsupp.mem_support_iff] at hi 
+    rw [sum_apply, Finsupp.sum] at hi 
     contrapose! hi
     rw [Finset.sum_eq_zero]
     intro j hj
-    simp only [exists_prop, mem_degrees] at hi
+    simp only [exists_prop, mem_degrees] at hi 
     specialize hi j ⟨x, hx, hj⟩
     rw [single_apply, if_neg hi]
 #align mv_polynomial.degrees_rename MvPolynomial.degrees_rename
@@ -302,7 +302,7 @@ theorem vars_X [Nontrivial R] : (X n : MvPolynomial σ R).vars = {n} := by
   rw [X, vars_monomial (one_ne_zero' R), Finsupp.support_single_ne_zero _ (one_ne_zero' ℕ)]
 #align mv_polynomial.vars_X MvPolynomial.vars_X
 
-theorem mem_vars (i : σ) : i ∈ p.vars ↔ ∃ (d : σ →₀ ℕ)(H : d ∈ p.support), i ∈ d.support := by
+theorem mem_vars (i : σ) : i ∈ p.vars ↔ ∃ (d : σ →₀ ℕ) (H : d ∈ p.support), i ∈ d.support := by
   simp only [vars, Multiset.mem_toFinset, mem_degrees, mem_support_iff, exists_prop]
 #align mv_polynomial.mem_vars MvPolynomial.mem_vars
 
@@ -310,7 +310,7 @@ theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ
     {v : σ} (h : v ∉ vars f) : x v = 0 :=
   by
   letI := Classical.decEq σ
-  rw [vars_def, Multiset.mem_toFinset] at h
+  rw [vars_def, Multiset.mem_toFinset] at h 
   rw [← Finsupp.not_mem_support_iff]
   contrapose! h
   rw [degrees_def]
@@ -318,13 +318,13 @@ theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ
   rw [Finset.sup_insert]
   simp only [Multiset.mem_union, Multiset.sup_eq_union]
   left
-  rwa [← to_finset_to_multiset, Multiset.mem_toFinset] at h
+  rwa [← to_finset_to_multiset, Multiset.mem_toFinset] at h 
 #align mv_polynomial.mem_support_not_mem_vars_zero MvPolynomial.mem_support_not_mem_vars_zero
 
 theorem vars_add_subset [DecidableEq σ] (p q : MvPolynomial σ R) : (p + q).vars ⊆ p.vars ∪ q.vars :=
   by
   intro x hx
-  simp only [vars, Finset.mem_union, Multiset.mem_toFinset] at hx⊢
+  simp only [vars, Finset.mem_union, Multiset.mem_toFinset] at hx ⊢
   simpa using Multiset.mem_of_le (degrees_add _ _) hx
 #align mv_polynomial.vars_add_subset MvPolynomial.vars_add_subset
 
@@ -333,7 +333,7 @@ theorem vars_add_of_disjoint [DecidableEq σ] (h : Disjoint p.vars q.vars) :
   by
   apply Finset.Subset.antisymm (vars_add_subset p q)
   intro x hx
-  simp only [vars_def, Multiset.disjoint_toFinset] at h hx⊢
+  simp only [vars_def, Multiset.disjoint_toFinset] at h hx ⊢
   rw [degrees_add_of_disjoint h, Multiset.toFinset_union]
   exact hx
 #align mv_polynomial.vars_add_of_disjoint MvPolynomial.vars_add_of_disjoint
@@ -345,18 +345,18 @@ theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars 
   intro i
   simp only [mem_vars, Finset.mem_union]
   rintro ⟨d, hd, hi⟩
-  rw [mem_support_iff, coeff_mul] at hd
+  rw [mem_support_iff, coeff_mul] at hd 
   contrapose! hd; cases hd
   rw [Finset.sum_eq_zero]
   rintro ⟨d₁, d₂⟩ H
-  rw [Finsupp.mem_antidiagonal] at H
+  rw [Finsupp.mem_antidiagonal] at H 
   subst H
   obtain H | H : i ∈ d₁.support ∨ i ∈ d₂.support := by
     simpa only [Finset.mem_union] using Finsupp.support_add hi
   · suffices coeff d₁ φ = 0 by simp [this]
-    rw [coeff, ← Finsupp.not_mem_support_iff]; intro ; solve_by_elim
+    rw [coeff, ← Finsupp.not_mem_support_iff]; intro; solve_by_elim
   · suffices coeff d₂ ψ = 0 by simp [this]
-    rw [coeff, ← Finsupp.not_mem_support_iff]; intro ; solve_by_elim
+    rw [coeff, ← Finsupp.not_mem_support_iff]; intro; solve_by_elim
 #align mv_polynomial.vars_mul MvPolynomial.vars_mul
 
 @[simp]
@@ -430,11 +430,11 @@ theorem vars_sum_of_disjoint [DecidableEq σ] (h : Pairwise <| (Disjoint on fun
     · simp
     · intro a s has hsum
       rw [Finset.biUnion_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
-      unfold Pairwise on_fun at h
+      unfold Pairwise on_fun at h 
       rw [hsum]
-      simp only [Finset.disjoint_iff_ne] at h⊢
+      simp only [Finset.disjoint_iff_ne] at h ⊢
       intro v hv v2 hv2
-      rw [Finset.mem_biUnion] at hv2
+      rw [Finset.mem_biUnion] at hv2 
       rcases hv2 with ⟨i, his, hi⟩
       refine' h _ _ hv _ hi
       rintro rfl
@@ -591,7 +591,7 @@ theorem totalDegree_eq (p : MvPolynomial σ R) :
     p.totalDegree = p.support.sup fun m => m.toMultiset.card :=
   by
   rw [total_degree]
-  congr ; funext m
+  congr; funext m
   exact (Finsupp.card_toMultiset _).symm
 #align mv_polynomial.total_degree_eq MvPolynomial.totalDegree_eq
 
@@ -606,7 +606,7 @@ theorem totalDegree_C (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
   Nat.eq_zero_of_le_zero <|
     Finset.sup_le fun n hn => by
       have := Finsupp.support_single_subset hn
-      rw [Finset.mem_singleton] at this
+      rw [Finset.mem_singleton] at this 
       subst this
       exact le_rfl
 #align mv_polynomial.total_degree_C MvPolynomial.totalDegree_C
@@ -636,7 +636,7 @@ theorem totalDegree_add (a b : MvPolynomial σ R) :
   Finset.sup_le fun n hn => by
     classical
       have := Finsupp.support_add hn
-      rw [Finset.mem_union] at this
+      rw [Finset.mem_union] at this 
       cases this
       · exact le_max_of_le_left (Finset.le_sup this)
       · exact le_max_of_le_right (Finset.le_sup this)
@@ -676,7 +676,7 @@ theorem totalDegree_mul (a b : MvPolynomial σ R) :
   Finset.sup_le fun n hn => by
     classical
       have := AddMonoidAlgebra.support_mul a b hn
-      simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
+      simp only [Finset.mem_biUnion, Finset.mem_singleton] at this 
       rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
       rw [Finsupp.sum_add_index']
       · exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
@@ -754,7 +754,7 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
     n * Fintype.card σ = ∑ s : σ, n := by
       rw [Finset.sum_const, Nat.nsmul_eq_mul, mul_comm, Finset.card_univ]
     _ ≤ ∑ s, d s := (Finset.sum_le_sum fun s _ => h s)
-    _ ≤ d.sum fun i e => e := by rw [Finsupp.sum_fintype]; intros ; rfl
+    _ ≤ d.sum fun i e => e := by rw [Finsupp.sum_fintype]; intros; rfl
     _ ≤ f.total_degree := Finset.le_sup hd
     
 #align mv_polynomial.exists_degree_lt MvPolynomial.exists_degree_lt
@@ -762,8 +762,8 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
 theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ ℕ}
     (h : f.totalDegree < ∑ i in d.support, d i) : coeff d f = 0 := by
   classical
-    rw [total_degree, Finset.sup_lt_iff] at h
-    · specialize h d; rw [mem_support_iff] at h
+    rw [total_degree, Finset.sup_lt_iff] at h 
+    · specialize h d; rw [mem_support_iff] at h 
       refine' not_not.mp (mt h _); exact lt_irrefl _
     · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_lt
@@ -772,10 +772,10 @@ theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     (rename f p).totalDegree ≤ p.totalDegree :=
   Finset.sup_le fun b => by
     intro h
-    rw [rename_eq] at h
+    rw [rename_eq] at h 
     classical
       have h' := Finsupp.mapDomain_support h
-      rw [Finset.mem_image] at h'
+      rw [Finset.mem_image] at h' 
       rcases h' with ⟨s, hs, rfl⟩
       rw [Finsupp.sum_mapDomain_index]
       exact le_trans le_rfl (Finset.le_sup hs)
@@ -809,15 +809,15 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
   repeat'
     obtain ⟨i, hi⟩ : d.support.nonempty :=
       by
-      rw [constant_coeff_eq, coeff, ← Finsupp.not_mem_support_iff] at h0
+      rw [constant_coeff_eq, coeff, ← Finsupp.not_mem_support_iff] at h0 
       rw [Finset.nonempty_iff_ne_empty, Ne.def, Finsupp.support_eq_empty]
       rintro rfl; contradiction
     rw [Finsupp.prod, Finset.prod_eq_zero hi, MulZeroClass.mul_zero]
     rw [hp, zero_pow (Nat.pos_of_ne_zero <| finsupp.mem_support_iff.mp hi)]
     rw [mem_vars]
     exact ⟨d, hd, hi⟩
-  · rw [constant_coeff_eq, coeff, ← Ne.def, ← Finsupp.mem_support_iff] at h0
-    intro ; contradiction
+  · rw [constant_coeff_eq, coeff, ← Ne.def, ← Finsupp.mem_support_iff] at h0 
+    intro; contradiction
 #align mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars
 
 theorem aeval_eq_constantCoeff_of_vars [Algebra R S] {g : σ → S} {p : MvPolynomial σ R}
@@ -874,7 +874,7 @@ theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ 
 theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).vars ⊆ φ.vars.image f := by
   intro i hi
-  simp only [vars, exists_prop, Multiset.mem_toFinset, Finset.mem_image] at hi⊢
+  simp only [vars, exists_prop, Multiset.mem_toFinset, Finset.mem_image] at hi ⊢
   simpa only [Multiset.mem_map] using degrees_rename _ _ hi
 #align mv_polynomial.vars_rename MvPolynomial.vars_rename
 

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

@@ -66,7 +66,7 @@ noncomputable section
 
 open Set Function Finsupp AddMonoidAlgebra
 
-open BigOperators
+open scoped BigOperators
 
 universe u v w
 

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

@@ -96,22 +96,10 @@ def degrees (p : MvPolynomial σ R) : Multiset σ :=
 #align mv_polynomial.degrees MvPolynomial.degrees
 -/
 
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 theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
     p.degrees = p.support.sup fun s : σ →₀ ℕ => s.toMultiset := by convert rfl
 #align mv_polynomial.degrees_def MvPolynomial.degrees_def
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomialₓ'. -/
 theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ s.toMultiset := by
   classical
     refine' Finset.sup_le fun t h => _
@@ -120,12 +108,6 @@ theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) 
     rw [this]
 #align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomial
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eqₓ'. -/
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
     degrees (monomial s a) = s.toMultiset := by
   classical
@@ -133,64 +115,28 @@ theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
     rw [support_monomial, if_neg ha, Finset.mem_singleton]
 #align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eq
 
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 theorem degrees_C (a : R) : degrees (C a : MvPolynomial σ R) = 0 :=
   Multiset.le_zero.1 <| degrees_monomial _ _
 #align mv_polynomial.degrees_C MvPolynomial.degrees_C
 
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 theorem degrees_X' (n : σ) : degrees (X n : MvPolynomial σ R) ≤ {n} :=
   le_trans (degrees_monomial _ _) <| le_of_eq <| toMultiset_single _ _
 #align mv_polynomial.degrees_X' MvPolynomial.degrees_X'
 
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 @[simp]
 theorem degrees_X [Nontrivial R] (n : σ) : degrees (X n : MvPolynomial σ R) = {n} :=
   (degrees_monomial_eq _ (1 : R) one_ne_zero).trans (toMultiset_single _ _)
 #align mv_polynomial.degrees_X MvPolynomial.degrees_X
 
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 @[simp]
 theorem degrees_zero : degrees (0 : MvPolynomial σ R) = 0 := by rw [← C_0]; exact degrees_C 0
 #align mv_polynomial.degrees_zero MvPolynomial.degrees_zero
 
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 @[simp]
 theorem degrees_one : degrees (1 : MvPolynomial σ R) = 0 :=
   degrees_C 1
 #align mv_polynomial.degrees_one MvPolynomial.degrees_one
 
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 theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
     (p + q).degrees ≤ p.degrees ⊔ q.degrees := by
   classical
@@ -203,12 +149,6 @@ theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
     · exact le_sup_of_le_right (Finset.le_sup this)
 #align mv_polynomial.degrees_add MvPolynomial.degrees_add
 
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 theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by
   classical
@@ -219,12 +159,6 @@ theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → M
       exact le_trans (degrees_add _ _) (sup_le_sup_left ih _)
 #align mv_polynomial.degrees_sum MvPolynomial.degrees_sum
 
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 theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees := by
   classical
     refine' Finset.sup_le fun b hb => _
@@ -235,12 +169,6 @@ theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees +
     exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
 #align mv_polynomial.degrees_mul MvPolynomial.degrees_mul
 
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 theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees := by
   classical
@@ -251,12 +179,6 @@ theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R
       exact le_trans (degrees_mul _ _) (add_le_add_left ih _)
 #align mv_polynomial.degrees_prod MvPolynomial.degrees_prod
 
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 theorem degrees_pow (p : MvPolynomial σ R) : ∀ n : ℕ, (p ^ n).degrees ≤ n • p.degrees
   | 0 => by rw [pow_zero, degrees_one]; exact Multiset.zero_le _
   | n + 1 => by
@@ -264,23 +186,11 @@ theorem degrees_pow (p : MvPolynomial σ R) : ∀ n : ℕ, (p ^ n).degrees ≤ n
     exact le_trans (degrees_mul _ _) (add_le_add_left (degrees_pow n) _)
 #align mv_polynomial.degrees_pow MvPolynomial.degrees_pow
 
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 theorem mem_degrees {p : MvPolynomial σ R} {i : σ} :
     i ∈ p.degrees ↔ ∃ d, p.coeff d ≠ 0 ∧ i ∈ d.support := by
   simp only [degrees, Multiset.mem_sup, ← mem_support_iff, Finsupp.mem_toMultiset, exists_prop]
 #align mv_polynomial.mem_degrees MvPolynomial.mem_degrees
 
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 theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degrees) :
     p.degrees ≤ (p + q).degrees := by
   classical
@@ -304,12 +214,6 @@ theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degre
       all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
 #align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_add
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_add_of_disjoint MvPolynomial.degrees_add_of_disjointₓ'. -/
 theorem degrees_add_of_disjoint [DecidableEq σ] {p q : MvPolynomial σ R}
     (h : Multiset.Disjoint p.degrees q.degrees) : (p + q).degrees = p.degrees ∪ q.degrees :=
   by
@@ -320,12 +224,6 @@ theorem degrees_add_of_disjoint [DecidableEq σ] {p q : MvPolynomial σ R}
     · rw [add_comm]; apply le_degrees_add h.symm
 #align mv_polynomial.degrees_add_of_disjoint MvPolynomial.degrees_add_of_disjoint
 
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 theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
     (map f p).degrees ⊆ p.degrees := by
   dsimp only [degrees]
@@ -334,9 +232,6 @@ theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
   apply MvPolynomial.support_map_subset
 #align mv_polynomial.degrees_map MvPolynomial.degrees_map
 
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 theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).degrees ⊆ φ.degrees.map f := by
   classical
@@ -354,17 +249,11 @@ theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
     rw [single_apply, if_neg hi]
 #align mv_polynomial.degrees_rename MvPolynomial.degrees_rename
 
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 theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R →+* S}
     (hf : Injective f) : (map f p).degrees = p.degrees := by
   simp only [degrees, MvPolynomial.support_map_of_injective _ hf]
 #align mv_polynomial.degrees_map_of_injective MvPolynomial.degrees_map_of_injective
 
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 theorem degrees_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f) :
     degrees (rename f p) = (degrees p).map f := by
   classical
@@ -389,76 +278,34 @@ def vars (p : MvPolynomial σ R) : Finset σ :=
 #align mv_polynomial.vars MvPolynomial.vars
 -/
 
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 theorem vars_def [DecidableEq σ] (p : MvPolynomial σ R) : p.vars = p.degrees.toFinset := by
   convert rfl
 #align mv_polynomial.vars_def MvPolynomial.vars_def
 
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 @[simp]
 theorem vars_0 : (0 : MvPolynomial σ R).vars = ∅ := by
   classical rw [vars_def, degrees_zero, Multiset.toFinset_zero]
 #align mv_polynomial.vars_0 MvPolynomial.vars_0
 
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 @[simp]
 theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by
   classical rw [vars_def, degrees_monomial_eq _ _ h, Finsupp.toFinset_toMultiset]
 #align mv_polynomial.vars_monomial MvPolynomial.vars_monomial
 
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 @[simp]
 theorem vars_C : (C r : MvPolynomial σ R).vars = ∅ := by
   classical rw [vars_def, degrees_C, Multiset.toFinset_zero]
 #align mv_polynomial.vars_C MvPolynomial.vars_C
 
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 @[simp]
 theorem vars_X [Nontrivial R] : (X n : MvPolynomial σ R).vars = {n} := by
   rw [X, vars_monomial (one_ne_zero' R), Finsupp.support_single_ne_zero _ (one_ne_zero' ℕ)]
 #align mv_polynomial.vars_X MvPolynomial.vars_X
 
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 theorem mem_vars (i : σ) : i ∈ p.vars ↔ ∃ (d : σ →₀ ℕ)(H : d ∈ p.support), i ∈ d.support := by
   simp only [vars, Multiset.mem_toFinset, mem_degrees, mem_support_iff, exists_prop]
 #align mv_polynomial.mem_vars MvPolynomial.mem_vars
 
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 theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ} (H : x ∈ f.support)
     {v : σ} (h : v ∉ vars f) : x v = 0 :=
   by
@@ -474,12 +321,6 @@ theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ
   rwa [← to_finset_to_multiset, Multiset.mem_toFinset] at h
 #align mv_polynomial.mem_support_not_mem_vars_zero MvPolynomial.mem_support_not_mem_vars_zero
 
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 theorem vars_add_subset [DecidableEq σ] (p q : MvPolynomial σ R) : (p + q).vars ⊆ p.vars ∪ q.vars :=
   by
   intro x hx
@@ -487,12 +328,6 @@ theorem vars_add_subset [DecidableEq σ] (p q : MvPolynomial σ R) : (p + q).var
   simpa using Multiset.mem_of_le (degrees_add _ _) hx
 #align mv_polynomial.vars_add_subset MvPolynomial.vars_add_subset
 
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 theorem vars_add_of_disjoint [DecidableEq σ] (h : Disjoint p.vars q.vars) :
     (p + q).vars = p.vars ∪ q.vars :=
   by
@@ -505,12 +340,6 @@ theorem vars_add_of_disjoint [DecidableEq σ] (h : Disjoint p.vars q.vars) :
 
 section Mul
 
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 theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars ⊆ φ.vars ∪ ψ.vars :=
   by
   intro i
@@ -530,23 +359,11 @@ theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars 
     rw [coeff, ← Finsupp.not_mem_support_iff]; intro ; solve_by_elim
 #align mv_polynomial.vars_mul MvPolynomial.vars_mul
 
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 @[simp]
 theorem vars_one : (1 : MvPolynomial σ R).vars = ∅ :=
   vars_C
 #align mv_polynomial.vars_one MvPolynomial.vars_one
 
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 theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars := by
   classical
     simp_rw [vars_def]
@@ -557,12 +374,6 @@ theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars
       exact Finset.union_subset (Finset.Subset.refl _) ih
 #align mv_polynomial.vars_pow MvPolynomial.vars_pow
 
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 /-- The variables of the product of a family of polynomials
 are a subset of the union of the sets of variables of each polynomial.
 -/
@@ -581,9 +392,6 @@ section IsDomain
 
 variable {A : Type _} [CommRing A] [IsDomain A]
 
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 theorem vars_C_mul (a : A) (ha : a ≠ 0) (φ : MvPolynomial σ A) : (C a * φ).vars = φ.vars :=
   by
   ext1 i
@@ -602,12 +410,6 @@ section Sum
 
 variable {ι : Type _} (t : Finset ι) (φ : ι → MvPolynomial σ R)
 
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 theorem vars_sum_subset [DecidableEq σ] :
     (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by
   classical
@@ -621,12 +423,6 @@ theorem vars_sum_subset [DecidableEq σ] :
       assumption
 #align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subset
 
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 theorem vars_sum_of_disjoint [DecidableEq σ] (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
     (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars := by
   classical
@@ -653,41 +449,20 @@ variable [CommSemiring S] (f : R →+* S)
 
 variable (p)
 
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 theorem vars_map : (map f p).vars ⊆ p.vars := by simp [vars, degrees_map]
 #align mv_polynomial.vars_map MvPolynomial.vars_map
 
 variable {f}
 
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 theorem vars_map_of_injective (hf : Injective f) : (map f p).vars = p.vars := by
   simp [vars, degrees_map_of_injective _ hf]
 #align mv_polynomial.vars_map_of_injective MvPolynomial.vars_map_of_injective
 
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 theorem vars_monomial_single (i : σ) {e : ℕ} {r : R} (he : e ≠ 0) (hr : r ≠ 0) :
     (monomial (Finsupp.single i e) r).vars = {i} := by
   rw [vars_monomial hr, Finsupp.support_single_ne_zero _ he]
 #align mv_polynomial.vars_monomial_single MvPolynomial.vars_monomial_single
 
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 theorem vars_eq_support_biUnion_support [DecidableEq σ] :
     p.vars = p.support.biUnion Finsupp.support := by ext i; rw [mem_vars, Finset.mem_biUnion]
 #align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_biUnion_support
@@ -709,22 +484,10 @@ def degreeOf (n : σ) (p : MvPolynomial σ R) : ℕ :=
 #align mv_polynomial.degree_of MvPolynomial.degreeOf
 -/
 
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 theorem degreeOf_def [DecidableEq σ] (n : σ) (p : MvPolynomial σ R) :
     p.degreeOf n = p.degrees.count n := by convert rfl
 #align mv_polynomial.degree_of_def MvPolynomial.degreeOf_def
 
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 theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
     degreeOf n f = f.support.sup fun m => m n := by
   classical
@@ -734,45 +497,21 @@ theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
     simp
 #align mv_polynomial.degree_of_eq_sup MvPolynomial.degreeOf_eq_sup
 
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 theorem degreeOf_lt_iff {n : σ} {f : MvPolynomial σ R} {d : ℕ} (h : 0 < d) :
     degreeOf n f < d ↔ ∀ m : σ →₀ ℕ, m ∈ f.support → m n < d := by
   rwa [degree_of_eq_sup n f, Finset.sup_lt_iff]
 #align mv_polynomial.degree_of_lt_iff MvPolynomial.degreeOf_lt_iff
 
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 @[simp]
 theorem degreeOf_zero (n : σ) : degreeOf n (0 : MvPolynomial σ R) = 0 := by
   simp only [degree_of, degrees_zero, Multiset.count_zero]
 #align mv_polynomial.degree_of_zero MvPolynomial.degreeOf_zero
 
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 @[simp]
 theorem degreeOf_C (a : R) (x : σ) : degreeOf x (C a : MvPolynomial σ R) = 0 := by
   simp [degree_of, degrees_C]
 #align mv_polynomial.degree_of_C MvPolynomial.degreeOf_C
 
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 theorem degreeOf_X [DecidableEq σ] (i j : σ) [Nontrivial R] :
     degreeOf i (X j : MvPolynomial σ R) = if i = j then 1 else 0 :=
   by
@@ -781,12 +520,6 @@ theorem degreeOf_X [DecidableEq σ] (i j : σ) [Nontrivial R] :
   simp [c, if_false, degree_of, degrees_X]
 #align mv_polynomial.degree_of_X MvPolynomial.degreeOf_X
 
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 theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
     degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) := by
   classical
@@ -796,24 +529,12 @@ theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
     rw [Multiset.count_union]
 #align mv_polynomial.degree_of_add_le MvPolynomial.degreeOf_add_le
 
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 theorem monomial_le_degreeOf (i : σ) {f : MvPolynomial σ R} {m : σ →₀ ℕ} (h_m : m ∈ f.support) :
     m i ≤ degreeOf i f := by
   rw [degree_of_eq_sup i]
   apply Finset.le_sup h_m
 #align mv_polynomial.monomial_le_degree_of MvPolynomial.monomial_le_degreeOf
 
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 -- TODO we can prove equality here if R is a domain
 theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
     degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g := by
@@ -823,12 +544,6 @@ theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
     rw [Multiset.count_add]
 #align mv_polynomial.degree_of_mul_le MvPolynomial.degreeOf_mul_le
 
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 theorem degreeOf_mul_X_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
     degreeOf i (f * X j) = degreeOf i f := by
   classical
@@ -841,12 +556,6 @@ theorem degreeOf_mul_X_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
       Pi.add_apply, comp_app, ite_eq_right_iff, Finsupp.coe_add, Pi.single_eq_of_ne h]
 #align mv_polynomial.degree_of_mul_X_ne MvPolynomial.degreeOf_mul_X_ne
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eqₓ'. -/
 -- TODO in the following we have equality iff f ≠ 0
 theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
     degreeOf j (f * X j) ≤ degreeOf j f + 1 := by
@@ -858,9 +567,6 @@ theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
     rw [Multiset.count_singleton_self]
 #align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eq
 
-/- warning: mv_polynomial.degree_of_rename_of_injective -> MvPolynomial.degreeOf_rename_of_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_rename_of_injective MvPolynomial.degreeOf_rename_of_injectiveₓ'. -/
 theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
     (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by
   classical simp only [degree_of_def, degrees_rename_of_injective h,
@@ -881,12 +587,6 @@ def totalDegree (p : MvPolynomial σ R) : ℕ :=
 #align mv_polynomial.total_degree MvPolynomial.totalDegree
 -/
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_eq MvPolynomial.totalDegree_eqₓ'. -/
 theorem totalDegree_eq (p : MvPolynomial σ R) :
     p.totalDegree = p.support.sup fun m => m.toMultiset.card :=
   by
@@ -895,24 +595,12 @@ theorem totalDegree_eq (p : MvPolynomial σ R) :
   exact (Finsupp.card_toMultiset _).symm
 #align mv_polynomial.total_degree_eq MvPolynomial.totalDegree_eq
 
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 theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) : p.totalDegree ≤ p.degrees.card := by
   classical
     rw [total_degree_eq]
     exact Finset.sup_le fun s hs => Multiset.card_le_of_le <| Finset.le_sup hs
 #align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
 
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 @[simp]
 theorem totalDegree_C (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
   Nat.eq_zero_of_le_zero <|
@@ -923,23 +611,11 @@ theorem totalDegree_C (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
       exact le_rfl
 #align mv_polynomial.total_degree_C MvPolynomial.totalDegree_C
 
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 @[simp]
 theorem totalDegree_zero : (0 : MvPolynomial σ R).totalDegree = 0 := by
   rw [← C_0] <;> exact total_degree_C (0 : R)
 #align mv_polynomial.total_degree_zero MvPolynomial.totalDegree_zero
 
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 @[simp]
 theorem totalDegree_one : (1 : MvPolynomial σ R).totalDegree = 0 :=
   totalDegree_C (1 : R)
@@ -955,12 +631,6 @@ theorem totalDegree_X {R} [CommSemiring R] [Nontrivial R] (s : σ) :
 #align mv_polynomial.total_degree_X MvPolynomial.totalDegree_X
 -/
 
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 theorem totalDegree_add (a b : MvPolynomial σ R) :
     (a + b).totalDegree ≤ max a.totalDegree b.totalDegree :=
   Finset.sup_le fun n hn => by
@@ -972,12 +642,6 @@ theorem totalDegree_add (a b : MvPolynomial σ R) :
       · exact le_max_of_le_right (Finset.le_sup this)
 #align mv_polynomial.total_degree_add MvPolynomial.totalDegree_add
 
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 theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
     (h : q.totalDegree < p.totalDegree) : (p + q).totalDegree = p.totalDegree := by
   classical
@@ -1002,23 +666,11 @@ theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
     exact Finset.le_sup hbb
 #align mv_polynomial.total_degree_add_eq_left_of_total_degree_lt MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt
 
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 theorem totalDegree_add_eq_right_of_totalDegree_lt {p q : MvPolynomial σ R}
     (h : q.totalDegree < p.totalDegree) : (q + p).totalDegree = p.totalDegree := by
   rw [add_comm, total_degree_add_eq_left_of_total_degree_lt h]
 #align mv_polynomial.total_degree_add_eq_right_of_total_degree_lt MvPolynomial.totalDegree_add_eq_right_of_totalDegree_lt
 
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 theorem totalDegree_mul (a b : MvPolynomial σ R) :
     (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
   Finset.sup_le fun n hn => by
@@ -1032,23 +684,11 @@ theorem totalDegree_mul (a b : MvPolynomial σ R) :
       · intro a b₁ b₂; rfl
 #align mv_polynomial.total_degree_mul MvPolynomial.totalDegree_mul
 
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 theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f : MvPolynomial σ S) :
     (a • f).totalDegree ≤ f.totalDegree :=
   Finset.sup_mono support_smul
 #align mv_polynomial.total_degree_smul_le MvPolynomial.totalDegree_smul_le
 
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 theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree ≤ n * a.totalDegree :=
   by
   induction' n with n ih
@@ -1061,35 +701,17 @@ theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree
     
 #align mv_polynomial.total_degree_pow MvPolynomial.totalDegree_pow
 
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 @[simp]
 theorem totalDegree_monomial (s : σ →₀ ℕ) {c : R} (hc : c ≠ 0) :
     (monomial s c : MvPolynomial σ R).totalDegree = s.Sum fun _ e => e := by
   classical simp [total_degree, support_monomial, if_neg hc]
 #align mv_polynomial.total_degree_monomial MvPolynomial.totalDegree_monomial
 
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 @[simp]
 theorem totalDegree_X_pow [Nontrivial R] (s : σ) (n : ℕ) :
     (X s ^ n : MvPolynomial σ R).totalDegree = n := by simp [X_pow_eq_monomial, one_ne_zero]
 #align mv_polynomial.total_degree_X_pow MvPolynomial.totalDegree_X_pow
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem totalDegree_list_prod :
     ∀ s : List (MvPolynomial σ R), s.Prod.totalDegree ≤ (s.map MvPolynomial.totalDegree).Sum
@@ -1099,12 +721,6 @@ theorem totalDegree_list_prod :
     exact le_trans (total_degree_mul _ _) (add_le_add_left (total_degree_list_prod ps) _)
 #align mv_polynomial.total_degree_list_prod MvPolynomial.totalDegree_list_prod
 
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 theorem totalDegree_multiset_prod (s : Multiset (MvPolynomial σ R)) :
     s.Prod.totalDegree ≤ (s.map MvPolynomial.totalDegree).Sum :=
   by
@@ -1113,12 +729,6 @@ theorem totalDegree_multiset_prod (s : Multiset (MvPolynomial σ R)) :
   exact total_degree_list_prod l
 #align mv_polynomial.total_degree_multiset_prod MvPolynomial.totalDegree_multiset_prod
 
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 theorem totalDegree_finset_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (s.Prod f).totalDegree ≤ ∑ i in s, (f i).totalDegree :=
   by
@@ -1127,12 +737,6 @@ theorem totalDegree_finset_prod {ι : Type _} (s : Finset ι) (f : ι → MvPoly
   rfl
 #align mv_polynomial.total_degree_finset_prod MvPolynomial.totalDegree_finset_prod
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_finset_sum MvPolynomial.totalDegree_finset_sumₓ'. -/
 theorem totalDegree_finset_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (s.Sum f).totalDegree ≤ Finset.sup s fun i => (f i).totalDegree :=
   by
@@ -1142,12 +746,6 @@ theorem totalDegree_finset_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolyn
     exact (MvPolynomial.totalDegree_add _ _).trans (max_le_max le_rfl hind)
 #align mv_polynomial.total_degree_finset_sum MvPolynomial.totalDegree_finset_sum
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.exists_degree_lt MvPolynomial.exists_degree_ltₓ'. -/
 theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
     (h : f.totalDegree < n * Fintype.card σ) {d : σ →₀ ℕ} (hd : d ∈ f.support) : ∃ i, d i < n :=
   by
@@ -1161,12 +759,6 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
     
 #align mv_polynomial.exists_degree_lt MvPolynomial.exists_degree_lt
 
-/- warning: mv_polynomial.coeff_eq_zero_of_total_degree_lt -> MvPolynomial.coeff_eq_zero_of_totalDegree_lt is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {f : MvPolynomial.{u2, u1} σ R _inst_1} {d : Finsupp.{u2, 0} σ Nat Nat.hasZero}, (LT.lt.{0} Nat Nat.hasLt (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 f) (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat Nat.hasZero d) (fun (i : σ) => coeFn.{succ u2, succ u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u2, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u2, 0} σ Nat Nat.hasZero) d i))) -> (Eq.{succ u1} R (MvPolynomial.coeff.{u1, u2} R σ _inst_1 d f) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))
-but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {f : MvPolynomial.{u1, u2} σ R _inst_1} {d : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)}, (LT.lt.{0} Nat instLTNat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 f) (Finset.sum.{0, u1} Nat σ Nat.addCommMonoid (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => 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))) -> (Eq.{succ u2} R (MvPolynomial.coeff.{u2, u1} R σ _inst_1 d f) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_ltₓ'. -/
 theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ ℕ}
     (h : f.totalDegree < ∑ i in d.support, d i) : coeff d f = 0 := by
   classical
@@ -1176,9 +768,6 @@ theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ 
     · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_lt
 
-/- warning: mv_polynomial.total_degree_rename_le -> MvPolynomial.totalDegree_rename_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_rename_le MvPolynomial.totalDegree_rename_leₓ'. -/
 theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     (rename f p).totalDegree ≤ p.totalDegree :=
   Finset.sup_le fun b => by
@@ -1203,9 +792,6 @@ section EvalVars
 
 variable [CommSemiring S]
 
-/- warning: mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars -> MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars MvPolynomial.eval₂Hom_eq_constantCoeff_of_varsₓ'. -/
 theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p : MvPolynomial σ R}
     (hp : ∀ i ∈ p.vars, g i = 0) : eval₂Hom f g p = f (constantCoeff p) :=
   by
@@ -1234,17 +820,11 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
     intro ; contradiction
 #align mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars
 
-/- warning: mv_polynomial.aeval_eq_constant_coeff_of_vars -> MvPolynomial.aeval_eq_constantCoeff_of_vars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_eq_constant_coeff_of_vars MvPolynomial.aeval_eq_constantCoeff_of_varsₓ'. -/
 theorem aeval_eq_constantCoeff_of_vars [Algebra R S] {g : σ → S} {p : MvPolynomial σ R}
     (hp : ∀ i ∈ p.vars, g i = 0) : aeval g p = algebraMap _ _ (constantCoeff p) :=
   eval₂Hom_eq_constantCoeff_of_vars _ hp
 #align mv_polynomial.aeval_eq_constant_coeff_of_vars MvPolynomial.aeval_eq_constantCoeff_of_vars
 
-/- warning: mv_polynomial.eval₂_hom_congr' -> MvPolynomial.eval₂Hom_congr' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_congr' MvPolynomial.eval₂Hom_congr'ₓ'. -/
 theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p₂ : MvPolynomial σ R} :
     f₁ = f₂ →
       (∀ i, i ∈ p₁.vars → i ∈ p₂.vars → g₁ i = g₂ i) →
@@ -1264,9 +844,6 @@ theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p
   rw [h i this this]
 #align mv_polynomial.eval₂_hom_congr' MvPolynomial.eval₂Hom_congr'
 
-/- warning: mv_polynomial.hom_congr_vars -> MvPolynomial.hom_congr_vars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.hom_congr_vars MvPolynomial.hom_congr_varsₓ'. -/
 /-- If `f₁` and `f₂` are ring homs out of the polynomial ring and `p₁` and `p₂` are polynomials,
   then `f₁ p₁ = f₂ p₂` if `p₁ = p₂` and `f₁` and `f₂` are equal on `R` and on the variables
   of `p₁`.  -/
@@ -1280,9 +857,6 @@ theorem hom_congr_vars {f₁ f₂ : MvPolynomial σ R →+* S} {p₁ p₂ : MvPo
     
 #align mv_polynomial.hom_congr_vars MvPolynomial.hom_congr_vars
 
-/- warning: mv_polynomial.exists_rename_eq_of_vars_subset_range -> MvPolynomial.exists_rename_eq_of_vars_subset_range is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.exists_rename_eq_of_vars_subset_range MvPolynomial.exists_rename_eq_of_vars_subset_rangeₓ'. -/
 theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ → σ) (hfi : Injective f)
     (hf : ↑p.vars ⊆ Set.range f) : ∃ q : MvPolynomial τ R, rename f q = p :=
   ⟨aeval (fun i : σ => Option.elim' 0 X <| partialInv f i) p,
@@ -1297,9 +871,6 @@ theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ 
     · rfl⟩
 #align mv_polynomial.exists_rename_eq_of_vars_subset_range MvPolynomial.exists_rename_eq_of_vars_subset_range
 
-/- warning: mv_polynomial.vars_rename -> MvPolynomial.vars_rename is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_rename MvPolynomial.vars_renameₓ'. -/
 theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).vars ⊆ φ.vars.image f := by
   intro i hi
@@ -1307,9 +878,6 @@ theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
   simpa only [Multiset.mem_map] using degrees_rename _ _ hi
 #align mv_polynomial.vars_rename MvPolynomial.vars_rename
 
-/- warning: mv_polynomial.mem_vars_rename -> MvPolynomial.mem_vars_rename is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_vars_rename MvPolynomial.mem_vars_renameₓ'. -/
 theorem mem_vars_rename (f : σ → τ) (φ : MvPolynomial σ R) {j : τ} (h : j ∈ (rename f φ).vars) :
     ∃ i : σ, i ∈ φ.vars ∧ f i = j := by
   classical simpa only [exists_prop, Finset.mem_image] using vars_rename f φ h

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

@@ -171,10 +171,7 @@ but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R], Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (Zero.toOfNat0.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommMonoidWithZero.toZero.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toCommMonoidWithZero.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (OfNat.ofNat.{u1} (Multiset.{u1} σ) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} σ) (Multiset.instZeroMultiset.{u1} σ)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_zero MvPolynomial.degrees_zeroₓ'. -/
 @[simp]
-theorem degrees_zero : degrees (0 : MvPolynomial σ R) = 0 :=
-  by
-  rw [← C_0]
-  exact degrees_C 0
+theorem degrees_zero : degrees (0 : MvPolynomial σ R) = 0 := by rw [← C_0]; exact degrees_C 0
 #align mv_polynomial.degrees_zero MvPolynomial.degrees_zero
 
 /- warning: mv_polynomial.degrees_one -> MvPolynomial.degrees_one is a dubious translation:
@@ -216,8 +213,7 @@ theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → M
     (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by
   classical
     refine' s.induction _ _
-    · simp only [Finset.sum_empty, Finset.sup_empty, degrees_zero]
-      exact le_rfl
+    · simp only [Finset.sum_empty, Finset.sup_empty, degrees_zero]; exact le_rfl
     · intro i s his ih
       rw [Finset.sup_insert, Finset.sum_insert his]
       exact le_trans (degrees_add _ _) (sup_le_sup_left ih _)
@@ -321,8 +317,7 @@ theorem degrees_add_of_disjoint [DecidableEq σ] {p q : MvPolynomial σ R}
   · apply degrees_add
   · apply Multiset.union_le
     · apply le_degrees_add h
-    · rw [add_comm]
-      apply le_degrees_add h.symm
+    · rw [add_comm]; apply le_degrees_add h.symm
 #align mv_polynomial.degrees_add_of_disjoint MvPolynomial.degrees_add_of_disjoint
 
 /- warning: mv_polynomial.degrees_map -> MvPolynomial.degrees_map is a dubious translation:
@@ -522,8 +517,7 @@ theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars 
   simp only [mem_vars, Finset.mem_union]
   rintro ⟨d, hd, hi⟩
   rw [mem_support_iff, coeff_mul] at hd
-  contrapose! hd
-  cases hd
+  contrapose! hd; cases hd
   rw [Finset.sum_eq_zero]
   rintro ⟨d₁, d₂⟩ H
   rw [Finsupp.mem_antidiagonal] at H
@@ -531,13 +525,9 @@ theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars 
   obtain H | H : i ∈ d₁.support ∨ i ∈ d₂.support := by
     simpa only [Finset.mem_union] using Finsupp.support_add hi
   · suffices coeff d₁ φ = 0 by simp [this]
-    rw [coeff, ← Finsupp.not_mem_support_iff]
-    intro
-    solve_by_elim
+    rw [coeff, ← Finsupp.not_mem_support_iff]; intro ; solve_by_elim
   · suffices coeff d₂ ψ = 0 by simp [this]
-    rw [coeff, ← Finsupp.not_mem_support_iff]
-    intro
-    solve_by_elim
+    rw [coeff, ← Finsupp.not_mem_support_iff]; intro ; solve_by_elim
 #align mv_polynomial.vars_mul MvPolynomial.vars_mul
 
 /- warning: mv_polynomial.vars_one -> MvPolynomial.vars_one is a dubious translation:
@@ -699,10 +689,7 @@ but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) [_inst_3 : DecidableEq.{succ u1} σ], Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (Finset.biUnion.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (a : σ) (b : σ) => _inst_3 a b) (MvPolynomial.support.{u2, u1} R σ _inst_1 p) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_biUnion_supportₓ'. -/
 theorem vars_eq_support_biUnion_support [DecidableEq σ] :
-    p.vars = p.support.biUnion Finsupp.support :=
-  by
-  ext i
-  rw [mem_vars, Finset.mem_biUnion]
+    p.vars = p.support.biUnion Finsupp.support := by ext i; rw [mem_vars, Finset.mem_biUnion]
 #align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_biUnion_support
 
 end Map
@@ -1041,10 +1028,8 @@ theorem totalDegree_mul (a b : MvPolynomial σ R) :
       rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
       rw [Finsupp.sum_add_index']
       · exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
-      · intro a
-        rfl
-      · intro a b₁ b₂
-        rfl
+      · intro a; rfl
+      · intro a b₁ b₂; rfl
 #align mv_polynomial.total_degree_mul MvPolynomial.totalDegree_mul
 
 /- warning: mv_polynomial.total_degree_smul_le -> MvPolynomial.totalDegree_smul_le is a dubious translation:
@@ -1171,10 +1156,7 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
     n * Fintype.card σ = ∑ s : σ, n := by
       rw [Finset.sum_const, Nat.nsmul_eq_mul, mul_comm, Finset.card_univ]
     _ ≤ ∑ s, d s := (Finset.sum_le_sum fun s _ => h s)
-    _ ≤ d.sum fun i e => e := by
-      rw [Finsupp.sum_fintype]
-      intros
-      rfl
+    _ ≤ d.sum fun i e => e := by rw [Finsupp.sum_fintype]; intros ; rfl
     _ ≤ f.total_degree := Finset.le_sup hd
     
 #align mv_polynomial.exists_degree_lt MvPolynomial.exists_degree_lt
@@ -1189,10 +1171,8 @@ theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ 
     (h : f.totalDegree < ∑ i in d.support, d i) : coeff d f = 0 := by
   classical
     rw [total_degree, Finset.sup_lt_iff] at h
-    · specialize h d
-      rw [mem_support_iff] at h
-      refine' not_not.mp (mt h _)
-      exact lt_irrefl _
+    · specialize h d; rw [mem_support_iff] at h
+      refine' not_not.mp (mt h _); exact lt_irrefl _
     · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_lt
 
@@ -1245,15 +1225,13 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
       by
       rw [constant_coeff_eq, coeff, ← Finsupp.not_mem_support_iff] at h0
       rw [Finset.nonempty_iff_ne_empty, Ne.def, Finsupp.support_eq_empty]
-      rintro rfl
-      contradiction
+      rintro rfl; contradiction
     rw [Finsupp.prod, Finset.prod_eq_zero hi, MulZeroClass.mul_zero]
     rw [hp, zero_pow (Nat.pos_of_ne_zero <| finsupp.mem_support_iff.mp hi)]
     rw [mem_vars]
     exact ⟨d, hd, hi⟩
   · rw [constant_coeff_eq, coeff, ← Ne.def, ← Finsupp.mem_support_iff] at h0
-    intro
-    contradiction
+    intro ; contradiction
 #align mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars
 
 /- warning: mv_polynomial.aeval_eq_constant_coeff_of_vars -> MvPolynomial.aeval_eq_constantCoeff_of_vars is a dubious translation:
@@ -1282,9 +1260,7 @@ theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p
   simp only [Finsupp.prod]
   apply Finset.prod_congr rfl
   intro i hi
-  have : i ∈ p.vars := by
-    rw [mem_vars]
-    exact ⟨d, hd, hi⟩
+  have : i ∈ p.vars := by rw [mem_vars]; exact ⟨d, hd, hi⟩
   rw [h i this this]
 #align mv_polynomial.eval₂_hom_congr' MvPolynomial.eval₂Hom_congr'
 

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

@@ -340,10 +340,7 @@ theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
 #align mv_polynomial.degrees_map MvPolynomial.degrees_map
 
 /- warning: mv_polynomial.degrees_rename -> MvPolynomial.degrees_rename is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_rename MvPolynomial.degrees_renameₓ'. -/
 theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).degrees ⊆ φ.degrees.map f := by
@@ -363,10 +360,7 @@ theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
 #align mv_polynomial.degrees_rename MvPolynomial.degrees_rename
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_map_of_injective MvPolynomial.degrees_map_of_injectiveₓ'. -/
 theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R →+* S}
     (hf : Injective f) : (map f p).degrees = p.degrees := by
@@ -374,10 +368,7 @@ theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R
 #align mv_polynomial.degrees_map_of_injective MvPolynomial.degrees_map_of_injective
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_rename_of_injective MvPolynomial.degrees_rename_of_injectiveₓ'. -/
 theorem degrees_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f) :
     degrees (rename f p) = (degrees p).map f := by
@@ -601,10 +592,7 @@ section IsDomain
 variable {A : Type _} [CommRing A] [IsDomain A]
 
 /- warning: mv_polynomial.vars_C_mul -> MvPolynomial.vars_C_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_C_mul MvPolynomial.vars_C_mulₓ'. -/
 theorem vars_C_mul (a : A) (ha : a ≠ 0) (φ : MvPolynomial σ A) : (C a * φ).vars = φ.vars :=
   by
@@ -687,10 +675,7 @@ theorem vars_map : (map f p).vars ⊆ p.vars := by simp [vars, degrees_map]
 variable {f}
 
 /- warning: mv_polynomial.vars_map_of_injective -> MvPolynomial.vars_map_of_injective is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_map_of_injective MvPolynomial.vars_map_of_injectiveₓ'. -/
 theorem vars_map_of_injective (hf : Injective f) : (map f p).vars = p.vars := by
   simp [vars, degrees_map_of_injective _ hf]
@@ -887,10 +872,7 @@ theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
 #align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eq
 
 /- warning: mv_polynomial.degree_of_rename_of_injective -> MvPolynomial.degreeOf_rename_of_injective is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_rename_of_injective MvPolynomial.degreeOf_rename_of_injectiveₓ'. -/
 theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
     (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by
@@ -1215,10 +1197,7 @@ theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ 
 #align mv_polynomial.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_lt
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_rename_le MvPolynomial.totalDegree_rename_leₓ'. -/
 theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     (rename f p).totalDegree ≤ p.totalDegree :=
@@ -1245,10 +1224,7 @@ section EvalVars
 variable [CommSemiring S]
 
 /- warning: mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars -> MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars MvPolynomial.eval₂Hom_eq_constantCoeff_of_varsₓ'. -/
 theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p : MvPolynomial σ R}
     (hp : ∀ i ∈ p.vars, g i = 0) : eval₂Hom f g p = f (constantCoeff p) :=
@@ -1281,10 +1257,7 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
 #align mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars
 
 /- warning: mv_polynomial.aeval_eq_constant_coeff_of_vars -> MvPolynomial.aeval_eq_constantCoeff_of_vars is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_eq_constant_coeff_of_vars MvPolynomial.aeval_eq_constantCoeff_of_varsₓ'. -/
 theorem aeval_eq_constantCoeff_of_vars [Algebra R S] {g : σ → S} {p : MvPolynomial σ R}
     (hp : ∀ i ∈ p.vars, g i = 0) : aeval g p = algebraMap _ _ (constantCoeff p) :=
@@ -1292,10 +1265,7 @@ theorem aeval_eq_constantCoeff_of_vars [Algebra R S] {g : σ → S} {p : MvPolyn
 #align mv_polynomial.aeval_eq_constant_coeff_of_vars MvPolynomial.aeval_eq_constantCoeff_of_vars
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_congr' MvPolynomial.eval₂Hom_congr'ₓ'. -/
 theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p₂ : MvPolynomial σ R} :
     f₁ = f₂ →
@@ -1319,10 +1289,7 @@ theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p
 #align mv_polynomial.eval₂_hom_congr' MvPolynomial.eval₂Hom_congr'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.hom_congr_vars MvPolynomial.hom_congr_varsₓ'. -/
 /-- If `f₁` and `f₂` are ring homs out of the polynomial ring and `p₁` and `p₂` are polynomials,
   then `f₁ p₁ = f₂ p₂` if `p₁ = p₂` and `f₁` and `f₂` are equal on `R` and on the variables
@@ -1338,10 +1305,7 @@ theorem hom_congr_vars {f₁ f₂ : MvPolynomial σ R →+* S} {p₁ p₂ : MvPo
 #align mv_polynomial.hom_congr_vars MvPolynomial.hom_congr_vars
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.exists_rename_eq_of_vars_subset_range MvPolynomial.exists_rename_eq_of_vars_subset_rangeₓ'. -/
 theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ → σ) (hfi : Injective f)
     (hf : ↑p.vars ⊆ Set.range f) : ∃ q : MvPolynomial τ R, rename f q = p :=
@@ -1358,10 +1322,7 @@ theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ 
 #align mv_polynomial.exists_rename_eq_of_vars_subset_range MvPolynomial.exists_rename_eq_of_vars_subset_range
 
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(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))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, 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} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))) (Algebra.toModule.{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, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} 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))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, 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} σ 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)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (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))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))) (Algebra.toModule.{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, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u2) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} 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))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} 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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ 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)))) (Module.toDistribMulAction.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (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))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))) (Algebra.toModule.{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, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u1 u3, max u2 u3, max (max u1 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)) (AlgHom.{u3, max u3 u1, max u3 u2} 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))) (AlgHom.algHomClass.{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 f) φ)) (Finset.image.{u1, u2} σ τ (fun (a : τ) (b : τ) => _inst_3 a b) f (MvPolynomial.vars.{u3, u1} R σ _inst_1 φ))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_rename MvPolynomial.vars_renameₓ'. -/
 theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).vars ⊆ φ.vars.image f := by
@@ -1371,10 +1332,7 @@ theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
 #align mv_polynomial.vars_rename MvPolynomial.vars_rename
 
 /- warning: mv_polynomial.mem_vars_rename -> MvPolynomial.mem_vars_rename is a dubious translation:
-lean 3 declaration is
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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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) φ))) -> (Exists.{succ u2} σ (fun (i : σ) => And (Membership.mem.{u2, u2} σ (Finset.{u2} σ) (Finset.instMembershipFinset.{u2} σ) i (MvPolynomial.vars.{u3, u2} R σ _inst_1 φ)) (Eq.{succ u1} τ (f i) j)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_vars_rename MvPolynomial.mem_vars_renameₓ'. -/
 theorem mem_vars_rename (f : σ → τ) (φ : MvPolynomial σ R) {j : τ} (h : j ∈ (rename f φ).vars) :
     ∃ i : σ, i ∈ φ.vars ∧ f i = j := by

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

@@ -110,7 +110,7 @@ theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (s : Finsupp.{u2, 0} σ Nat Nat.hasZero) (a : R), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toHasLe.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 s) a)) (coeFn.{succ u2, succ u2} (AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (fun (_x : AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) => (Finsupp.{u2, 0} σ Nat Nat.hasZero) -> (Multiset.{u2} σ)) (AddEquiv.hasCoeToFun.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (Finsupp.toMultiset.{u2} σ) s)
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s)
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomialₓ'. -/
 theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ s.toMultiset := by
   classical
@@ -124,7 +124,7 @@ theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) 
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (s : Finsupp.{u2, 0} σ Nat Nat.hasZero) (a : R), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) -> (Eq.{succ u2} (Multiset.{u2} σ) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 s) a)) (coeFn.{succ u2, succ u2} (AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (fun (_x : AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) => (Finsupp.{u2, 0} σ Nat Nat.hasZero) -> (Multiset.{u2} σ)) (AddEquiv.hasCoeToFun.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (Finsupp.toMultiset.{u2} σ) s))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), (Ne.{succ u2} R a (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), (Ne.{succ u2} R a (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eqₓ'. -/
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
     degrees (monomial s a) = s.toMultiset := by
@@ -343,7 +343,7 @@ theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} {τ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] (f : σ -> τ) (φ : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u3} (Multiset.{u3} τ) (Multiset.hasSubset.{u3} τ) (MvPolynomial.degrees.{u1, u3} R τ _inst_1 (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) => (MvPolynomial.{u2, u1} σ R _inst_1) -> (MvPolynomial.{u3, u1} τ R _inst_1)) ([anonymous].{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.rename.{u2, u3, u1} σ τ R _inst_1 f) φ)) (Multiset.map.{u2, u3} σ τ f (MvPolynomial.degrees.{u1, u2} R σ _inst_1 φ))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> τ) (φ : MvPolynomial.{u2, u3} σ R _inst_1), HasSubset.Subset.{u1} (Multiset.{u1} τ) (Multiset.instHasSubsetMultiset.{u1} τ) (MvPolynomial.degrees.{u3, u1} R τ _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 (_x : 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) _x) (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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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))))))) (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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) φ)) (Multiset.map.{u2, u1} σ τ f (MvPolynomial.degrees.{u3, u2} R σ _inst_1 φ))
+  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> τ) (φ : MvPolynomial.{u2, u3} σ R _inst_1), HasSubset.Subset.{u1} (Multiset.{u1} τ) (Multiset.instHasSubsetMultiset.{u1} τ) (MvPolynomial.degrees.{u3, u1} R τ _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 (_x : 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) _x) (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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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))))))) (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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) φ)) (Multiset.map.{u2, u1} σ τ f (MvPolynomial.degrees.{u3, u2} R σ _inst_1 φ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_rename MvPolynomial.degrees_renameₓ'. -/
 theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).degrees ⊆ φ.degrees.map f := by
@@ -377,7 +377,7 @@ theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} {τ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] {p : MvPolynomial.{u2, u1} σ R _inst_1} {f : σ -> τ}, (Function.Injective.{succ u2, succ u3} σ τ f) -> (Eq.{succ u3} (Multiset.{u3} τ) (MvPolynomial.degrees.{u1, u3} R τ _inst_1 (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) => (MvPolynomial.{u2, u1} σ R _inst_1) -> (MvPolynomial.{u3, u1} τ R _inst_1)) ([anonymous].{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.rename.{u2, u3, u1} σ τ R _inst_1 f) p)) (Multiset.map.{u2, u3} σ τ f (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p)))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {p : MvPolynomial.{u2, u3} σ R _inst_1} {f : σ -> τ}, (Function.Injective.{succ u2, succ u1} σ τ f) -> (Eq.{succ u1} (Multiset.{u1} τ) (MvPolynomial.degrees.{u3, u1} R τ _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 (_x : 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) _x) (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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} 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_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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) p)) (Multiset.map.{u2, u1} σ τ f (MvPolynomial.degrees.{u3, u2} R σ _inst_1 p)))
+  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {p : MvPolynomial.{u2, u3} σ R _inst_1} {f : σ -> τ}, (Function.Injective.{succ u2, succ u1} σ τ f) -> (Eq.{succ u1} (Multiset.{u1} τ) (MvPolynomial.degrees.{u3, u1} R τ _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 (_x : 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) _x) (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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} 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(MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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))))))) (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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) p)) (Multiset.map.{u2, u1} σ τ f (MvPolynomial.degrees.{u3, u2} R σ _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_rename_of_injective MvPolynomial.degrees_rename_of_injectiveₓ'. -/
 theorem degrees_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f) :
     degrees (rename f p) = (degrees p).map f := by
@@ -428,7 +428,7 @@ theorem vars_0 : (0 : MvPolynomial σ R).vars = ∅ := by
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} {r : R} {s : Finsupp.{u2, 0} σ Nat Nat.hasZero} [_inst_1 : CommSemiring.{u1} R], (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 s) r)) (Finsupp.support.{u2, 0} σ Nat Nat.hasZero s))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} {r : R} {s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)} [_inst_1 : CommSemiring.{u2} R], (Ne.{succ u2} R r (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) r)) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s))
+  forall {R : Type.{u2}} {σ : Type.{u1}} {r : R} {s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)} [_inst_1 : CommSemiring.{u2} R], (Ne.{succ u2} R r (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) r)) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_monomial MvPolynomial.vars_monomialₓ'. -/
 @[simp]
 theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by
@@ -700,7 +700,7 @@ theorem vars_map_of_injective (hf : Injective f) : (map f p).vars = p.vars := by
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (i : σ) {e : Nat} {r : R}, (Ne.{1} Nat e (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 (Finsupp.single.{u2, 0} σ Nat Nat.hasZero i e)) r)) (Singleton.singleton.{u2, u2} σ (Finset.{u2} σ) (Finset.hasSingleton.{u2} σ) i))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (i : σ) {e : Nat} {r : R}, (Ne.{1} Nat e (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Ne.{succ u2} R r (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 (Finsupp.single.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) i e)) r)) (Singleton.singleton.{u1, u1} σ (Finset.{u1} σ) (Finset.instSingletonFinset.{u1} σ) i))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (i : σ) {e : Nat} {r : R}, (Ne.{1} Nat e (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Ne.{succ u2} R r (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 (Finsupp.single.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) i e)) r)) (Singleton.singleton.{u1, u1} σ (Finset.{u1} σ) (Finset.instSingletonFinset.{u1} σ) i))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_monomial_single MvPolynomial.vars_monomial_singleₓ'. -/
 theorem vars_monomial_single (i : σ) {e : ℕ} {r : R} (he : e ≠ 0) (hr : r ≠ 0) :
     (monomial (Finsupp.single i e) r).vars = {i} := by
@@ -890,7 +890,7 @@ theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} {τ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] {p : MvPolynomial.{u2, u1} σ R _inst_1} {f : σ -> τ}, (Function.Injective.{succ u2, succ u3} σ τ f) -> (forall (i : σ), Eq.{1} Nat (MvPolynomial.degreeOf.{u1, u3} R τ _inst_1 (f i) (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) => (MvPolynomial.{u2, u1} σ R _inst_1) -> (MvPolynomial.{u3, u1} τ R _inst_1)) ([anonymous].{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.rename.{u2, u3, u1} σ τ R _inst_1 f) p)) (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 i p))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {p : MvPolynomial.{u2, u3} σ R _inst_1} {f : σ -> τ}, (Function.Injective.{succ u2, succ u1} σ τ f) -> (forall (i : σ), Eq.{1} Nat (MvPolynomial.degreeOf.{u3, u1} R τ _inst_1 (f i) (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 (_x : 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) _x) (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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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))))))) (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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) p)) (MvPolynomial.degreeOf.{u3, u2} R σ _inst_1 i p))
+  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {p : MvPolynomial.{u2, u3} σ R _inst_1} {f : σ -> τ}, (Function.Injective.{succ u2, succ u1} σ τ f) -> (forall (i : σ), Eq.{1} Nat (MvPolynomial.degreeOf.{u3, u1} R τ _inst_1 (f i) (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 (_x : 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) _x) (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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} 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(MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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} 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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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) p)) (MvPolynomial.degreeOf.{u3, u2} R σ _inst_1 i p))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_rename_of_injective MvPolynomial.degreeOf_rename_of_injectiveₓ'. -/
 theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
     (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by
@@ -1098,7 +1098,7 @@ theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (s : Finsupp.{u2, 0} σ Nat Nat.hasZero) {c : R}, (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) -> (Eq.{1} Nat (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 s) c)) (Finsupp.sum.{u2, 0, 0} σ Nat Nat Nat.hasZero Nat.addCommMonoid s (fun (_x : σ) (e : Nat) => e)))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) {c : R}, (Ne.{succ u2} R c (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) c)) (Finsupp.sum.{u1, 0, 0} σ Nat Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) Nat.addCommMonoid s (fun (_x : σ) (e : Nat) => e)))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) {c : R}, (Ne.{succ u2} R c (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) c)) (Finsupp.sum.{u1, 0, 0} σ Nat Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) Nat.addCommMonoid s (fun (_x : σ) (e : Nat) => e)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_monomial MvPolynomial.totalDegree_monomialₓ'. -/
 @[simp]
 theorem totalDegree_monomial (s : σ →₀ ℕ) {c : R} (hc : c ≠ 0) :
@@ -1218,7 +1218,7 @@ theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ 
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} {τ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] (f : σ -> τ) (p : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{0} Nat Nat.hasLe (MvPolynomial.totalDegree.{u1, u3} R τ _inst_1 (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) => (MvPolynomial.{u2, u1} σ R _inst_1) -> (MvPolynomial.{u3, u1} τ R _inst_1)) ([anonymous].{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.rename.{u2, u3, u1} σ τ R _inst_1 f) p)) (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 p)
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> τ) (p : MvPolynomial.{u2, u3} σ R _inst_1), LE.le.{0} Nat instLENat (MvPolynomial.totalDegree.{u3, u1} R τ _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 (_x : 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) _x) (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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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))))))) (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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) p)) (MvPolynomial.totalDegree.{u3, u2} R σ _inst_1 p)
+  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> τ) (p : MvPolynomial.{u2, u3} σ R _inst_1), LE.le.{0} Nat instLENat (MvPolynomial.totalDegree.{u3, u1} R τ _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 (_x : 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) _x) (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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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))))))) (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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) p)) (MvPolynomial.totalDegree.{u3, u2} R σ _inst_1 p)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_rename_le MvPolynomial.totalDegree_rename_leₓ'. -/
 theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     (rename f p).totalDegree ≤ p.totalDegree :=
@@ -1284,7 +1284,7 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {g : σ -> S} {p : MvPolynomial.{u3, u1} σ R _inst_1}, (forall (i : σ), (Membership.Mem.{u3, u3} σ (Finset.{u3} σ) (Finset.hasMem.{u3} σ) i (MvPolynomial.vars.{u1, u3} R σ _inst_1 p)) -> (Eq.{succ u2} S (g i) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))))))) -> (Eq.{succ u2} S (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (AlgHom.{u1, max u3 u1, u2} R (MvPolynomial.{u3, u1} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (CommSemiring.toSemiring.{u2} S _inst_2) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgHom.{u1, max u3 u1, u2} R (MvPolynomial.{u3, u1} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (CommSemiring.toSemiring.{u2} S _inst_2) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) => (MvPolynomial.{u3, u1} σ R _inst_1) -> S) ([anonymous].{u1, max u3 u1, u2} R (MvPolynomial.{u3, u1} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (CommSemiring.toSemiring.{u2} S _inst_2) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) (MvPolynomial.aeval.{u1, u2, u3} R S σ _inst_1 _inst_2 _inst_3 g) p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ u1), max (succ (max u3 u1)) (succ u1)} (RingHom.{max u3 u1, u1} (MvPolynomial.{u3, u1} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{max u3 u1, u1} (MvPolynomial.{u3, u1} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> R) (RingHom.hasCoeToFun.{max u3 u1, u1} (MvPolynomial.{u3, u1} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.constantCoeff.{u1, u3} R σ _inst_1) p)))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {g : σ -> S} {p : MvPolynomial.{u1, u2} σ R _inst_1}, (forall (i : σ), (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 p)) -> (Eq.{succ u3} S (g i) (OfNat.ofNat.{u3} S 0 (Zero.toOfNat0.{u3} S (CommMonoidWithZero.toZero.{u3} S (CommSemiring.toCommMonoidWithZero.{u3} S _inst_2)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => S) p) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (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) => S) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (MvPolynomial.{u1, u2} σ R _inst_1) S (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 u2 u1} (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 u2 u1} (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 u2 u1} (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 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))))))) (SMulZeroClass.toSMul.{u2, 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.{u2, 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.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} 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.{u2, u3} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (MvPolynomial.{u1, u2} σ R _inst_1) S (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 u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _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.{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, u3} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (MvPolynomial.{u1, u2} σ R _inst_1) S (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.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (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, u3} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, u3, max (max u3 u1) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (AlgHom.algHomClass.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3))))) (MvPolynomial.aeval.{u2, u3, u1} R S σ _inst_1 _inst_2 _inst_3 g) p) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) S (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) 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(Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) S (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} ((fun 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(CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) S (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (RingHom.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) 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(MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u2} (RingHom.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (MvPolynomial.constantCoeff.{u2, u1} R σ _inst_1) p)))
+  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {g : σ -> S} {p : MvPolynomial.{u1, u2} σ R _inst_1}, (forall (i : σ), (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 p)) -> (Eq.{succ u3} S (g i) (OfNat.ofNat.{u3} S 0 (Zero.toOfNat0.{u3} S (CommMonoidWithZero.toZero.{u3} S (CommSemiring.toCommMonoidWithZero.{u3} S _inst_2)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} σ R _inst_1) => S) p) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S 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(DistribMulAction.toDistribSMul.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} 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.{u2, u3} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ 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(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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (MvPolynomial.constantCoeff.{u2, u1} R σ _inst_1) p)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_eq_constant_coeff_of_vars MvPolynomial.aeval_eq_constantCoeff_of_varsₓ'. -/
 theorem aeval_eq_constantCoeff_of_vars [Algebra R S] {g : σ → S} {p : MvPolynomial σ R}
     (hp : ∀ i ∈ p.vars, g i = 0) : aeval g p = algebraMap _ _ (constantCoeff p) :=
@@ -1341,7 +1341,7 @@ theorem hom_congr_vars {f₁ f₂ : MvPolynomial σ R →+* S} {p₁ p₂ : MvPo
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} {τ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1) (f : τ -> σ), (Function.Injective.{succ u3, succ u2} τ σ f) -> (HasSubset.Subset.{u2} (Set.{u2} σ) (Set.hasSubset.{u2} σ) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} σ) (Set.{u2} σ) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} σ) (Set.{u2} σ) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} σ) (Set.{u2} σ) (Finset.Set.hasCoeT.{u2} σ))) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p)) (Set.range.{u2, succ u3} σ τ f)) -> (Exists.{max (succ u3) (succ u1)} (MvPolynomial.{u3, u1} τ R _inst_1) (fun (q : MvPolynomial.{u3, u1} τ R _inst_1) => Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R _inst_1) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (AlgHom.{u1, max u3 u1, max u2 u1} R (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _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, u3} R R τ _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))) (fun (_x : AlgHom.{u1, max u3 u1, max u2 u1} R (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _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, u3} R R τ _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.{u3, u1} τ R _inst_1) -> (MvPolynomial.{u2, u1} σ R _inst_1)) ([anonymous].{u1, max u3 u1, max u2 u1} R (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _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, u3} R R τ _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.rename.{u3, u2, u1} τ σ R _inst_1 f) q) p))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] (p : MvPolynomial.{u2, u3} σ R _inst_1) (f : τ -> σ), (Function.Injective.{succ u1, succ u2} τ σ f) -> (HasSubset.Subset.{u2} (Set.{u2} σ) (Set.instHasSubsetSet.{u2} σ) (Finset.toSet.{u2} σ (MvPolynomial.vars.{u3, u2} R σ _inst_1 p)) (Set.range.{u2, succ u1} σ τ f)) -> (Exists.{max (succ u3) (succ u1)} (MvPolynomial.{u1, u3} τ R _inst_1) (fun (q : MvPolynomial.{u1, u3} τ R _inst_1) => Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u3} τ R _inst_1) => MvPolynomial.{u2, u3} σ R _inst_1) q) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u1) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u3, max u3 u1, max u3 u2} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.{u1, u3} τ R _inst_1) (fun (_x : MvPolynomial.{u1, u3} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u3} τ R _inst_1) => MvPolynomial.{u2, u3} σ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u2 u1) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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))))))) (SMulZeroClass.toSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)))))) (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)))))) (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)))) (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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u2 u1) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} 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)))) (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)))) (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)))) (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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u1 u3, max u2 u3, max (max u2 u1) u3} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (AlgHom.{u3, max u3 u1, max u3 u2} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (AlgHom.algHomClass.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (MvPolynomial.rename.{u1, u2, u3} τ σ R _inst_1 f) q) p))
+  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] (p : MvPolynomial.{u2, u3} σ R _inst_1) (f : τ -> σ), (Function.Injective.{succ u1, succ u2} τ σ f) -> (HasSubset.Subset.{u2} (Set.{u2} σ) (Set.instHasSubsetSet.{u2} σ) (Finset.toSet.{u2} σ (MvPolynomial.vars.{u3, u2} R σ _inst_1 p)) (Set.range.{u2, succ u1} σ τ f)) -> (Exists.{max (succ u3) (succ u1)} (MvPolynomial.{u1, u3} τ R _inst_1) (fun (q : MvPolynomial.{u1, u3} τ R _inst_1) => Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u3} τ R _inst_1) => MvPolynomial.{u2, u3} σ R _inst_1) q) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u1) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u3, max u3 u1, max u3 u2} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) 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_inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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} 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(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))))))) (SMulZeroClass.toSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toZero.{max u2 u3} 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(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))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)))))) (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)))))) (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)))) (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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u2 u1) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} 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)))) (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)))) (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)))) (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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u1 u3, max u2 u3, max (max u2 u1) u3} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (AlgHom.{u3, max u3 u1, max u3 u2} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (AlgHom.algHomClass.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (MvPolynomial.rename.{u1, u2, u3} τ σ R _inst_1 f) q) p))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.exists_rename_eq_of_vars_subset_range MvPolynomial.exists_rename_eq_of_vars_subset_rangeₓ'. -/
 theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ → σ) (hfi : Injective f)
     (hf : ↑p.vars ⊆ Set.range f) : ∃ q : MvPolynomial τ R, rename f q = p :=
@@ -1361,7 +1361,7 @@ theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ 
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} {τ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_3 : DecidableEq.{succ u3} τ] (f : σ -> τ) (φ : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u3} (Finset.{u3} τ) (Finset.hasSubset.{u3} τ) (MvPolynomial.vars.{u1, u3} R τ _inst_1 (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) => (MvPolynomial.{u2, u1} σ R _inst_1) -> (MvPolynomial.{u3, u1} τ R _inst_1)) ([anonymous].{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.rename.{u2, u3, u1} σ τ R _inst_1 f) φ)) (Finset.image.{u2, u3} σ τ (fun (a : τ) (b : τ) => _inst_3 a b) f (MvPolynomial.vars.{u1, u2} R σ _inst_1 φ))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u1}} {τ : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_3 : DecidableEq.{succ u2} τ] (f : σ -> τ) (φ : MvPolynomial.{u1, u3} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} τ) (Finset.instHasSubsetFinset.{u2} τ) (MvPolynomial.vars.{u3, u2} R τ _inst_1 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u3, max u3 u1, max u3 u2} 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) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u2, u3} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} 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))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (SMulZeroClass.toSMul.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toZero.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ 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))))))) (DistribSMul.toSMulZeroClass.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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} σ 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)))))) (Module.toDistribMulAction.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (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))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, 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} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))) (Algebra.toModule.{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, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} 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))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, 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} σ 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)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (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))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))) (Algebra.toModule.{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, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u2) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} 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))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} 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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ 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)))) (Module.toDistribMulAction.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (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))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))) (Algebra.toModule.{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, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u1 u3, max u2 u3, max (max u1 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)) (AlgHom.{u3, max u3 u1, max u3 u2} 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))) (AlgHom.algHomClass.{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 f) φ)) (Finset.image.{u1, u2} σ τ (fun (a : τ) (b : τ) => _inst_3 a b) f (MvPolynomial.vars.{u3, u1} R σ _inst_1 φ))
+  forall {R : Type.{u3}} {σ : Type.{u1}} {τ : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_3 : DecidableEq.{succ u2} τ] (f : σ -> τ) (φ : MvPolynomial.{u1, u3} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} τ) (Finset.instHasSubsetFinset.{u2} τ) (MvPolynomial.vars.{u3, u2} R τ _inst_1 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u3, max u3 u1, max u3 u2} 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) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u2, u3} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} 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))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (SMulZeroClass.toSMul.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toZero.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ 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))))))) (DistribSMul.toSMulZeroClass.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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} σ 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)))))) (Module.toDistribMulAction.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (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))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, 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} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))) (Algebra.toModule.{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, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} 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))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, 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} σ 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)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (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))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))) (Algebra.toModule.{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, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u2) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} 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))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} 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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ 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)))) (Module.toDistribMulAction.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (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))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))) (Algebra.toModule.{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, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u1 u3, max u2 u3, max (max u1 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)) (AlgHom.{u3, max u3 u1, max u3 u2} 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))) (AlgHom.algHomClass.{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 f) φ)) (Finset.image.{u1, u2} σ τ (fun (a : τ) (b : τ) => _inst_3 a b) f (MvPolynomial.vars.{u3, u1} R σ _inst_1 φ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_rename MvPolynomial.vars_renameₓ'. -/
 theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).vars ⊆ φ.vars.image f := by
@@ -1374,7 +1374,7 @@ theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} {τ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] (f : σ -> τ) (φ : MvPolynomial.{u2, u1} σ R _inst_1) {j : τ}, (Membership.Mem.{u3, u3} τ (Finset.{u3} τ) (Finset.hasMem.{u3} τ) j (MvPolynomial.vars.{u1, u3} R τ _inst_1 (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) => (MvPolynomial.{u2, u1} σ R _inst_1) -> (MvPolynomial.{u3, u1} τ R _inst_1)) ([anonymous].{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.rename.{u2, u3, u1} σ τ R _inst_1 f) φ))) -> (Exists.{succ u2} σ (fun (i : σ) => And (Membership.Mem.{u2, u2} σ (Finset.{u2} σ) (Finset.hasMem.{u2} σ) i (MvPolynomial.vars.{u1, u2} R σ _inst_1 φ)) (Eq.{succ u3} τ (f i) j)))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> τ) (φ : MvPolynomial.{u2, u3} σ R _inst_1) {j : τ}, (Membership.mem.{u1, u1} τ (Finset.{u1} τ) (Finset.instMembershipFinset.{u1} τ) j (MvPolynomial.vars.{u3, u1} R τ _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 (_x : 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) _x) (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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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))))))) (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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) φ))) -> (Exists.{succ u2} σ (fun (i : σ) => And (Membership.mem.{u2, u2} σ (Finset.{u2} σ) (Finset.instMembershipFinset.{u2} σ) i (MvPolynomial.vars.{u3, u2} R σ _inst_1 φ)) (Eq.{succ u1} τ (f i) j)))
+  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> τ) (φ : MvPolynomial.{u2, u3} σ R _inst_1) {j : τ}, (Membership.mem.{u1, u1} τ (Finset.{u1} τ) (Finset.instMembershipFinset.{u1} τ) j (MvPolynomial.vars.{u3, u1} R τ _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 (_x : 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) _x) (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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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))))))) (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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) φ))) -> (Exists.{succ u2} σ (fun (i : σ) => And (Membership.mem.{u2, u2} σ (Finset.{u2} σ) (Finset.instMembershipFinset.{u2} σ) i (MvPolynomial.vars.{u3, u2} R σ _inst_1 φ)) (Eq.{succ u1} τ (f i) j)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_vars_rename MvPolynomial.mem_vars_renameₓ'. -/
 theorem mem_vars_rename (f : σ → τ) (φ : MvPolynomial σ R) {j : τ} (h : j ∈ (rename f φ).vars) :
     ∃ i : σ, i ∈ φ.vars ∧ f i = j := by

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

@@ -96,6 +96,12 @@ def degrees (p : MvPolynomial σ R) : Multiset σ :=
 #align mv_polynomial.degrees MvPolynomial.degrees
 -/
 
+/- warning: mv_polynomial.degrees_def -> MvPolynomial.degrees_def is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (p : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{succ u2} (Multiset.{u2} σ) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (Finset.sup.{u2, u2} (Multiset.{u2} σ) (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Lattice.toSemilatticeSup.{u2} (Multiset.{u2} σ) (Multiset.lattice.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b))) (Multiset.orderBot.{u2} σ) (MvPolynomial.support.{u1, u2} R σ _inst_1 p) (fun (s : Finsupp.{u2, 0} σ Nat Nat.hasZero) => coeFn.{succ u2, succ u2} (AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (fun (_x : AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) => (Finsupp.{u2, 0} σ Nat Nat.hasZero) -> (Multiset.{u2} σ)) (AddEquiv.hasCoeToFun.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (Finsupp.toMultiset.{u2} σ) s))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (p : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p) (Finset.sup.{u1, u1} (Multiset.{u1} σ) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Lattice.toSemilatticeSup.{u1} (Multiset.{u1} σ) (Multiset.instLatticeMultiset.{u1} σ (fun (a : σ) (b : σ) => _inst_2 a b))) (Multiset.instOrderBotMultisetToLEToPreorderInstPartialOrderMultiset.{u1} σ) (MvPolynomial.support.{u2, u1} R σ _inst_1 p) (fun (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_def MvPolynomial.degrees_defₓ'. -/
 theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
     p.degrees = p.support.sup fun s : σ →₀ ℕ => s.toMultiset := by convert rfl
 #align mv_polynomial.degrees_def MvPolynomial.degrees_def
@@ -186,7 +192,7 @@ theorem degrees_one : degrees (1 : MvPolynomial σ R) = 0 :=
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (p : MvPolynomial.{u2, u1} σ R _inst_1) (q : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toHasLe.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Sup.sup.{u2} (Multiset.{u2} σ) (SemilatticeSup.toHasSup.{u2} (Multiset.{u2} σ) (Lattice.toSemilatticeSup.{u2} (Multiset.{u2} σ) (Multiset.lattice.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b)))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (_inst_2 : MvPolynomial.{u1, u2} σ R _inst_1) (p : MvPolynomial.{u1, u2} σ R _inst_1), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) _inst_2 p)) (Sup.sup.{u1} (Multiset.{u1} σ) (SemilatticeSup.toSup.{u1} (Multiset.{u1} σ) (Lattice.toSemilatticeSup.{u1} (Multiset.{u1} σ) (Multiset.instLatticeMultiset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 _inst_2) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (p : MvPolynomial.{u1, u2} σ R _inst_1) (q : MvPolynomial.{u1, u2} σ R _inst_1), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)) (Sup.sup.{u1} (Multiset.{u1} σ) (SemilatticeSup.toSup.{u1} (Multiset.{u1} σ) (Lattice.toSemilatticeSup.{u1} (Multiset.{u1} σ) (Multiset.instLatticeMultiset.{u1} σ (fun (a : σ) (b : σ) => _inst_2 a b)))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 q))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_add MvPolynomial.degrees_addₓ'. -/
 theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
     (p + q).degrees ≤ p.degrees ⊔ q.degrees := by
@@ -204,7 +210,7 @@ theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} σ] (s : Finset.{u3} ι) (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toHasLe.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) s (fun (i : ι) => f i))) (Finset.sup.{u2, u3} (Multiset.{u2} σ) ι (Lattice.toSemilatticeSup.{u2} (Multiset.{u2} σ) (Multiset.lattice.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b))) (Multiset.orderBot.{u2} σ) s (fun (i : ι) => MvPolynomial.degrees.{u1, u2} R σ _inst_1 (f i)))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (_inst_2 : Finset.{u2} ι) (s : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u3, u1} R σ _inst_1 (Finset.sum.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (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))))) _inst_2 (fun (i : ι) => s i))) (Finset.sup.{u1, u2} (Multiset.{u1} σ) ι (Lattice.toSemilatticeSup.{u1} (Multiset.{u1} σ) (Multiset.instLatticeMultiset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)))) (Multiset.instOrderBotMultisetToLEToPreorderInstPartialOrderMultiset.{u1} σ) _inst_2 (fun (i : ι) => MvPolynomial.degrees.{u3, u1} R σ _inst_1 (s i)))
+  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} σ] (s : Finset.{u2} ι) (f : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u3, u1} R σ _inst_1 (Finset.sum.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (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))))) s (fun (i : ι) => f i))) (Finset.sup.{u1, u2} (Multiset.{u1} σ) ι (Lattice.toSemilatticeSup.{u1} (Multiset.{u1} σ) (Multiset.instLatticeMultiset.{u1} σ (fun (a : σ) (b : σ) => _inst_2 a b))) (Multiset.instOrderBotMultisetToLEToPreorderInstPartialOrderMultiset.{u1} σ) s (fun (i : ι) => MvPolynomial.degrees.{u3, u1} R σ _inst_1 (f i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_sum MvPolynomial.degrees_sumₓ'. -/
 theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by
@@ -306,7 +312,7 @@ theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degre
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] {p : MvPolynomial.{u2, u1} σ R _inst_1} {q : MvPolynomial.{u2, u1} σ R _inst_1}, (Multiset.Disjoint.{u2} σ (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q)) -> (Eq.{succ u2} (Multiset.{u2} σ) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Union.union.{u2} (Multiset.{u2} σ) (Multiset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b)) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q)))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {_inst_2 : MvPolynomial.{u1, u2} σ R _inst_1} {p : MvPolynomial.{u1, u2} σ R _inst_1}, (Multiset.Disjoint.{u1} σ (MvPolynomial.degrees.{u2, u1} R σ _inst_1 _inst_2) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p)) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) _inst_2 p)) (Union.union.{u1} (Multiset.{u1} σ) (Multiset.instUnionMultiset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 _inst_2) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p)))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] {p : MvPolynomial.{u1, u2} σ R _inst_1} {q : MvPolynomial.{u1, u2} σ R _inst_1}, (Multiset.Disjoint.{u1} σ (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 q)) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)) (Union.union.{u1} (Multiset.{u1} σ) (Multiset.instUnionMultiset.{u1} σ (fun (a : σ) (b : σ) => _inst_2 a b)) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 q)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_add_of_disjoint MvPolynomial.degrees_add_of_disjointₓ'. -/
 theorem degrees_add_of_disjoint [DecidableEq σ] {p q : MvPolynomial σ R}
     (h : Multiset.Disjoint p.degrees q.degrees) : (p + q).degrees = p.degrees ∪ q.degrees :=
@@ -397,6 +403,12 @@ def vars (p : MvPolynomial σ R) : Finset σ :=
 #align mv_polynomial.vars MvPolynomial.vars
 -/
 
+/- warning: mv_polynomial.vars_def -> MvPolynomial.vars_def is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (p : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (Multiset.toFinset.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (p : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (Multiset.toFinset.{u1} σ (fun (a : σ) (b : σ) => _inst_2 a b) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_def MvPolynomial.vars_defₓ'. -/
 theorem vars_def [DecidableEq σ] (p : MvPolynomial σ R) : p.vars = p.degrees.toFinset := by
   convert rfl
 #align mv_polynomial.vars_def MvPolynomial.vars_def
@@ -480,7 +492,7 @@ theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (p : MvPolynomial.{u2, u1} σ R _inst_1) (q : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Union.union.{u2} (Finset.{u2} σ) (Finset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b)) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (MvPolynomial.vars.{u1, u2} R σ _inst_1 q))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (_inst_2 : MvPolynomial.{u1, u2} σ R _inst_1) (p : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) _inst_2 p)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.vars.{u2, u1} R σ _inst_1 _inst_2) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (p : MvPolynomial.{u1, u2} σ R _inst_1) (q : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => _inst_2 a b)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (MvPolynomial.vars.{u2, u1} R σ _inst_1 q))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_add_subset MvPolynomial.vars_add_subsetₓ'. -/
 theorem vars_add_subset [DecidableEq σ] (p q : MvPolynomial σ R) : (p + q).vars ⊆ p.vars ∪ q.vars :=
   by
@@ -493,7 +505,7 @@ theorem vars_add_subset [DecidableEq σ] (p q : MvPolynomial σ R) : (p + q).var
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {p : MvPolynomial.{u2, u1} σ R _inst_1} {q : MvPolynomial.{u2, u1} σ R _inst_1} [_inst_2 : DecidableEq.{succ u2} σ], (Disjoint.{u2} (Finset.{u2} σ) (Finset.partialOrder.{u2} σ) (Finset.orderBot.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (MvPolynomial.vars.{u1, u2} R σ _inst_1 q)) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Union.union.{u2} (Finset.{u2} σ) (Finset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b)) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (MvPolynomial.vars.{u1, u2} R σ _inst_1 q)))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {p : MvPolynomial.{u1, u2} σ R _inst_1} {q : MvPolynomial.{u1, u2} σ R _inst_1}, (Disjoint.{u1} (Finset.{u1} σ) (Finset.partialOrder.{u1} σ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (MvPolynomial.vars.{u2, u1} R σ _inst_1 q)) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (MvPolynomial.vars.{u2, u1} R σ _inst_1 q)))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {p : MvPolynomial.{u1, u2} σ R _inst_1} {q : MvPolynomial.{u1, u2} σ R _inst_1} [_inst_2 : DecidableEq.{succ u1} σ], (Disjoint.{u1} (Finset.{u1} σ) (Finset.partialOrder.{u1} σ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (MvPolynomial.vars.{u2, u1} R σ _inst_1 q)) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => _inst_2 a b)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (MvPolynomial.vars.{u2, u1} R σ _inst_1 q)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_add_of_disjoint MvPolynomial.vars_add_of_disjointₓ'. -/
 theorem vars_add_of_disjoint [DecidableEq σ] (h : Disjoint p.vars q.vars) :
     (p + q).vars = p.vars ∪ q.vars :=
@@ -511,7 +523,7 @@ section Mul
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (φ : MvPolynomial.{u2, u1} σ R _inst_1) (ψ : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) φ ψ)) (Union.union.{u2} (Finset.{u2} σ) (Finset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b)) (MvPolynomial.vars.{u1, u2} R σ _inst_1 φ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 ψ))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (_inst_2 : MvPolynomial.{u1, u2} σ R _inst_1) (φ : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{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)))))) _inst_2 φ)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.vars.{u2, u1} R σ _inst_1 _inst_2) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (φ : MvPolynomial.{u1, u2} σ R _inst_1) (ψ : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{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)))))) φ ψ)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => _inst_2 a b)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 ψ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_mul MvPolynomial.vars_mulₓ'. -/
 theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars ⊆ φ.vars ∪ ψ.vars :=
   by
@@ -568,7 +580,7 @@ theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} σ] {s : Finset.{u3} ι} (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.prod.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.biUnion.{u3, u2} ι σ (fun (a : σ) (b : σ) => _inst_2 a b) s (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (f i)))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} {_inst_2 : Finset.{u2} ι} (s : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u3, u1} R σ _inst_1 (Finset.prod.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) _inst_2 (fun (i : ι) => s i))) (Finset.biUnion.{u2, u1} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) _inst_2 (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (s i)))
+  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} σ] {s : Finset.{u2} ι} (f : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u3, u1} R σ _inst_1 (Finset.prod.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.biUnion.{u2, u1} ι σ (fun (a : σ) (b : σ) => _inst_2 a b) s (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (f i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_prod MvPolynomial.vars_prodₓ'. -/
 /-- The variables of the product of a family of polynomials
 are a subset of the union of the sets of variables of each polynomial.
@@ -616,7 +628,7 @@ variable {ι : Type _} (t : Finset ι) (φ : ι → MvPolynomial σ R)
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (t : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)) [_inst_2 : DecidableEq.{succ u2} σ], HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u3, u2} ι σ (fun (a : σ) (b : σ) => _inst_2 a b) t (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i)))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u1}} (t : Finset.{u1} ι) (φ : ι -> (MvPolynomial.{u2, u3} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.instHasSubsetFinset.{u2} σ) (MvPolynomial.vars.{u3, u2} R σ _inst_1 (Finset.sum.{max u3 u2, u1} (MvPolynomial.{u2, u3} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u1, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u3, u2} R σ _inst_1 (φ i)))
+  forall {R : Type.{u3}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u1}} (t : Finset.{u1} ι) (φ : ι -> (MvPolynomial.{u2, u3} σ R _inst_1)) [_inst_2 : DecidableEq.{succ u2} σ], HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.instHasSubsetFinset.{u2} σ) (MvPolynomial.vars.{u3, u2} R σ _inst_1 (Finset.sum.{max u3 u2, u1} (MvPolynomial.{u2, u3} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u1, u2} ι σ (fun (a : σ) (b : σ) => _inst_2 a b) t (fun (i : ι) => MvPolynomial.vars.{u3, u2} R σ _inst_1 (φ i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subsetₓ'. -/
 theorem vars_sum_subset [DecidableEq σ] :
     (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by
@@ -635,7 +647,7 @@ theorem vars_sum_subset [DecidableEq σ] :
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (t : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)) [_inst_2 : DecidableEq.{succ u2} σ], (Pairwise.{u3} ι (Function.onFun.{succ u3, succ u2, 1} ι (Finset.{u2} σ) Prop (Disjoint.{u2} (Finset.{u2} σ) (Finset.partialOrder.{u2} σ) (Finset.orderBot.{u2} σ)) (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i)))) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u3, u2} ι σ (fun (a : σ) (b : σ) => _inst_2 a b) t (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i))))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (t : Finset.{u2} ι) (φ : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Finset.{u1} σ) Prop (Disjoint.{u1} (Finset.{u1} σ) (Finset.partialOrder.{u1} σ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} σ)) (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (φ i)))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u3, u1} R σ _inst_1 (Finset.sum.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (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))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u2, u1} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (φ i))))
+  forall {R : Type.{u3}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u1}} (t : Finset.{u1} ι) (φ : ι -> (MvPolynomial.{u2, u3} σ R _inst_1)) [_inst_2 : DecidableEq.{succ u2} σ], (Pairwise.{u1} ι (Function.onFun.{succ u1, succ u2, 1} ι (Finset.{u2} σ) Prop (Disjoint.{u2} (Finset.{u2} σ) (Finset.partialOrder.{u2} σ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u2} σ)) (fun (i : ι) => MvPolynomial.vars.{u3, u2} R σ _inst_1 (φ i)))) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u3, u2} R σ _inst_1 (Finset.sum.{max u3 u2, u1} (MvPolynomial.{u2, u3} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u1, u2} ι σ (fun (a : σ) (b : σ) => _inst_2 a b) t (fun (i : ι) => MvPolynomial.vars.{u3, u2} R σ _inst_1 (φ i))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_sum_of_disjoint MvPolynomial.vars_sum_of_disjointₓ'. -/
 theorem vars_sum_of_disjoint [DecidableEq σ] (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
     (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars := by
@@ -699,7 +711,7 @@ theorem vars_monomial_single (i : σ) {e : ℕ} {r : R} (he : e ≠ 0) (hr : r 
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1) [_inst_3 : DecidableEq.{succ u2} σ], Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (Finset.biUnion.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) σ (fun (a : σ) (b : σ) => _inst_3 a b) (MvPolynomial.support.{u1, u2} R σ _inst_1 p) (Finsupp.support.{u2, 0} σ Nat Nat.hasZero))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (Finset.biUnion.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) (MvPolynomial.support.{u2, u1} R σ _inst_1 p) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) [_inst_3 : DecidableEq.{succ u1} σ], Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (Finset.biUnion.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (a : σ) (b : σ) => _inst_3 a b) (MvPolynomial.support.{u2, u1} R σ _inst_1 p) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_biUnion_supportₓ'. -/
 theorem vars_eq_support_biUnion_support [DecidableEq σ] :
     p.vars = p.support.biUnion Finsupp.support :=
@@ -725,6 +737,12 @@ def degreeOf (n : σ) (p : MvPolynomial σ R) : ℕ :=
 #align mv_polynomial.degree_of MvPolynomial.degreeOf
 -/
 
+/- warning: mv_polynomial.degree_of_def -> MvPolynomial.degreeOf_def is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (n : σ) (p : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{1} Nat (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 n p) (Multiset.count.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b) n (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (n : σ) (p : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{1} Nat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 n p) (Multiset.count.{u1} σ (fun (a : σ) (b : σ) => _inst_2 a b) n (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_def MvPolynomial.degreeOf_defₓ'. -/
 theorem degreeOf_def [DecidableEq σ] (n : σ) (p : MvPolynomial σ R) :
     p.degreeOf n = p.degrees.count n := by convert rfl
 #align mv_polynomial.degree_of_def MvPolynomial.degreeOf_def
@@ -781,7 +799,7 @@ theorem degreeOf_C (a : R) (x : σ) : degreeOf x (C a : MvPolynomial σ R) = 0 :
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (i : σ) (j : σ) [_inst_3 : Nontrivial.{u1} R], Eq.{1} Nat (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 i (MvPolynomial.X.{u1, u2} R σ _inst_1 j)) (ite.{1} Nat (Eq.{succ u2} σ i j) (_inst_2 i j) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (_inst_2 : σ) (i : σ) [j : Nontrivial.{u2} R], Eq.{1} Nat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 _inst_2 (MvPolynomial.X.{u2, u1} R σ _inst_1 i)) (ite.{1} Nat (Eq.{succ u1} σ _inst_2 i) (Classical.propDecidable (Eq.{succ u1} σ _inst_2 i)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (i : σ) (j : σ) [_inst_3 : Nontrivial.{u2} R], Eq.{1} Nat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 i (MvPolynomial.X.{u2, u1} R σ _inst_1 j)) (ite.{1} Nat (Eq.{succ u1} σ i j) (_inst_2 i j) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_X MvPolynomial.degreeOf_Xₓ'. -/
 theorem degreeOf_X [DecidableEq σ] (i j : σ) [Nontrivial R] :
     degreeOf i (X j : MvPolynomial σ R) = if i = j then 1 else 0 :=
@@ -1343,7 +1361,7 @@ theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ 
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} {τ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_3 : DecidableEq.{succ u3} τ] (f : σ -> τ) (φ : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u3} (Finset.{u3} τ) (Finset.hasSubset.{u3} τ) (MvPolynomial.vars.{u1, u3} R τ _inst_1 (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) => (MvPolynomial.{u2, u1} σ R _inst_1) -> (MvPolynomial.{u3, u1} τ R _inst_1)) ([anonymous].{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.rename.{u2, u3, u1} σ τ R _inst_1 f) φ)) (Finset.image.{u2, u3} σ τ (fun (a : τ) (b : τ) => _inst_3 a b) f (MvPolynomial.vars.{u1, u2} R σ _inst_1 φ))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] (_inst_3 : σ -> τ) (f : MvPolynomial.{u2, u3} σ R _inst_1), HasSubset.Subset.{u1} (Finset.{u1} τ) (Finset.instHasSubsetFinset.{u1} τ) (MvPolynomial.vars.{u3, u1} R τ _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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} 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(MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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} 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_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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 _inst_3) f)) (Finset.image.{u2, u1} σ τ (fun (a : τ) (b : τ) => Classical.propDecidable (Eq.{succ u1} τ a b)) _inst_3 (MvPolynomial.vars.{u3, u2} R σ _inst_1 f))
+  forall {R : Type.{u3}} {σ : Type.{u1}} {τ : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_3 : DecidableEq.{succ u2} τ] (f : σ -> τ) (φ : MvPolynomial.{u1, u3} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} τ) (Finset.instHasSubsetFinset.{u2} τ) (MvPolynomial.vars.{u3, u2} R τ _inst_1 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u3, max u3 u1, max u3 u2} 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) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u2, u3} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} 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))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (SMulZeroClass.toSMul.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toZero.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ 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))))))) (DistribSMul.toSMulZeroClass.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u3} (MvPolynomial.{u1, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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} σ 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)))))) (Module.toDistribMulAction.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (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))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, 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} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))) (Algebra.toModule.{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, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} 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))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, 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} σ 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)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)))))) (Module.toDistribMulAction.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (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))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))) (Algebra.toModule.{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, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u2) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} 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))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} 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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ 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)))) (Module.toDistribMulAction.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (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))))) (Algebra.toModule.{u3, max u1 u3} R (MvPolynomial.{u1, u3} σ 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)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1))))) (Algebra.toModule.{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, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u1 u3, max u2 u3, max (max u1 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)) (AlgHom.{u3, max u3 u1, max u3 u2} 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))) (AlgHom.algHomClass.{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 f) φ)) (Finset.image.{u1, u2} σ τ (fun (a : τ) (b : τ) => _inst_3 a b) f (MvPolynomial.vars.{u3, u1} R σ _inst_1 φ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_rename MvPolynomial.vars_renameₓ'. -/
 theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).vars ⊆ φ.vars.image f := by

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

@@ -131,7 +131,7 @@ theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (a : R), Eq.{succ u2} (Multiset.{u2} σ) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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)))) (fun (_x : RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (RingHom.hasCoeToFun.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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)))) (MvPolynomial.C.{u1, u2} R σ _inst_1) a)) (OfNat.ofNat.{u2} (Multiset.{u2} σ) 0 (OfNat.mk.{u2} (Multiset.{u2} σ) 0 (Zero.zero.{u2} (Multiset.{u2} σ) (Multiset.hasZero.{u2} σ))))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (a : R), Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _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 (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (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) a)) (OfNat.ofNat.{u1} (Multiset.{u1} σ) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} σ) (Multiset.instZeroMultiset.{u1} σ)))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (a : R), Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _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 (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (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) a)) (OfNat.ofNat.{u1} (Multiset.{u1} σ) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} σ) (Multiset.instZeroMultiset.{u1} σ)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_C MvPolynomial.degrees_Cₓ'. -/
 theorem degrees_C (a : R) : degrees (C a : MvPolynomial σ R) = 0 :=
   Multiset.le_zero.1 <| degrees_monomial _ _
@@ -323,7 +323,7 @@ theorem degrees_add_of_disjoint [DecidableEq σ] {p q : MvPolynomial σ R}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (p : MvPolynomial.{u3, u1} σ R _inst_1) (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), HasSubset.Subset.{u3} (Multiset.{u3} σ) (Multiset.hasSubset.{u3} σ) (MvPolynomial.degrees.{u2, u3} S σ _inst_2 (coeFn.{max (succ (max u3 u1)) (succ (max u3 u2)), max (succ (max u3 u1)) (succ (max u3 u2))} (RingHom.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) (fun (_x : RingHom.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> (MvPolynomial.{u3, u2} σ S _inst_2)) (RingHom.hasCoeToFun.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) (MvPolynomial.map.{u1, u2, u3} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.degrees.{u1, u3} R σ _inst_1 p)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (p : MvPolynomial.{u1, u2} σ R _inst_1) (f : 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))), HasSubset.Subset.{u1} (Multiset.{u1} σ) (Multiset.instHasSubsetMultiset.{u1} σ) (MvPolynomial.degrees.{u3, u1} S σ _inst_2 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u3} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{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))))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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)))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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 u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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.{u2, u3, u1} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p)
+  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (p : MvPolynomial.{u1, u2} σ R _inst_1) (f : 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))), HasSubset.Subset.{u1} (Multiset.{u1} σ) (Multiset.instHasSubsetMultiset.{u1} σ) (MvPolynomial.degrees.{u3, u1} S σ _inst_2 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u3} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{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))))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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)))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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 u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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.{u2, u3, u1} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_map MvPolynomial.degrees_mapₓ'. -/
 theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
     (map f p).degrees ⊆ p.degrees := by
@@ -360,7 +360,7 @@ theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (p : MvPolynomial.{u3, u1} σ R _inst_1) {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))}, (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f)) -> (Eq.{succ u3} (Multiset.{u3} σ) (MvPolynomial.degrees.{u2, u3} S σ _inst_2 (coeFn.{max (succ (max u3 u1)) (succ (max u3 u2)), max (succ (max u3 u1)) (succ (max u3 u2))} (RingHom.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) (fun (_x : RingHom.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> (MvPolynomial.{u3, u2} σ S _inst_2)) (RingHom.hasCoeToFun.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) (MvPolynomial.map.{u1, u2, u3} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.degrees.{u1, u3} R σ _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (p : MvPolynomial.{u1, u2} σ R _inst_1) {f : 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))}, (Function.Injective.{succ u2, succ u3} R S (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (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))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (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))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (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))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) f)) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u3, u1} S σ _inst_2 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u3} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{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))))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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)))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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 u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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.{u2, u3, u1} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p))
+  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (p : MvPolynomial.{u1, u2} σ R _inst_1) {f : 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))}, (Function.Injective.{succ u2, succ u3} R S (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (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))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (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))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (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))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) f)) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u3, u1} S σ _inst_2 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u3} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{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))))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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)))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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 u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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.{u2, u3, u1} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_map_of_injective MvPolynomial.degrees_map_of_injectiveₓ'. -/
 theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R →+* S}
     (hf : Injective f) : (map f p).degrees = p.degrees := by
@@ -427,7 +427,7 @@ theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} {r : R} [_inst_1 : CommSemiring.{u1} R], Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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)))) (fun (_x : RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (RingHom.hasCoeToFun.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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)))) (MvPolynomial.C.{u1, u2} R σ _inst_1) r)) (EmptyCollection.emptyCollection.{u2} (Finset.{u2} σ) (Finset.hasEmptyc.{u2} σ))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} {r : R} [_inst_1 : CommSemiring.{u2} R], Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _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 (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (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) r)) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} σ) (Finset.instEmptyCollectionFinset.{u1} σ))
+  forall {R : Type.{u2}} {σ : Type.{u1}} {r : R} [_inst_1 : CommSemiring.{u2} R], Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _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 (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (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) r)) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} σ) (Finset.instEmptyCollectionFinset.{u1} σ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_C MvPolynomial.vars_Cₓ'. -/
 @[simp]
 theorem vars_C : (C r : MvPolynomial σ R).vars = ∅ := by
@@ -592,7 +592,7 @@ variable {A : Type _} [CommRing A] [IsDomain A]
 lean 3 declaration is
   forall {σ : Type.{u1}} {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (a : A), (Ne.{succ u2} A a (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))))) -> (forall (φ : MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (instHMul.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))))))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) (fun (_x : RingHom.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) => A -> (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.hasCoeToFun.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) (MvPolynomial.C.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)) a) φ)) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) φ))
 but is expected to have type
-  forall {σ : Type.{u1}} {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] (a : A), (Ne.{succ u2} A a (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) _inst_3)))))) -> (forall (φ : MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) (HMul.hMul.{max u2 u1, max u1 u2, max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (Semiring.toNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (CommSemiring.toSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))))))) (MvPolynomial.C.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)) a) φ)) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) φ))
+  forall {σ : Type.{u1}} {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] (a : A), (Ne.{succ u2} A a (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) _inst_3)))))) -> (forall (φ : MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) (HMul.hMul.{max u2 u1, max u1 u2, max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (Semiring.toNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (CommSemiring.toSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))))))) (MvPolynomial.C.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)) a) φ)) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) φ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_C_mul MvPolynomial.vars_C_mulₓ'. -/
 theorem vars_C_mul (a : A) (ha : a ≠ 0) (φ : MvPolynomial σ A) : (C a * φ).vars = φ.vars :=
   by
@@ -667,7 +667,7 @@ variable (p)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u3, u1} σ R _inst_1) [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), HasSubset.Subset.{u3} (Finset.{u3} σ) (Finset.hasSubset.{u3} σ) (MvPolynomial.vars.{u2, u3} S σ _inst_2 (coeFn.{max (succ (max u3 u1)) (succ (max u3 u2)), max (succ (max u3 u1)) (succ (max u3 u2))} (RingHom.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) (fun (_x : RingHom.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> (MvPolynomial.{u3, u2} σ S _inst_2)) (RingHom.hasCoeToFun.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) (MvPolynomial.map.{u1, u2, u3} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.vars.{u1, u3} R σ _inst_1 p)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) [_inst_2 : CommSemiring.{u3} S] (f : 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))), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u3, u1} S σ _inst_2 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u3} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{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))))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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)))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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 u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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.{u2, u3, u1} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p)
+  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) [_inst_2 : CommSemiring.{u3} S] (f : 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))), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u3, u1} S σ _inst_2 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u3} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{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))))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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)))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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 u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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.{u2, u3, u1} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_map MvPolynomial.vars_mapₓ'. -/
 theorem vars_map : (map f p).vars ⊆ p.vars := by simp [vars, degrees_map]
 #align mv_polynomial.vars_map MvPolynomial.vars_map
@@ -678,7 +678,7 @@ variable {f}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u3, u1} σ R _inst_1) [_inst_2 : CommSemiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))}, (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f)) -> (Eq.{succ u3} (Finset.{u3} σ) (MvPolynomial.vars.{u2, u3} S σ _inst_2 (coeFn.{max (succ (max u3 u1)) (succ (max u3 u2)), max (succ (max u3 u1)) (succ (max u3 u2))} (RingHom.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) (fun (_x : RingHom.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> (MvPolynomial.{u3, u2} σ S _inst_2)) (RingHom.hasCoeToFun.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) (MvPolynomial.map.{u1, u2, u3} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.vars.{u1, u3} R σ _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) [_inst_2 : CommSemiring.{u3} S] {f : 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))}, (Function.Injective.{succ u2, succ u3} R S (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (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))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (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))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (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))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) f)) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u3, u1} S σ _inst_2 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u3} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{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))))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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)))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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 u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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.{u2, u3, u1} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p))
+  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) [_inst_2 : CommSemiring.{u3} S] {f : 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))}, (Function.Injective.{succ u2, succ u3} R S (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (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))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (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))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (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))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) f)) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u3, u1} S σ _inst_2 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u3} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{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))))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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)))) (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 u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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 u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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.{u2, u3, u1} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_map_of_injective MvPolynomial.vars_map_of_injectiveₓ'. -/
 theorem vars_map_of_injective (hf : Injective f) : (map f p).vars = p.vars := by
   simp [vars, degrees_map_of_injective _ hf]
@@ -770,7 +770,7 @@ theorem degreeOf_zero (n : σ) : degreeOf n (0 : MvPolynomial σ R) = 0 := by
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (a : R) (x : σ), Eq.{1} Nat (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 x (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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)))) (fun (_x : RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (RingHom.hasCoeToFun.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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)))) (MvPolynomial.C.{u1, u2} R σ _inst_1) a)) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (a : R) (x : σ), Eq.{1} Nat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 x (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 (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (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) a)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (a : R) (x : σ), Eq.{1} Nat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 x (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 (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (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) a)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_C MvPolynomial.degreeOf_Cₓ'. -/
 @[simp]
 theorem degreeOf_C (a : R) (x : σ) : degreeOf x (C a : MvPolynomial σ R) = 0 := by
@@ -924,7 +924,7 @@ theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) : p.totalDegree ≤
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (a : R), Eq.{1} Nat (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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)))) (fun (_x : RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (RingHom.hasCoeToFun.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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)))) (MvPolynomial.C.{u1, u2} R σ _inst_1) a)) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (a : R), Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _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 (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (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) a)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (a : R), Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _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 (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (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) a)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_C MvPolynomial.totalDegree_Cₓ'. -/
 @[simp]
 theorem totalDegree_C (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
@@ -1230,7 +1230,7 @@ variable [CommSemiring S]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) {g : σ -> S} {p : MvPolynomial.{u3, u1} σ R _inst_1}, (forall (i : σ), (Membership.Mem.{u3, u3} σ (Finset.{u3} σ) (Finset.hasMem.{u3} σ) i (MvPolynomial.vars.{u1, u3} R σ _inst_1 p)) -> (Eq.{succ u2} S (g i) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))))))) -> (Eq.{succ u2} S (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (RingHom.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.eval₂Hom.{u1, u2, u3} R S σ _inst_1 _inst_2 f g) p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f (coeFn.{max (succ (max u3 u1)) (succ u1), max (succ (max u3 u1)) (succ u1)} (RingHom.{max u3 u1, u1} (MvPolynomial.{u3, u1} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{max u3 u1, u1} (MvPolynomial.{u3, u1} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> R) (RingHom.hasCoeToFun.{max u3 u1, u1} (MvPolynomial.{u3, u1} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.constantCoeff.{u1, u3} R σ _inst_1) p)))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : 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))) {g : σ -> S} {p : MvPolynomial.{u1, u2} σ R _inst_1}, (forall (i : σ), (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 p)) -> (Eq.{succ u3} S (g i) (OfNat.ofNat.{u3} S 0 (Zero.toOfNat0.{u3} S (CommMonoidWithZero.toZero.{u3} S (CommSemiring.toCommMonoidWithZero.{u3} S _inst_2)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => S) p) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, u3} (RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u2} σ R _inst_1) S (NonUnitalNonAssocSemiring.toMul.{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))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u1, u3} (RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u2} σ R _inst_1) S (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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u1, u3} (RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (MvPolynomial.eval₂Hom.{u2, u3, u1} R S σ _inst_1 _inst_2 f g) p) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (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))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (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))) R S 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R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (MvPolynomial.constantCoeff.{u2, u1} R σ _inst_1) p)))
+  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : 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))) {g : σ -> S} {p : MvPolynomial.{u1, u2} σ R _inst_1}, (forall (i : σ), (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 p)) -> (Eq.{succ u3} S (g i) (OfNat.ofNat.{u3} S 0 (Zero.toOfNat0.{u3} S (CommMonoidWithZero.toZero.{u3} S (CommSemiring.toCommMonoidWithZero.{u3} S _inst_2)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => S) p) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) 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(NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (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))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u2} (RingHom.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) R (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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u2} (RingHom.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (MvPolynomial.constantCoeff.{u2, u1} R σ _inst_1) p)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars MvPolynomial.eval₂Hom_eq_constantCoeff_of_varsₓ'. -/
 theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p : MvPolynomial σ R}
     (hp : ∀ i ∈ p.vars, g i = 0) : eval₂Hom f g p = f (constantCoeff p) :=
@@ -1266,7 +1266,7 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {g : σ -> S} {p : MvPolynomial.{u3, u1} σ R _inst_1}, (forall (i : σ), (Membership.Mem.{u3, u3} σ (Finset.{u3} σ) (Finset.hasMem.{u3} σ) i (MvPolynomial.vars.{u1, u3} R σ _inst_1 p)) -> (Eq.{succ u2} S (g i) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))))))) -> (Eq.{succ u2} S (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (AlgHom.{u1, max u3 u1, u2} R (MvPolynomial.{u3, u1} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (CommSemiring.toSemiring.{u2} S _inst_2) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgHom.{u1, max u3 u1, u2} R (MvPolynomial.{u3, u1} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (CommSemiring.toSemiring.{u2} S _inst_2) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) => (MvPolynomial.{u3, u1} σ R _inst_1) -> S) ([anonymous].{u1, max u3 u1, u2} R (MvPolynomial.{u3, u1} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (CommSemiring.toSemiring.{u2} S _inst_2) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) (MvPolynomial.aeval.{u1, u2, u3} R S σ _inst_1 _inst_2 _inst_3 g) p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ u1), max (succ (max u3 u1)) (succ u1)} (RingHom.{max u3 u1, u1} (MvPolynomial.{u3, u1} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{max u3 u1, u1} (MvPolynomial.{u3, u1} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> R) (RingHom.hasCoeToFun.{max u3 u1, u1} (MvPolynomial.{u3, u1} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.constantCoeff.{u1, u3} R σ _inst_1) p)))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {g : σ -> S} {p : MvPolynomial.{u1, u2} σ R _inst_1}, (forall (i : σ), (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 p)) -> (Eq.{succ u3} S (g i) (OfNat.ofNat.{u3} S 0 (Zero.toOfNat0.{u3} S (CommMonoidWithZero.toZero.{u3} S (CommSemiring.toCommMonoidWithZero.{u3} S _inst_2)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => S) p) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (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) => S) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (MvPolynomial.{u1, u2} σ R _inst_1) S (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 u2 u1} (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 u2 u1} (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 u2 u1} (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 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))))))) (SMulZeroClass.toSMul.{u2, 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.{u2, 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.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} 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.{u2, u3} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (MvPolynomial.{u1, u2} σ R _inst_1) S (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 u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _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.{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, u3} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S _inst_2) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (MvPolynomial.{u1, u2} σ R _inst_1) S (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) 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(Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) S (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} ((fun 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(CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) S (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => R) p) S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (RingHom.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) 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(MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u2} (RingHom.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (MvPolynomial.constantCoeff.{u2, u1} R σ _inst_1) p)))
+  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {g : σ -> S} {p : MvPolynomial.{u1, u2} σ R _inst_1}, (forall (i : σ), (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 p)) -> (Eq.{succ u3} S (g i) (OfNat.ofNat.{u3} S 0 (Zero.toOfNat0.{u3} S (CommMonoidWithZero.toZero.{u3} S (CommSemiring.toCommMonoidWithZero.{u3} S _inst_2)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => S) p) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} σ R _inst_1) S _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{u3} S 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(MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{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.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u2} (RingHom.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) R (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))))) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u2} (RingHom.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) R (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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u2} (RingHom.{max u2 u1, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{max u1 u2, u2} (MvPolynomial.{u1, u2} σ R _inst_1) R (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.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (MvPolynomial.constantCoeff.{u2, u1} R σ _inst_1) p)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_eq_constant_coeff_of_vars MvPolynomial.aeval_eq_constantCoeff_of_varsₓ'. -/
 theorem aeval_eq_constantCoeff_of_vars [Algebra R S] {g : σ → S} {p : MvPolynomial σ R}
     (hp : ∀ i ∈ p.vars, g i = 0) : aeval g p = algebraMap _ _ (constantCoeff p) :=
@@ -1277,7 +1277,7 @@ theorem aeval_eq_constantCoeff_of_vars [Algebra R S] {g : σ → S} {p : MvPolyn
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] {f₁ : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {f₂ : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {g₁ : σ -> S} {g₂ : σ -> S} {p₁ : MvPolynomial.{u3, u1} σ R _inst_1} {p₂ : MvPolynomial.{u3, u1} σ R _inst_1}, (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f₁ f₂) -> (forall (i : σ), (Membership.Mem.{u3, u3} σ (Finset.{u3} σ) (Finset.hasMem.{u3} σ) i (MvPolynomial.vars.{u1, u3} R σ _inst_1 p₁)) -> (Membership.Mem.{u3, u3} σ (Finset.{u3} σ) (Finset.hasMem.{u3} σ) i (MvPolynomial.vars.{u1, u3} R σ _inst_1 p₂)) -> (Eq.{succ u2} S (g₁ i) (g₂ i))) -> (Eq.{max (succ u3) (succ u1)} (MvPolynomial.{u3, u1} σ R _inst_1) p₁ p₂) -> (Eq.{succ u2} S (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (RingHom.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.eval₂Hom.{u1, u2, u3} R S σ _inst_1 _inst_2 f₁ g₁) p₁) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (RingHom.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.eval₂Hom.{u1, u2, u3} R S σ _inst_1 _inst_2 f₂ g₂) p₂))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] {f₁ : 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))} {f₂ : 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))} {g₁ : σ -> S} {g₂ : σ -> S} {p₁ : MvPolynomial.{u1, u2} σ R _inst_1} {p₂ : MvPolynomial.{u1, u2} σ R _inst_1}, (Eq.{max (succ u2) (succ u3)} (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))) f₁ f₂) -> (forall (i : σ), (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 p₁)) -> (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 p₂)) -> (Eq.{succ u3} S (g₁ i) (g₂ i))) -> (Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u1, u2} σ R _inst_1) p₁ p₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => S) p₁) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, u3} 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(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} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (MvPolynomial.eval₂Hom.{u2, u3, u1} R S σ _inst_1 _inst_2 f₁ g₁) p₁) 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S _inst_2))) (MvPolynomial.{u1, u2} σ R _inst_1) S (NonUnitalNonAssocSemiring.toMul.{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))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u1, u3} (RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u2} σ R _inst_1) S (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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u1, u3} (RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (MvPolynomial.eval₂Hom.{u2, u3, u1} R S σ _inst_1 _inst_2 f₂ g₂) p₂))
+  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] {f₁ : 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))} {f₂ : 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))} {g₁ : σ -> S} {g₂ : σ -> S} {p₁ : MvPolynomial.{u1, u2} σ R _inst_1} {p₂ : MvPolynomial.{u1, u2} σ R _inst_1}, (Eq.{max (succ u2) (succ u3)} (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))) f₁ f₂) -> (forall (i : σ), (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 p₁)) -> (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 p₂)) -> (Eq.{succ u3} S (g₁ i) (g₂ i))) -> (Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u1, u2} σ R _inst_1) p₁ p₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => S) p₁) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), succ u3} (RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u2} σ R _inst_1) => S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, u3} 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(CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u2} σ R _inst_1) S (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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u1, u3} (RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (MvPolynomial.eval₂Hom.{u2, u3, u1} R S σ _inst_1 _inst_2 f₂ g₂) p₂))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_congr' MvPolynomial.eval₂Hom_congr'ₓ'. -/
 theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p₂ : MvPolynomial σ R} :
     f₁ = f₂ →
@@ -1304,7 +1304,7 @@ theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] {f₁ : RingHom.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {f₂ : RingHom.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))} {p₁ : MvPolynomial.{u3, u1} σ R _inst_1} {p₂ : MvPolynomial.{u3, u1} σ R _inst_1}, (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R 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(CommSemiring.toSemiring.{u2} S _inst_2)) f₂ (MvPolynomial.C.{u1, u3} R σ _inst_1))) -> (forall (i : σ), (Membership.Mem.{u3, u3} σ (Finset.{u3} σ) (Finset.hasMem.{u3} σ) i (MvPolynomial.vars.{u1, u3} R σ _inst_1 p₁)) -> (Membership.Mem.{u3, u3} σ (Finset.{u3} σ) (Finset.hasMem.{u3} σ) i (MvPolynomial.vars.{u1, u3} R σ _inst_1 p₂)) -> (Eq.{succ u2} S (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (RingHom.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) 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 but is expected to have type
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+  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] {f₁ : RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2))} {f₂ : RingHom.{max u2 u1, u3} (MvPolynomial.{u1, u2} σ R _inst_1) S (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} S (CommSemiring.toSemiring.{u3} S _inst_2))} {p₁ : MvPolynomial.{u1, u2} σ R _inst_1} {p₂ : MvPolynomial.{u1, u2} σ R _inst_1}, (Eq.{max (succ u2) (succ u3)} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R 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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.hom_congr_vars MvPolynomial.hom_congr_varsₓ'. -/
 /-- If `f₁` and `f₂` are ring homs out of the polynomial ring and `p₁` and `p₂` are polynomials,
   then `f₁ p₁ = f₂ p₂` if `p₁ = p₂` and `f₁` and `f₂` are equal on `R` and on the variables

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

@@ -104,7 +104,7 @@ theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (s : Finsupp.{u2, 0} σ Nat Nat.hasZero) (a : R), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toHasLe.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 s) a)) (coeFn.{succ u2, succ u2} (AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (fun (_x : AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) => (Finsupp.{u2, 0} σ Nat Nat.hasZero) -> (Multiset.{u2} σ)) (AddEquiv.hasCoeToFun.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (Finsupp.toMultiset.{u2} σ) s)
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s)
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomialₓ'. -/
 theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ s.toMultiset := by
   classical
@@ -118,7 +118,7 @@ theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) 
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (s : Finsupp.{u2, 0} σ Nat Nat.hasZero) (a : R), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) -> (Eq.{succ u2} (Multiset.{u2} σ) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 s) a)) (coeFn.{succ u2, succ u2} (AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (fun (_x : AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) => (Finsupp.{u2, 0} σ Nat Nat.hasZero) -> (Multiset.{u2} σ)) (AddEquiv.hasCoeToFun.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (Finsupp.toMultiset.{u2} σ) s))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), (Ne.{succ u2} R a (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), (Ne.{succ u2} R a (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eqₓ'. -/
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
     degrees (monomial s a) = s.toMultiset := by
@@ -416,7 +416,7 @@ theorem vars_0 : (0 : MvPolynomial σ R).vars = ∅ := by
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} {r : R} {s : Finsupp.{u2, 0} σ Nat Nat.hasZero} [_inst_1 : CommSemiring.{u1} R], (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 s) r)) (Finsupp.support.{u2, 0} σ Nat Nat.hasZero s))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} {r : R} {s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)} [_inst_1 : CommSemiring.{u2} R], (Ne.{succ u2} R r (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) r)) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s))
+  forall {R : Type.{u2}} {σ : Type.{u1}} {r : R} {s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)} [_inst_1 : CommSemiring.{u2} R], (Ne.{succ u2} R r (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) r)) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) s))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_monomial MvPolynomial.vars_monomialₓ'. -/
 @[simp]
 theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by
@@ -688,7 +688,7 @@ theorem vars_map_of_injective (hf : Injective f) : (map f p).vars = p.vars := by
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (i : σ) {e : Nat} {r : R}, (Ne.{1} Nat e (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 (Finsupp.single.{u2, 0} σ Nat Nat.hasZero i e)) r)) (Singleton.singleton.{u2, u2} σ (Finset.{u2} σ) (Finset.hasSingleton.{u2} σ) i))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (i : σ) {e : Nat} {r : R}, (Ne.{1} Nat e (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Ne.{succ u2} R r (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 (Finsupp.single.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) i e)) r)) (Singleton.singleton.{u1, u1} σ (Finset.{u1} σ) (Finset.instSingletonFinset.{u1} σ) i))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (i : σ) {e : Nat} {r : R}, (Ne.{1} Nat e (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Ne.{succ u2} R r (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 (Finsupp.single.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) i e)) r)) (Singleton.singleton.{u1, u1} σ (Finset.{u1} σ) (Finset.instSingletonFinset.{u1} σ) i))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_monomial_single MvPolynomial.vars_monomial_singleₓ'. -/
 theorem vars_monomial_single (i : σ) {e : ℕ} {r : R} (he : e ≠ 0) (hr : r ≠ 0) :
     (monomial (Finsupp.single i e) r).vars = {i} := by
@@ -1080,7 +1080,7 @@ theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (s : Finsupp.{u2, 0} σ Nat Nat.hasZero) {c : R}, (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) -> (Eq.{1} Nat (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 s) c)) (Finsupp.sum.{u2, 0, 0} σ Nat Nat Nat.hasZero Nat.addCommMonoid s (fun (_x : σ) (e : Nat) => e)))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) {c : R}, (Ne.{succ u2} R c (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) c)) (Finsupp.sum.{u1, 0, 0} σ Nat Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) Nat.addCommMonoid s (fun (_x : σ) (e : Nat) => e)))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) {c : R}, (Ne.{succ u2} R c (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) c)) (Finsupp.sum.{u1, 0, 0} σ Nat Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) Nat.addCommMonoid s (fun (_x : σ) (e : Nat) => e)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_monomial MvPolynomial.totalDegree_monomialₓ'. -/
 @[simp]
 theorem totalDegree_monomial (s : σ →₀ ℕ) {c : R} (hc : c ≠ 0) :

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

@@ -102,7 +102,7 @@ theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
 
 /- warning: mv_polynomial.degrees_monomial -> MvPolynomial.degrees_monomial is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (s : Finsupp.{u2, 0} σ Nat Nat.hasZero) (a : R), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 s) a)) (coeFn.{succ u2, succ u2} (AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (fun (_x : AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) => (Finsupp.{u2, 0} σ Nat Nat.hasZero) -> (Multiset.{u2} σ)) (AddEquiv.hasCoeToFun.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (Finsupp.toMultiset.{u2} σ) s)
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (s : Finsupp.{u2, 0} σ Nat Nat.hasZero) (a : R), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toHasLe.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 s) a)) (coeFn.{succ u2, succ u2} (AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (fun (_x : AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) => (Finsupp.{u2, 0} σ Nat Nat.hasZero) -> (Multiset.{u2} σ)) (AddEquiv.hasCoeToFun.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (Finsupp.toMultiset.{u2} σ) s)
 but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomialₓ'. -/
@@ -139,7 +139,7 @@ theorem degrees_C (a : R) : degrees (C a : MvPolynomial σ R) = 0 :=
 
 /- warning: mv_polynomial.degrees_X' -> MvPolynomial.degrees_X' is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (n : σ), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (MvPolynomial.X.{u1, u2} R σ _inst_1 n)) (Singleton.singleton.{u2, u2} σ (Multiset.{u2} σ) (Multiset.hasSingleton.{u2} σ) n)
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (n : σ), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toHasLe.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (MvPolynomial.X.{u1, u2} R σ _inst_1 n)) (Singleton.singleton.{u2, u2} σ (Multiset.{u2} σ) (Multiset.hasSingleton.{u2} σ) n)
 but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (n : σ), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (MvPolynomial.X.{u2, u1} R σ _inst_1 n)) (Singleton.singleton.{u1, u1} σ (Multiset.{u1} σ) (Multiset.instSingletonMultiset.{u1} σ) n)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_X' MvPolynomial.degrees_X'ₓ'. -/
@@ -184,7 +184,7 @@ theorem degrees_one : degrees (1 : MvPolynomial σ R) = 0 :=
 
 /- warning: mv_polynomial.degrees_add -> MvPolynomial.degrees_add is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (p : MvPolynomial.{u2, u1} σ R _inst_1) (q : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Sup.sup.{u2} (Multiset.{u2} σ) (SemilatticeSup.toHasSup.{u2} (Multiset.{u2} σ) (Lattice.toSemilatticeSup.{u2} (Multiset.{u2} σ) (Multiset.lattice.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b)))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (p : MvPolynomial.{u2, u1} σ R _inst_1) (q : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toHasLe.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Sup.sup.{u2} (Multiset.{u2} σ) (SemilatticeSup.toHasSup.{u2} (Multiset.{u2} σ) (Lattice.toSemilatticeSup.{u2} (Multiset.{u2} σ) (Multiset.lattice.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b)))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q))
 but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (_inst_2 : MvPolynomial.{u1, u2} σ R _inst_1) (p : MvPolynomial.{u1, u2} σ R _inst_1), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) _inst_2 p)) (Sup.sup.{u1} (Multiset.{u1} σ) (SemilatticeSup.toSup.{u1} (Multiset.{u1} σ) (Lattice.toSemilatticeSup.{u1} (Multiset.{u1} σ) (Multiset.instLatticeMultiset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 _inst_2) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_add MvPolynomial.degrees_addₓ'. -/
@@ -202,7 +202,7 @@ theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
 
 /- warning: mv_polynomial.degrees_sum -> MvPolynomial.degrees_sum is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} σ] (s : Finset.{u3} ι) (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) s (fun (i : ι) => f i))) (Finset.sup.{u2, u3} (Multiset.{u2} σ) ι (Lattice.toSemilatticeSup.{u2} (Multiset.{u2} σ) (Multiset.lattice.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b))) (Multiset.orderBot.{u2} σ) s (fun (i : ι) => MvPolynomial.degrees.{u1, u2} R σ _inst_1 (f i)))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} σ] (s : Finset.{u3} ι) (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toHasLe.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) s (fun (i : ι) => f i))) (Finset.sup.{u2, u3} (Multiset.{u2} σ) ι (Lattice.toSemilatticeSup.{u2} (Multiset.{u2} σ) (Multiset.lattice.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b))) (Multiset.orderBot.{u2} σ) s (fun (i : ι) => MvPolynomial.degrees.{u1, u2} R σ _inst_1 (f i)))
 but is expected to have type
   forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (_inst_2 : Finset.{u2} ι) (s : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u3, u1} R σ _inst_1 (Finset.sum.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (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))))) _inst_2 (fun (i : ι) => s i))) (Finset.sup.{u1, u2} (Multiset.{u1} σ) ι (Lattice.toSemilatticeSup.{u1} (Multiset.{u1} σ) (Multiset.instLatticeMultiset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)))) (Multiset.instOrderBotMultisetToLEToPreorderInstPartialOrderMultiset.{u1} σ) _inst_2 (fun (i : ι) => MvPolynomial.degrees.{u3, u1} R σ _inst_1 (s i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_sum MvPolynomial.degrees_sumₓ'. -/
@@ -219,7 +219,7 @@ theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → M
 
 /- warning: mv_polynomial.degrees_mul -> MvPolynomial.degrees_mul is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1) (q : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (HAdd.hAdd.{u2, u2, u2} (Multiset.{u2} σ) (Multiset.{u2} σ) (Multiset.{u2} σ) (instHAdd.{u2} (Multiset.{u2} σ) (Multiset.hasAdd.{u2} σ)) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1) (q : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toHasLe.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (HAdd.hAdd.{u2, u2, u2} (Multiset.{u2} σ) (Multiset.{u2} σ) (Multiset.{u2} σ) (instHAdd.{u2} (Multiset.{u2} σ) (Multiset.hasAdd.{u2} σ)) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q))
 but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) (q : MvPolynomial.{u1, u2} σ R _inst_1), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{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)))))) p q)) (HAdd.hAdd.{u1, u1, u1} (Multiset.{u1} σ) (Multiset.{u1} σ) (Multiset.{u1} σ) (instHAdd.{u1} (Multiset.{u1} σ) (Multiset.instAddMultiset.{u1} σ)) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 q))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_mul MvPolynomial.degrees_mulₓ'. -/
@@ -235,7 +235,7 @@ theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees +
 
 /- warning: mv_polynomial.degrees_prod -> MvPolynomial.degrees_prod is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (s : Finset.{u3} ι) (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (Finset.prod.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.sum.{u2, u3} (Multiset.{u2} σ) ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)) s (fun (i : ι) => MvPolynomial.degrees.{u1, u2} R σ _inst_1 (f i)))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (s : Finset.{u3} ι) (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toHasLe.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (Finset.prod.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.sum.{u2, u3} (Multiset.{u2} σ) ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)) s (fun (i : ι) => MvPolynomial.degrees.{u1, u2} R σ _inst_1 (f i)))
 but is expected to have type
   forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (s : Finset.{u2} ι) (f : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u3, u1} R σ _inst_1 (Finset.prod.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.sum.{u1, u2} (Multiset.{u1} σ) ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)) s (fun (i : ι) => MvPolynomial.degrees.{u3, u1} R σ _inst_1 (f i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_prod MvPolynomial.degrees_prodₓ'. -/
@@ -251,7 +251,7 @@ theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R
 
 /- warning: mv_polynomial.degrees_pow -> MvPolynomial.degrees_pow is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1) (n : Nat), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (MvPolynomial.{u2, u1} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (Monoid.Pow.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toMonoidWithZero.{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)))))) p n)) (SMul.smul.{0, u2} Nat (Multiset.{u2} σ) (AddMonoid.SMul.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) n (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1) (n : Nat), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toHasLe.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (MvPolynomial.{u2, u1} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (Monoid.Pow.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toMonoidWithZero.{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)))))) p n)) (SMul.smul.{0, u2} Nat (Multiset.{u2} σ) (AddMonoid.SMul.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) n (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p))
 but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) (n : Nat), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (Monoid.Pow.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toMonoidWithZero.{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)))))) p n)) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} σ) (Multiset.{u1} σ) (instHSMul.{0, u1} Nat (Multiset.{u1} σ) (AddMonoid.SMul.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ))))))) n (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_pow MvPolynomial.degrees_powₓ'. -/
@@ -275,7 +275,7 @@ theorem mem_degrees {p : MvPolynomial σ R} {i : σ} :
 
 /- warning: mv_polynomial.le_degrees_add -> MvPolynomial.le_degrees_add is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {p : MvPolynomial.{u2, u1} σ R _inst_1} {q : MvPolynomial.{u2, u1} σ R _inst_1}, (Multiset.Disjoint.{u2} σ (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q)) -> (LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {p : MvPolynomial.{u2, u1} σ R _inst_1} {q : MvPolynomial.{u2, u1} σ R _inst_1}, (Multiset.Disjoint.{u2} σ (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q)) -> (LE.le.{u2} (Multiset.{u2} σ) (Preorder.toHasLe.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)))
 but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {p : MvPolynomial.{u1, u2} σ R _inst_1} {q : MvPolynomial.{u1, u2} σ R _inst_1}, (Multiset.Disjoint.{u1} σ (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 q)) -> (LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_addₓ'. -/

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

@@ -104,7 +104,7 @@ theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (s : Finsupp.{u2, 0} σ Nat Nat.hasZero) (a : R), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 s) a)) (coeFn.{succ u2, succ u2} (AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (fun (_x : AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) => (Finsupp.{u2, 0} σ Nat Nat.hasZero) -> (Multiset.{u2} σ)) (AddEquiv.hasCoeToFun.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (Finsupp.toMultiset.{u2} σ) s)
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddZeroClass.toAdd.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (AddZeroClass.toAdd.{u1} (Multiset.{u1} σ) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddEquivClass.instAddMonoidHomClass.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s)
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomialₓ'. -/
 theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ s.toMultiset := by
   classical
@@ -118,7 +118,7 @@ theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) 
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (s : Finsupp.{u2, 0} σ Nat Nat.hasZero) (a : R), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) -> (Eq.{succ u2} (Multiset.{u2} σ) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (MvPolynomial.{u2, u1} σ R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 s) a)) (coeFn.{succ u2, succ u2} (AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (fun (_x : AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) => (Finsupp.{u2, 0} σ Nat Nat.hasZero) -> (Multiset.{u2} σ)) (AddEquiv.hasCoeToFun.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (Finsupp.toMultiset.{u2} σ) s))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), (Ne.{succ u2} R a (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddZeroClass.toAdd.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (AddZeroClass.toAdd.{u1} (Multiset.{u1} σ) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddEquivClass.instAddMonoidHomClass.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), (Ne.{succ u2} R a (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eqₓ'. -/
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
     degrees (monomial s a) = s.toMultiset := by
@@ -898,7 +898,7 @@ def totalDegree (p : MvPolynomial σ R) : ℕ :=
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{1} Nat (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 p) (Finset.sup.{0, u2} Nat (Finsupp.{u2, 0} σ Nat Nat.hasZero) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) Nat.orderBot (MvPolynomial.support.{u1, u2} R σ _inst_1 p) (fun (m : Finsupp.{u2, 0} σ Nat Nat.hasZero) => coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} σ) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} σ) (coeFn.{succ u2, succ u2} (AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (fun (_x : AddEquiv.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) => (Finsupp.{u2, 0} σ Nat Nat.hasZero) -> (Multiset.{u2} σ)) (AddEquiv.hasCoeToFun.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Multiset.{u2} σ) (Finsupp.add.{u2, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.hasAdd.{u2} σ)) (Finsupp.toMultiset.{u2} σ) m)))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 p) (Finset.sup.{0, u1} Nat (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) Nat.orderBot (MvPolynomial.support.{u2, u1} R σ _inst_1 p) (fun (m : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} σ) (fun (_x : Multiset.{u1} σ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} σ) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} σ) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} σ) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} σ) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 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(AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddEquivClass.instAddMonoidHomClass.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) m)))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 p) (Finset.sup.{0, u1} Nat (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) Nat.orderBot (MvPolynomial.support.{u2, u1} R σ _inst_1 p) (fun (m : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} σ) (fun (_x : Multiset.{u1} σ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} σ) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} σ) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} σ) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} σ) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) m)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_eq MvPolynomial.totalDegree_eqₓ'. -/
 theorem totalDegree_eq (p : MvPolynomial σ R) :
     p.totalDegree = p.support.sup fun m => m.toMultiset.card :=

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: Johannes Hölzl, Johan Commelin, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.variables
-! leanprover-community/mathlib commit 1dac236edca9b4b6f5f00b1ad831e35f89472837
+! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -64,8 +64,6 @@ This will give rise to a monomial in `mv_polynomial σ R` which mathematicians m
 
 noncomputable section
 
-open Classical BigOperators
-
 open Set Function Finsupp AddMonoidAlgebra
 
 open BigOperators
@@ -93,18 +91,24 @@ section Degrees
 (For example, `degrees (x^2 * y + y^3)` would be `{x, x, y, y, y}`.)
 -/
 def degrees (p : MvPolynomial σ R) : Multiset σ :=
+  letI := Classical.decEq σ
   p.support.sup fun s : σ →₀ ℕ => s.toMultiset
 #align mv_polynomial.degrees MvPolynomial.degrees
 -/
 
+theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
+    p.degrees = p.support.sup fun s : σ →₀ ℕ => s.toMultiset := by convert rfl
+#align mv_polynomial.degrees_def MvPolynomial.degrees_def
+
 /- warning: mv_polynomial.degrees_monomial -> MvPolynomial.degrees_monomial is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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 s) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Multiset.{u1} σ) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (AddZeroClass.toAdd.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (AddZeroClass.toAdd.{u1} (Multiset.{u1} σ) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddEquivClass.instAddMonoidHomClass.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomialₓ'. -/
-theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ s.toMultiset :=
-  Finset.sup_le fun t h => by
+theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ s.toMultiset := by
+  classical
+    refine' Finset.sup_le fun t h => _
     have := Finsupp.support_single_subset h
     rw [Finset.mem_singleton] at this
     rw [this]
@@ -117,9 +121,10 @@ but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (a : R), (Ne.{succ u2} R a (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _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} (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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 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(LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (AddZeroClass.toAdd.{u1} (Multiset.{u1} σ) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddEquivClass.instAddMonoidHomClass.{u1, u1, u1} (AddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ)) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.addZeroClass.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Multiset.{u1} σ) (Finsupp.add.{u1, 0} σ Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.instAddMultiset.{u1} σ))))) (Finsupp.toMultiset.{u1} σ) s))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eqₓ'. -/
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
-    degrees (monomial s a) = s.toMultiset :=
-  le_antisymm (degrees_monomial s a) <|
-    Finset.le_sup <| by rw [support_monomial, if_neg ha, Finset.mem_singleton]
+    degrees (monomial s a) = s.toMultiset := by
+  classical
+    refine' le_antisymm (degrees_monomial s a) <| Finset.le_sup <| _
+    rw [support_monomial, if_neg ha, Finset.mem_singleton]
 #align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eq
 
 /- warning: mv_polynomial.degrees_C -> MvPolynomial.degrees_C is a dubious translation:
@@ -179,34 +184,37 @@ theorem degrees_one : degrees (1 : MvPolynomial σ R) = 0 :=
 
 /- warning: mv_polynomial.degrees_add -> MvPolynomial.degrees_add is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1) (q : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Sup.sup.{u2} (Multiset.{u2} σ) (SemilatticeSup.toHasSup.{u2} (Multiset.{u2} σ) (Lattice.toSemilatticeSup.{u2} (Multiset.{u2} σ) (Multiset.lattice.{u2} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b))))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (p : MvPolynomial.{u2, u1} σ R _inst_1) (q : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Sup.sup.{u2} (Multiset.{u2} σ) (SemilatticeSup.toHasSup.{u2} (Multiset.{u2} σ) (Lattice.toSemilatticeSup.{u2} (Multiset.{u2} σ) (Multiset.lattice.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b)))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) (q : MvPolynomial.{u1, u2} σ R _inst_1), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)) (Sup.sup.{u1} (Multiset.{u1} σ) (SemilatticeSup.toSup.{u1} (Multiset.{u1} σ) (Lattice.toSemilatticeSup.{u1} (Multiset.{u1} σ) (Multiset.instLatticeMultiset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 q))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (_inst_2 : MvPolynomial.{u1, u2} σ R _inst_1) (p : MvPolynomial.{u1, u2} σ R _inst_1), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) _inst_2 p)) (Sup.sup.{u1} (Multiset.{u1} σ) (SemilatticeSup.toSup.{u1} (Multiset.{u1} σ) (Lattice.toSemilatticeSup.{u1} (Multiset.{u1} σ) (Multiset.instLatticeMultiset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 _inst_2) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_add MvPolynomial.degrees_addₓ'. -/
-theorem degrees_add (p q : MvPolynomial σ R) : (p + q).degrees ≤ p.degrees ⊔ q.degrees :=
-  by
-  refine' Finset.sup_le fun b hb => _
-  have := Finsupp.support_add hb; rw [Finset.mem_union] at this
-  cases this
-  · exact le_sup_of_le_left (Finset.le_sup this)
-  · exact le_sup_of_le_right (Finset.le_sup this)
+theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
+    (p + q).degrees ≤ p.degrees ⊔ q.degrees := by
+  classical
+    simp_rw [degrees_def]
+    refine' Finset.sup_le fun b hb => _
+    have := Finsupp.support_add hb
+    rw [Finset.mem_union] at this
+    cases this
+    · exact le_sup_of_le_left (Finset.le_sup this)
+    · exact le_sup_of_le_right (Finset.le_sup this)
 #align mv_polynomial.degrees_add MvPolynomial.degrees_add
 
 /- warning: mv_polynomial.degrees_sum -> MvPolynomial.degrees_sum is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (s : Finset.{u3} ι) (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) s (fun (i : ι) => f i))) (Finset.sup.{u2, u3} (Multiset.{u2} σ) ι (Lattice.toSemilatticeSup.{u2} (Multiset.{u2} σ) (Multiset.lattice.{u2} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)))) (Multiset.orderBot.{u2} σ) s (fun (i : ι) => MvPolynomial.degrees.{u1, u2} R σ _inst_1 (f i)))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} σ] (s : Finset.{u3} ι) (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), LE.le.{u2} (Multiset.{u2} σ) (Preorder.toLE.{u2} (Multiset.{u2} σ) (PartialOrder.toPreorder.{u2} (Multiset.{u2} σ) (Multiset.partialOrder.{u2} σ))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) s (fun (i : ι) => f i))) (Finset.sup.{u2, u3} (Multiset.{u2} σ) ι (Lattice.toSemilatticeSup.{u2} (Multiset.{u2} σ) (Multiset.lattice.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b))) (Multiset.orderBot.{u2} σ) s (fun (i : ι) => MvPolynomial.degrees.{u1, u2} R σ _inst_1 (f i)))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (s : Finset.{u2} ι) (f : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u3, u1} R σ _inst_1 (Finset.sum.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (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))))) s (fun (i : ι) => f i))) (Finset.sup.{u1, u2} (Multiset.{u1} σ) ι (Lattice.toSemilatticeSup.{u1} (Multiset.{u1} σ) (Multiset.instLatticeMultiset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)))) (Multiset.instOrderBotMultisetToLEToPreorderInstPartialOrderMultiset.{u1} σ) s (fun (i : ι) => MvPolynomial.degrees.{u3, u1} R σ _inst_1 (f i)))
+  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (_inst_2 : Finset.{u2} ι) (s : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u3, u1} R σ _inst_1 (Finset.sum.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (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))))) _inst_2 (fun (i : ι) => s i))) (Finset.sup.{u1, u2} (Multiset.{u1} σ) ι (Lattice.toSemilatticeSup.{u1} (Multiset.{u1} σ) (Multiset.instLatticeMultiset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)))) (Multiset.instOrderBotMultisetToLEToPreorderInstPartialOrderMultiset.{u1} σ) _inst_2 (fun (i : ι) => MvPolynomial.degrees.{u3, u1} R σ _inst_1 (s i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_sum MvPolynomial.degrees_sumₓ'. -/
-theorem degrees_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
-    (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees :=
-  by
-  refine' s.induction _ _
-  · simp only [Finset.sum_empty, Finset.sup_empty, degrees_zero]
-    exact le_rfl
-  · intro i s his ih
-    rw [Finset.sup_insert, Finset.sum_insert his]
-    exact le_trans (degrees_add _ _) (sup_le_sup_left ih _)
+theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → MvPolynomial σ R) :
+    (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by
+  classical
+    refine' s.induction _ _
+    · simp only [Finset.sum_empty, Finset.sup_empty, degrees_zero]
+      exact le_rfl
+    · intro i s his ih
+      rw [Finset.sup_insert, Finset.sum_insert his]
+      exact le_trans (degrees_add _ _) (sup_le_sup_left ih _)
 #align mv_polynomial.degrees_sum MvPolynomial.degrees_sum
 
 /- warning: mv_polynomial.degrees_mul -> MvPolynomial.degrees_mul is a dubious translation:
@@ -215,14 +223,14 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) (q : MvPolynomial.{u1, u2} σ R _inst_1), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{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)))))) p q)) (HAdd.hAdd.{u1, u1, u1} (Multiset.{u1} σ) (Multiset.{u1} σ) (Multiset.{u1} σ) (instHAdd.{u1} (Multiset.{u1} σ) (Multiset.instAddMultiset.{u1} σ)) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 q))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_mul MvPolynomial.degrees_mulₓ'. -/
-theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees :=
-  by
-  refine' Finset.sup_le fun b hb => _
-  have := support_mul p q hb
-  simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
-  rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
-  rw [Finsupp.toMultiset_add]
-  exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
+theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees := by
+  classical
+    refine' Finset.sup_le fun b hb => _
+    have := support_mul p q hb
+    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
+    rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
+    rw [Finsupp.toMultiset_add]
+    exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
 #align mv_polynomial.degrees_mul MvPolynomial.degrees_mul
 
 /- warning: mv_polynomial.degrees_prod -> MvPolynomial.degrees_prod is a dubious translation:
@@ -232,13 +240,13 @@ but is expected to have type
   forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (s : Finset.{u2} ι) (f : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), LE.le.{u1} (Multiset.{u1} σ) (Preorder.toLE.{u1} (Multiset.{u1} σ) (PartialOrder.toPreorder.{u1} (Multiset.{u1} σ) (Multiset.instPartialOrderMultiset.{u1} σ))) (MvPolynomial.degrees.{u3, u1} R σ _inst_1 (Finset.prod.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.sum.{u1, u2} (Multiset.{u1} σ) ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)) s (fun (i : ι) => MvPolynomial.degrees.{u3, u1} R σ _inst_1 (f i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_prod MvPolynomial.degrees_prodₓ'. -/
 theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
-    (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees :=
-  by
-  refine' s.induction _ _
-  · simp only [Finset.prod_empty, Finset.sum_empty, degrees_one]
-  · intro i s his ih
-    rw [Finset.prod_insert his, Finset.sum_insert his]
-    exact le_trans (degrees_mul _ _) (add_le_add_left ih _)
+    (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees := by
+  classical
+    refine' s.induction _ _
+    · simp only [Finset.prod_empty, Finset.sum_empty, degrees_one]
+    · intro i s his ih
+      rw [Finset.prod_insert his, Finset.sum_insert his]
+      exact le_trans (degrees_mul _ _) (add_le_add_left ih _)
 #align mv_polynomial.degrees_prod MvPolynomial.degrees_prod
 
 /- warning: mv_polynomial.degrees_pow -> MvPolynomial.degrees_pow is a dubious translation:
@@ -273,33 +281,34 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_addₓ'. -/
 theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degrees) :
     p.degrees ≤ (p + q).degrees := by
-  apply Finset.sup_le
-  intro d hd
-  rw [Multiset.disjoint_iff_ne] at h
-  rw [Multiset.le_iff_count]
-  intro i
-  rw [degrees, Multiset.count_finset_sup]
-  simp only [Finsupp.count_toMultiset]
-  by_cases h0 : d = 0
-  · simp only [h0, zero_le, Finsupp.zero_apply]
-  · refine' @Finset.le_sup _ _ _ _ (p + q).support _ d _
-    rw [mem_support_iff, coeff_add]
-    suffices q.coeff d = 0 by rwa [this, add_zero, coeff, ← Finsupp.mem_support_iff]
-    rw [← Finsupp.support_eq_empty, ← Ne.def, ← Finset.nonempty_iff_ne_empty] at h0
-    obtain ⟨j, hj⟩ := h0
-    contrapose! h
-    rw [mem_support_iff] at hd
-    refine' ⟨j, _, j, _, rfl⟩
-    all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
+  classical
+    apply Finset.sup_le
+    intro d hd
+    rw [Multiset.disjoint_iff_ne] at h
+    rw [Multiset.le_iff_count]
+    intro i
+    rw [degrees, Multiset.count_finset_sup]
+    simp only [Finsupp.count_toMultiset]
+    by_cases h0 : d = 0
+    · simp only [h0, zero_le, Finsupp.zero_apply]
+    · refine' @Finset.le_sup _ _ _ _ (p + q).support _ d _
+      rw [mem_support_iff, coeff_add]
+      suffices q.coeff d = 0 by rwa [this, add_zero, coeff, ← Finsupp.mem_support_iff]
+      rw [← Finsupp.support_eq_empty, ← Ne.def, ← Finset.nonempty_iff_ne_empty] at h0
+      obtain ⟨j, hj⟩ := h0
+      contrapose! h
+      rw [mem_support_iff] at hd
+      refine' ⟨j, _, j, _, rfl⟩
+      all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
 #align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_add
 
 /- warning: mv_polynomial.degrees_add_of_disjoint -> MvPolynomial.degrees_add_of_disjoint is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {p : MvPolynomial.{u2, u1} σ R _inst_1} {q : MvPolynomial.{u2, u1} σ R _inst_1}, (Multiset.Disjoint.{u2} σ (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q)) -> (Eq.{succ u2} (Multiset.{u2} σ) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Union.union.{u2} (Multiset.{u2} σ) (Multiset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b))) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q)))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] {p : MvPolynomial.{u2, u1} σ R _inst_1} {q : MvPolynomial.{u2, u1} σ R _inst_1}, (Multiset.Disjoint.{u2} σ (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q)) -> (Eq.{succ u2} (Multiset.{u2} σ) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Union.union.{u2} (Multiset.{u2} σ) (Multiset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b)) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 p) (MvPolynomial.degrees.{u1, u2} R σ _inst_1 q)))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {p : MvPolynomial.{u1, u2} σ R _inst_1} {q : MvPolynomial.{u1, u2} σ R _inst_1}, (Multiset.Disjoint.{u1} σ (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 q)) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)) (Union.union.{u1} (Multiset.{u1} σ) (Multiset.instUnionMultiset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 q)))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {_inst_2 : MvPolynomial.{u1, u2} σ R _inst_1} {p : MvPolynomial.{u1, u2} σ R _inst_1}, (Multiset.Disjoint.{u1} σ (MvPolynomial.degrees.{u2, u1} R σ _inst_1 _inst_2) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p)) -> (Eq.{succ u1} (Multiset.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) _inst_2 p)) (Union.union.{u1} (Multiset.{u1} σ) (Multiset.instUnionMultiset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 _inst_2) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_add_of_disjoint MvPolynomial.degrees_add_of_disjointₓ'. -/
-theorem degrees_add_of_disjoint {p q : MvPolynomial σ R}
+theorem degrees_add_of_disjoint [DecidableEq σ] {p q : MvPolynomial σ R}
     (h : Multiset.Disjoint p.degrees q.degrees) : (p + q).degrees = p.degrees ∪ q.degrees :=
   by
   apply le_antisymm
@@ -332,18 +341,19 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_rename MvPolynomial.degrees_renameₓ'. -/
 theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).degrees ⊆ φ.degrees.map f := by
-  intro i
-  rw [mem_degrees, Multiset.mem_map]
-  rintro ⟨d, hd, hi⟩
-  obtain ⟨x, rfl, hx⟩ := coeff_rename_ne_zero _ _ _ hd
-  simp only [map_domain, Finsupp.mem_support_iff] at hi
-  rw [sum_apply, Finsupp.sum] at hi
-  contrapose! hi
-  rw [Finset.sum_eq_zero]
-  intro j hj
-  simp only [exists_prop, mem_degrees] at hi
-  specialize hi j ⟨x, hx, hj⟩
-  rw [single_apply, if_neg hi]
+  classical
+    intro i
+    rw [mem_degrees, Multiset.mem_map]
+    rintro ⟨d, hd, hi⟩
+    obtain ⟨x, rfl, hx⟩ := coeff_rename_ne_zero _ _ _ hd
+    simp only [map_domain, Finsupp.mem_support_iff] at hi
+    rw [sum_apply, Finsupp.sum] at hi
+    contrapose! hi
+    rw [Finset.sum_eq_zero]
+    intro j hj
+    simp only [exists_prop, mem_degrees] at hi
+    specialize hi j ⟨x, hx, hj⟩
+    rw [single_apply, if_neg hi]
 #align mv_polynomial.degrees_rename MvPolynomial.degrees_rename
 
 /- warning: mv_polynomial.degrees_map_of_injective -> MvPolynomial.degrees_map_of_injective is a dubious translation:
@@ -364,12 +374,12 @@ but is expected to have type
   forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {p : MvPolynomial.{u2, u3} σ R _inst_1} {f : σ -> τ}, (Function.Injective.{succ u2, succ u1} σ τ f) -> (Eq.{succ u1} (Multiset.{u1} τ) (MvPolynomial.degrees.{u3, u1} R τ _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 (_x : 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) _x) (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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} σ 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) 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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 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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 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 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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) p)) (Multiset.map.{u2, u1} σ τ f (MvPolynomial.degrees.{u3, u2} R σ _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_rename_of_injective MvPolynomial.degrees_rename_of_injectiveₓ'. -/
 theorem degrees_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f) :
-    degrees (rename f p) = (degrees p).map f :=
-  by
-  simp only [degrees, Multiset.map_finset_sup p.support Finsupp.toMultiset f h,
-    support_rename_of_injective h, Finset.sup_image]
-  refine' Finset.sup_congr rfl fun x hx => _
-  exact (Finsupp.toMultiset_map _ _).symm
+    degrees (rename f p) = (degrees p).map f := by
+  classical
+    simp only [degrees, Multiset.map_finset_sup p.support Finsupp.toMultiset f h,
+      support_rename_of_injective h, Finset.sup_image]
+    refine' Finset.sup_congr rfl fun x hx => _
+    exact (Finsupp.toMultiset_map _ _).symm
 #align mv_polynomial.degrees_rename_of_injective MvPolynomial.degrees_rename_of_injective
 
 end Degrees
@@ -382,10 +392,15 @@ section Vars
 #print MvPolynomial.vars /-
 /-- `vars p` is the set of variables appearing in the polynomial `p` -/
 def vars (p : MvPolynomial σ R) : Finset σ :=
-  p.degrees.toFinset
+  letI := Classical.decEq σ
+  p.degrees.to_finset
 #align mv_polynomial.vars MvPolynomial.vars
 -/
 
+theorem vars_def [DecidableEq σ] (p : MvPolynomial σ R) : p.vars = p.degrees.toFinset := by
+  convert rfl
+#align mv_polynomial.vars_def MvPolynomial.vars_def
+
 /- warning: mv_polynomial.vars_0 -> MvPolynomial.vars_0 is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R], Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 0 (OfNat.mk.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 0 (Zero.zero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MulZeroClass.toHasZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (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)))))))))) (EmptyCollection.emptyCollection.{u2} (Finset.{u2} σ) (Finset.hasEmptyc.{u2} σ))
@@ -394,7 +409,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_0 MvPolynomial.vars_0ₓ'. -/
 @[simp]
 theorem vars_0 : (0 : MvPolynomial σ R).vars = ∅ := by
-  rw [vars, degrees_zero, Multiset.toFinset_zero]
+  classical rw [vars_def, degrees_zero, Multiset.toFinset_zero]
 #align mv_polynomial.vars_0 MvPolynomial.vars_0
 
 /- warning: mv_polynomial.vars_monomial -> MvPolynomial.vars_monomial is a dubious translation:
@@ -405,7 +420,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_monomial MvPolynomial.vars_monomialₓ'. -/
 @[simp]
 theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by
-  rw [vars, degrees_monomial_eq _ _ h, Finsupp.toFinset_toMultiset]
+  classical rw [vars_def, degrees_monomial_eq _ _ h, Finsupp.toFinset_toMultiset]
 #align mv_polynomial.vars_monomial MvPolynomial.vars_monomial
 
 /- warning: mv_polynomial.vars_C -> MvPolynomial.vars_C is a dubious translation:
@@ -416,7 +431,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_C MvPolynomial.vars_Cₓ'. -/
 @[simp]
 theorem vars_C : (C r : MvPolynomial σ R).vars = ∅ := by
-  rw [vars, degrees_C, Multiset.toFinset_zero]
+  classical rw [vars_def, degrees_C, Multiset.toFinset_zero]
 #align mv_polynomial.vars_C MvPolynomial.vars_C
 
 /- warning: mv_polynomial.vars_X -> MvPolynomial.vars_X is a dubious translation:
@@ -449,10 +464,11 @@ Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_supp
 theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ} (H : x ∈ f.support)
     {v : σ} (h : v ∉ vars f) : x v = 0 :=
   by
-  rw [vars, Multiset.mem_toFinset] at h
+  letI := Classical.decEq σ
+  rw [vars_def, Multiset.mem_toFinset] at h
   rw [← Finsupp.not_mem_support_iff]
   contrapose! h
-  unfold degrees
+  rw [degrees_def]
   rw [show f.support = insert x f.support from Eq.symm <| Finset.insert_eq_of_mem H]
   rw [Finset.sup_insert]
   simp only [Multiset.mem_union, Multiset.sup_eq_union]
@@ -462,11 +478,11 @@ theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ
 
 /- warning: mv_polynomial.vars_add_subset -> MvPolynomial.vars_add_subset is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1) (q : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Union.union.{u2} (Finset.{u2} σ) (Finset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b))) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (MvPolynomial.vars.{u1, u2} R σ _inst_1 q))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (p : MvPolynomial.{u2, u1} σ R _inst_1) (q : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Union.union.{u2} (Finset.{u2} σ) (Finset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b)) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (MvPolynomial.vars.{u1, u2} R σ _inst_1 q))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) (q : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (MvPolynomial.vars.{u2, u1} R σ _inst_1 q))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (_inst_2 : MvPolynomial.{u1, u2} σ R _inst_1) (p : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) _inst_2 p)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.vars.{u2, u1} R σ _inst_1 _inst_2) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_add_subset MvPolynomial.vars_add_subsetₓ'. -/
-theorem vars_add_subset (p q : MvPolynomial σ R) : (p + q).vars ⊆ p.vars ∪ q.vars :=
+theorem vars_add_subset [DecidableEq σ] (p q : MvPolynomial σ R) : (p + q).vars ⊆ p.vars ∪ q.vars :=
   by
   intro x hx
   simp only [vars, Finset.mem_union, Multiset.mem_toFinset] at hx⊢
@@ -475,15 +491,16 @@ theorem vars_add_subset (p q : MvPolynomial σ R) : (p + q).vars ⊆ p.vars ∪
 
 /- warning: mv_polynomial.vars_add_of_disjoint -> MvPolynomial.vars_add_of_disjoint is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {p : MvPolynomial.{u2, u1} σ R _inst_1} {q : MvPolynomial.{u2, u1} σ R _inst_1}, (Disjoint.{u2} (Finset.{u2} σ) (Finset.partialOrder.{u2} σ) (Finset.orderBot.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (MvPolynomial.vars.{u1, u2} R σ _inst_1 q)) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Union.union.{u2} (Finset.{u2} σ) (Finset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b))) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (MvPolynomial.vars.{u1, u2} R σ _inst_1 q)))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {p : MvPolynomial.{u2, u1} σ R _inst_1} {q : MvPolynomial.{u2, u1} σ R _inst_1} [_inst_2 : DecidableEq.{succ u2} σ], (Disjoint.{u2} (Finset.{u2} σ) (Finset.partialOrder.{u2} σ) (Finset.orderBot.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (MvPolynomial.vars.{u1, u2} R σ _inst_1 q)) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Union.union.{u2} (Finset.{u2} σ) (Finset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b)) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (MvPolynomial.vars.{u1, u2} R σ _inst_1 q)))
 but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {p : MvPolynomial.{u1, u2} σ R _inst_1} {q : MvPolynomial.{u1, u2} σ R _inst_1}, (Disjoint.{u1} (Finset.{u1} σ) (Finset.partialOrder.{u1} σ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (MvPolynomial.vars.{u2, u1} R σ _inst_1 q)) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (MvPolynomial.vars.{u2, u1} R σ _inst_1 q)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_add_of_disjoint MvPolynomial.vars_add_of_disjointₓ'. -/
-theorem vars_add_of_disjoint (h : Disjoint p.vars q.vars) : (p + q).vars = p.vars ∪ q.vars :=
+theorem vars_add_of_disjoint [DecidableEq σ] (h : Disjoint p.vars q.vars) :
+    (p + q).vars = p.vars ∪ q.vars :=
   by
   apply Finset.Subset.antisymm (vars_add_subset p q)
   intro x hx
-  simp only [vars, Multiset.disjoint_toFinset] at h hx⊢
+  simp only [vars_def, Multiset.disjoint_toFinset] at h hx⊢
   rw [degrees_add_of_disjoint h, Multiset.toFinset_union]
   exact hx
 #align mv_polynomial.vars_add_of_disjoint MvPolynomial.vars_add_of_disjoint
@@ -492,11 +509,11 @@ section Mul
 
 /- warning: mv_polynomial.vars_mul -> MvPolynomial.vars_mul is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (φ : MvPolynomial.{u2, u1} σ R _inst_1) (ψ : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) φ ψ)) (Union.union.{u2} (Finset.{u2} σ) (Finset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b))) (MvPolynomial.vars.{u1, u2} R σ _inst_1 φ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 ψ))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (φ : MvPolynomial.{u2, u1} σ R _inst_1) (ψ : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) φ ψ)) (Union.union.{u2} (Finset.{u2} σ) (Finset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => _inst_2 a b)) (MvPolynomial.vars.{u1, u2} R σ _inst_1 φ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 ψ))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{u1, u2} σ R _inst_1) (ψ : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{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)))))) φ ψ)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 ψ))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (_inst_2 : MvPolynomial.{u1, u2} σ R _inst_1) (φ : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{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)))))) _inst_2 φ)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.vars.{u2, u1} R σ _inst_1 _inst_2) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_mul MvPolynomial.vars_mulₓ'. -/
-theorem vars_mul (φ ψ : MvPolynomial σ R) : (φ * ψ).vars ⊆ φ.vars ∪ ψ.vars :=
+theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars ⊆ φ.vars ∪ ψ.vars :=
   by
   intro i
   simp only [mem_vars, Finset.mem_union]
@@ -537,33 +554,34 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{u1, u2} σ R _inst_1) (n : Nat), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (Monoid.Pow.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toMonoidWithZero.{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)))))) φ n)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_pow MvPolynomial.vars_powₓ'. -/
-theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars :=
-  by
-  induction' n with n ih
-  · simp
-  · rw [pow_succ]
-    apply Finset.Subset.trans (vars_mul _ _)
-    exact Finset.union_subset (Finset.Subset.refl _) ih
+theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars := by
+  classical
+    simp_rw [vars_def]
+    induction' n with n ih
+    · simp
+    · rw [pow_succ]
+      apply Finset.Subset.trans (vars_mul _ _)
+      exact Finset.union_subset (Finset.Subset.refl _) ih
 #align mv_polynomial.vars_pow MvPolynomial.vars_pow
 
 /- warning: mv_polynomial.vars_prod -> MvPolynomial.vars_prod is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} {s : Finset.{u3} ι} (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.prod.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.biUnion.{u3, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) s (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (f i)))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} σ] {s : Finset.{u3} ι} (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.prod.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.biUnion.{u3, u2} ι σ (fun (a : σ) (b : σ) => _inst_2 a b) s (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (f i)))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} {s : Finset.{u2} ι} (f : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u3, u1} R σ _inst_1 (Finset.prod.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.biUnion.{u2, u1} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) s (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (f i)))
+  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} {_inst_2 : Finset.{u2} ι} (s : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u3, u1} R σ _inst_1 (Finset.prod.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) _inst_2 (fun (i : ι) => s i))) (Finset.biUnion.{u2, u1} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) _inst_2 (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (s i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_prod MvPolynomial.vars_prodₓ'. -/
 /-- The variables of the product of a family of polynomials
 are a subset of the union of the sets of variables of each polynomial.
 -/
-theorem vars_prod {ι : Type _} {s : Finset ι} (f : ι → MvPolynomial σ R) :
-    (∏ i in s, f i).vars ⊆ s.biUnion fun i => (f i).vars :=
-  by
-  apply s.induction_on
-  · simp
-  · intro a s hs hsub
-    simp only [hs, Finset.biUnion_insert, Finset.prod_insert, not_false_iff]
-    apply Finset.Subset.trans (vars_mul _ _)
-    exact Finset.union_subset_union (Finset.Subset.refl _) hsub
+theorem vars_prod {ι : Type _} [DecidableEq σ] {s : Finset ι} (f : ι → MvPolynomial σ R) :
+    (∏ i in s, f i).vars ⊆ s.biUnion fun i => (f i).vars := by
+  classical
+    apply s.induction_on
+    · simp
+    · intro a s hs hsub
+      simp only [hs, Finset.biUnion_insert, Finset.prod_insert, not_false_iff]
+      apply Finset.Subset.trans (vars_mul _ _)
+      exact Finset.union_subset_union (Finset.Subset.refl _) hsub
 #align mv_polynomial.vars_prod MvPolynomial.vars_prod
 
 section IsDomain
@@ -596,43 +614,45 @@ variable {ι : Type _} (t : Finset ι) (φ : ι → MvPolynomial σ R)
 
 /- warning: mv_polynomial.vars_sum_subset -> MvPolynomial.vars_sum_subset is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (t : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u3, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i)))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (t : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)) [_inst_2 : DecidableEq.{succ u2} σ], HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u3, u2} ι σ (fun (a : σ) (b : σ) => _inst_2 a b) t (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i)))
 but is expected to have type
   forall {R : Type.{u3}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u1}} (t : Finset.{u1} ι) (φ : ι -> (MvPolynomial.{u2, u3} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.instHasSubsetFinset.{u2} σ) (MvPolynomial.vars.{u3, u2} R σ _inst_1 (Finset.sum.{max u3 u2, u1} (MvPolynomial.{u2, u3} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u1, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u3, u2} R σ _inst_1 (φ i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subsetₓ'. -/
-theorem vars_sum_subset : (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars :=
-  by
-  apply t.induction_on
-  · simp
-  · intro a s has hsum
-    rw [Finset.biUnion_insert, Finset.sum_insert has]
-    refine'
-      Finset.Subset.trans (vars_add_subset _ _) (Finset.union_subset_union (Finset.Subset.refl _) _)
-    assumption
+theorem vars_sum_subset [DecidableEq σ] :
+    (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by
+  classical
+    apply t.induction_on
+    · simp
+    · intro a s has hsum
+      rw [Finset.biUnion_insert, Finset.sum_insert has]
+      refine'
+        Finset.Subset.trans (vars_add_subset _ _)
+          (Finset.union_subset_union (Finset.Subset.refl _) _)
+      assumption
 #align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subset
 
 /- warning: mv_polynomial.vars_sum_of_disjoint -> MvPolynomial.vars_sum_of_disjoint is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (t : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), (Pairwise.{u3} ι (Function.onFun.{succ u3, succ u2, 1} ι (Finset.{u2} σ) Prop (Disjoint.{u2} (Finset.{u2} σ) (Finset.partialOrder.{u2} σ) (Finset.orderBot.{u2} σ)) (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i)))) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u3, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i))))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (t : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)) [_inst_2 : DecidableEq.{succ u2} σ], (Pairwise.{u3} ι (Function.onFun.{succ u3, succ u2, 1} ι (Finset.{u2} σ) Prop (Disjoint.{u2} (Finset.{u2} σ) (Finset.partialOrder.{u2} σ) (Finset.orderBot.{u2} σ)) (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i)))) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u3, u2} ι σ (fun (a : σ) (b : σ) => _inst_2 a b) t (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i))))
 but is expected to have type
   forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (t : Finset.{u2} ι) (φ : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Finset.{u1} σ) Prop (Disjoint.{u1} (Finset.{u1} σ) (Finset.partialOrder.{u1} σ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} σ)) (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (φ i)))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u3, u1} R σ _inst_1 (Finset.sum.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (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))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u2, u1} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (φ i))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_sum_of_disjoint MvPolynomial.vars_sum_of_disjointₓ'. -/
-theorem vars_sum_of_disjoint (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
-    (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars :=
-  by
-  apply t.induction_on
-  · simp
-  · intro a s has hsum
-    rw [Finset.biUnion_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
-    unfold Pairwise on_fun at h
-    rw [hsum]
-    simp only [Finset.disjoint_iff_ne] at h⊢
-    intro v hv v2 hv2
-    rw [Finset.mem_biUnion] at hv2
-    rcases hv2 with ⟨i, his, hi⟩
-    refine' h _ _ hv _ hi
-    rintro rfl
-    contradiction
+theorem vars_sum_of_disjoint [DecidableEq σ] (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
+    (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars := by
+  classical
+    apply t.induction_on
+    · simp
+    · intro a s has hsum
+      rw [Finset.biUnion_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
+      unfold Pairwise on_fun at h
+      rw [hsum]
+      simp only [Finset.disjoint_iff_ne] at h⊢
+      intro v hv v2 hv2
+      rw [Finset.mem_biUnion] at hv2
+      rcases hv2 with ⟨i, his, hi⟩
+      refine' h _ _ hv _ hi
+      rintro rfl
+      contradiction
 #align mv_polynomial.vars_sum_of_disjoint MvPolynomial.vars_sum_of_disjoint
 
 end Sum
@@ -677,11 +697,12 @@ theorem vars_monomial_single (i : σ) {e : ℕ} {r : R} (he : e ≠ 0) (hr : r 
 
 /- warning: mv_polynomial.vars_eq_support_bUnion_support -> MvPolynomial.vars_eq_support_biUnion_support is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (Finset.biUnion.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) (MvPolynomial.support.{u1, u2} R σ _inst_1 p) (Finsupp.support.{u2, 0} σ Nat Nat.hasZero))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1) [_inst_3 : DecidableEq.{succ u2} σ], Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (Finset.biUnion.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) σ (fun (a : σ) (b : σ) => _inst_3 a b) (MvPolynomial.support.{u1, u2} R σ _inst_1 p) (Finsupp.support.{u2, 0} σ Nat Nat.hasZero))
 but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (Finset.biUnion.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) (MvPolynomial.support.{u2, u1} R σ _inst_1 p) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_biUnion_supportₓ'. -/
-theorem vars_eq_support_biUnion_support : p.vars = p.support.biUnion Finsupp.support :=
+theorem vars_eq_support_biUnion_support [DecidableEq σ] :
+    p.vars = p.support.biUnion Finsupp.support :=
   by
   ext i
   rw [mem_vars, Finset.mem_biUnion]
@@ -699,10 +720,15 @@ section DegreeOf
 #print MvPolynomial.degreeOf /-
 /-- `degree_of n p` gives the highest power of X_n that appears in `p` -/
 def degreeOf (n : σ) (p : MvPolynomial σ R) : ℕ :=
+  letI := Classical.decEq σ
   p.degrees.count n
 #align mv_polynomial.degree_of MvPolynomial.degreeOf
 -/
 
+theorem degreeOf_def [DecidableEq σ] (n : σ) (p : MvPolynomial σ R) :
+    p.degreeOf n = p.degrees.count n := by convert rfl
+#align mv_polynomial.degree_of_def MvPolynomial.degreeOf_def
+
 /- warning: mv_polynomial.degree_of_eq_sup -> MvPolynomial.degreeOf_eq_sup is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (n : σ) (f : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{1} Nat (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 n f) (Finset.sup.{0, u2} Nat (Finsupp.{u2, 0} σ Nat Nat.hasZero) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) Nat.orderBot (MvPolynomial.support.{u1, u2} R σ _inst_1 f) (fun (m : Finsupp.{u2, 0} σ Nat Nat.hasZero) => coeFn.{succ u2, succ u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u2, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u2, 0} σ Nat Nat.hasZero) m n))
@@ -710,12 +736,12 @@ but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (n : σ) (f : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{1} Nat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 n f) (Finset.sup.{0, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) n) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Lattice.toSemilatticeSup.{0} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) n) Nat.instLatticeNat) Nat.orderBot (MvPolynomial.support.{u2, u1} R σ _inst_1 f) (fun (m : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => 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)) m n))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_eq_sup MvPolynomial.degreeOf_eq_supₓ'. -/
 theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
-    degreeOf n f = f.support.sup fun m => m n :=
-  by
-  rw [degree_of, degrees, Multiset.count_finset_sup]
-  congr
-  ext
-  simp
+    degreeOf n f = f.support.sup fun m => m n := by
+  classical
+    rw [degree_of_def, degrees_def, Multiset.count_finset_sup]
+    congr
+    ext
+    simp
 #align mv_polynomial.degree_of_eq_sup MvPolynomial.degreeOf_eq_sup
 
 /- warning: mv_polynomial.degree_of_lt_iff -> MvPolynomial.degreeOf_lt_iff is a dubious translation:
@@ -753,11 +779,11 @@ theorem degreeOf_C (a : R) (x : σ) : degreeOf x (C a : MvPolynomial σ R) = 0 :
 
 /- warning: mv_polynomial.degree_of_X -> MvPolynomial.degreeOf_X is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (i : σ) (j : σ) [_inst_2 : Nontrivial.{u1} R], Eq.{1} Nat (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 i (MvPolynomial.X.{u1, u2} R σ _inst_1 j)) (ite.{1} Nat (Eq.{succ u2} σ i j) (Classical.propDecidable (Eq.{succ u2} σ i j)) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : DecidableEq.{succ u2} σ] (i : σ) (j : σ) [_inst_3 : Nontrivial.{u1} R], Eq.{1} Nat (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 i (MvPolynomial.X.{u1, u2} R σ _inst_1 j)) (ite.{1} Nat (Eq.{succ u2} σ i j) (_inst_2 i j) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (i : σ) (j : σ) [_inst_2 : Nontrivial.{u2} R], Eq.{1} Nat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 i (MvPolynomial.X.{u2, u1} R σ _inst_1 j)) (ite.{1} Nat (Eq.{succ u1} σ i j) (Classical.propDecidable (Eq.{succ u1} σ i j)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (_inst_2 : σ) (i : σ) [j : Nontrivial.{u2} R], Eq.{1} Nat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 _inst_2 (MvPolynomial.X.{u2, u1} R σ _inst_1 i)) (ite.{1} Nat (Eq.{succ u1} σ _inst_2 i) (Classical.propDecidable (Eq.{succ u1} σ _inst_2 i)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_X MvPolynomial.degreeOf_Xₓ'. -/
-theorem degreeOf_X (i j : σ) [Nontrivial R] :
+theorem degreeOf_X [DecidableEq σ] (i j : σ) [Nontrivial R] :
     degreeOf i (X j : MvPolynomial σ R) = if i = j then 1 else 0 :=
   by
   by_cases c : i = j
@@ -772,12 +798,12 @@ but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (n : σ) (f : MvPolynomial.{u1, u2} σ R _inst_1) (g : MvPolynomial.{u1, u2} σ R _inst_1), LE.le.{0} Nat instLENat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 n (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) f g)) (Max.max.{0} Nat Nat.instMaxNat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 n f) (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 n g))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_add_le MvPolynomial.degreeOf_add_leₓ'. -/
 theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
-    degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) :=
-  by
-  repeat' rw [degree_of]
-  apply (Multiset.count_le_of_le n (degrees_add f g)).trans
-  dsimp
-  rw [Multiset.count_union]
+    degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) := by
+  classical
+    repeat' rw [degree_of_def]
+    apply (Multiset.count_le_of_le n (degrees_add f g)).trans
+    dsimp
+    rw [Multiset.count_union]
 #align mv_polynomial.degree_of_add_le MvPolynomial.degreeOf_add_le
 
 /- warning: mv_polynomial.monomial_le_degree_of -> MvPolynomial.monomial_le_degreeOf is a dubious translation:
@@ -800,11 +826,11 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_mul_le MvPolynomial.degreeOf_mul_leₓ'. -/
 -- TODO we can prove equality here if R is a domain
 theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
-    degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g :=
-  by
-  repeat' rw [degree_of]
-  convert Multiset.count_le_of_le i (degrees_mul f g)
-  rw [Multiset.count_add]
+    degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g := by
+  classical
+    repeat' rw [degree_of_def]
+    convert Multiset.count_le_of_le i (degrees_mul f g)
+    rw [Multiset.count_add]
 #align mv_polynomial.degree_of_mul_le MvPolynomial.degreeOf_mul_le
 
 /- warning: mv_polynomial.degree_of_mul_X_ne -> MvPolynomial.degreeOf_mul_X_ne is a dubious translation:
@@ -814,15 +840,15 @@ but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {i : σ} {j : σ} (f : MvPolynomial.{u1, u2} σ R _inst_1), (Ne.{succ u1} σ i j) -> (Eq.{1} Nat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 i (HMul.hMul.{max u2 u1, max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{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)))))) f (MvPolynomial.X.{u2, u1} R σ _inst_1 j))) (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 i f))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_mul_X_ne MvPolynomial.degreeOf_mul_X_neₓ'. -/
 theorem degreeOf_mul_X_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
-    degreeOf i (f * X j) = degreeOf i f :=
-  by
-  repeat' rw [degree_of_eq_sup i]
-  rw [support_mul_X]
-  simp only [Finset.sup_map]
-  congr
-  ext
-  simp only [single, Nat.one_ne_zero, add_right_eq_self, addRightEmbedding_apply, coe_mk,
-    Pi.add_apply, comp_app, ite_eq_right_iff, Finsupp.coe_add, Pi.single_eq_of_ne h]
+    degreeOf i (f * X j) = degreeOf i f := by
+  classical
+    repeat' rw [degree_of_eq_sup i]
+    rw [support_mul_X]
+    simp only [Finset.sup_map]
+    congr
+    ext
+    simp only [single, Nat.one_ne_zero, add_right_eq_self, addRightEmbedding_apply, coe_mk,
+      Pi.add_apply, comp_app, ite_eq_right_iff, Finsupp.coe_add, Pi.single_eq_of_ne h]
 #align mv_polynomial.degree_of_mul_X_ne MvPolynomial.degreeOf_mul_X_ne
 
 /- warning: mv_polynomial.degree_of_mul_X_eq -> MvPolynomial.degreeOf_mul_X_eq is a dubious translation:
@@ -833,13 +859,13 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eqₓ'. -/
 -- TODO in the following we have equality iff f ≠ 0
 theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
-    degreeOf j (f * X j) ≤ degreeOf j f + 1 :=
-  by
-  repeat' rw [degree_of]
-  apply (Multiset.count_le_of_le j (degrees_mul f (X j))).trans
-  simp only [Multiset.count_add, add_le_add_iff_left]
-  convert Multiset.count_le_of_le j (degrees_X' j)
-  rw [Multiset.count_singleton_self]
+    degreeOf j (f * X j) ≤ degreeOf j f + 1 := by
+  classical
+    repeat' rw [degree_of_def]
+    apply (Multiset.count_le_of_le j (degrees_mul f (X j))).trans
+    simp only [Multiset.count_add, add_le_add_iff_left]
+    convert Multiset.count_le_of_le j (degrees_X' j)
+    rw [Multiset.count_singleton_self]
 #align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eq
 
 /- warning: mv_polynomial.degree_of_rename_of_injective -> MvPolynomial.degreeOf_rename_of_injective is a dubious translation:
@@ -850,7 +876,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_rename_of_injective MvPolynomial.degreeOf_rename_of_injectiveₓ'. -/
 theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
     (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by
-  simp only [degree_of, degrees_rename_of_injective h, Multiset.count_map_eq_count' f p.degrees h]
+  classical simp only [degree_of_def, degrees_rename_of_injective h,
+      Multiset.count_map_eq_count' f p.degrees h]
 #align mv_polynomial.degree_of_rename_of_injective MvPolynomial.degreeOf_rename_of_injective
 
 end DegreeOf
@@ -887,10 +914,10 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1), LE.le.{0} Nat instLENat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 p) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} σ) (fun (_x : Multiset.{u1} σ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} σ) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} σ) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} σ) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} σ) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} σ) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} σ) (MvPolynomial.degrees.{u2, u1} R σ _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_cardₓ'. -/
-theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) : p.totalDegree ≤ p.degrees.card :=
-  by
-  rw [total_degree_eq]
-  exact Finset.sup_le fun s hs => Multiset.card_le_of_le <| Finset.le_sup hs
+theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) : p.totalDegree ≤ p.degrees.card := by
+  classical
+    rw [total_degree_eq]
+    exact Finset.sup_le fun s hs => Multiset.card_le_of_le <| Finset.le_sup hs
 #align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
 
 /- warning: mv_polynomial.total_degree_C -> MvPolynomial.totalDegree_C is a dubious translation:
@@ -950,11 +977,12 @@ Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_de
 theorem totalDegree_add (a b : MvPolynomial σ R) :
     (a + b).totalDegree ≤ max a.totalDegree b.totalDegree :=
   Finset.sup_le fun n hn => by
-    have := Finsupp.support_add hn
-    rw [Finset.mem_union] at this
-    cases this
-    · exact le_max_of_le_left (Finset.le_sup this)
-    · exact le_max_of_le_right (Finset.le_sup this)
+    classical
+      have := Finsupp.support_add hn
+      rw [Finset.mem_union] at this
+      cases this
+      · exact le_max_of_le_left (Finset.le_sup this)
+      · exact le_max_of_le_right (Finset.le_sup this)
 #align mv_polynomial.total_degree_add MvPolynomial.totalDegree_add
 
 /- warning: mv_polynomial.total_degree_add_eq_left_of_total_degree_lt -> MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt is a dubious translation:
@@ -1007,15 +1035,16 @@ Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_de
 theorem totalDegree_mul (a b : MvPolynomial σ R) :
     (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
   Finset.sup_le fun n hn => by
-    have := AddMonoidAlgebra.support_mul a b hn
-    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
-    rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
-    rw [Finsupp.sum_add_index']
-    · exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
-    · intro a
-      rfl
-    · intro a b₁ b₂
-      rfl
+    classical
+      have := AddMonoidAlgebra.support_mul a b hn
+      simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
+      rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
+      rw [Finsupp.sum_add_index']
+      · exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
+      · intro a
+        rfl
+      · intro a b₁ b₂
+        rfl
 #align mv_polynomial.total_degree_mul MvPolynomial.totalDegree_mul
 
 /- warning: mv_polynomial.total_degree_smul_le -> MvPolynomial.totalDegree_smul_le is a dubious translation:
@@ -1056,7 +1085,7 @@ Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_de
 @[simp]
 theorem totalDegree_monomial (s : σ →₀ ℕ) {c : R} (hc : c ≠ 0) :
     (monomial s c : MvPolynomial σ R).totalDegree = s.Sum fun _ e => e := by
-  simp [total_degree, support_monomial, if_neg hc]
+  classical simp [total_degree, support_monomial, if_neg hc]
 #align mv_polynomial.total_degree_monomial MvPolynomial.totalDegree_monomial
 
 /- warning: mv_polynomial.total_degree_X_pow -> MvPolynomial.totalDegree_X_pow is a dubious translation:
@@ -1178,13 +1207,14 @@ theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
   Finset.sup_le fun b => by
     intro h
     rw [rename_eq] at h
-    have h' := Finsupp.mapDomain_support h
-    rw [Finset.mem_image] at h'
-    rcases h' with ⟨s, hs, rfl⟩
-    rw [Finsupp.sum_mapDomain_index]
-    exact le_trans le_rfl (Finset.le_sup hs)
-    exact fun _ => rfl
-    exact fun _ _ _ => rfl
+    classical
+      have h' := Finsupp.mapDomain_support h
+      rw [Finset.mem_image] at h'
+      rcases h' with ⟨s, hs, rfl⟩
+      rw [Finsupp.sum_mapDomain_index]
+      exact le_trans le_rfl (Finset.le_sup hs)
+      exact fun _ => rfl
+      exact fun _ _ _ => rfl
 #align mv_polynomial.total_degree_rename_le MvPolynomial.totalDegree_rename_le
 
 end TotalDegree
@@ -1311,12 +1341,12 @@ theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ 
 
 /- warning: mv_polynomial.vars_rename -> MvPolynomial.vars_rename is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} {τ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] (f : σ -> τ) (φ : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u3} (Finset.{u3} τ) (Finset.hasSubset.{u3} τ) (MvPolynomial.vars.{u1, u3} R τ _inst_1 (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) => (MvPolynomial.{u2, u1} σ R _inst_1) -> (MvPolynomial.{u3, u1} τ R _inst_1)) ([anonymous].{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.rename.{u2, u3, u1} σ τ R _inst_1 f) φ)) (Finset.image.{u2, u3} σ τ (fun (a : τ) (b : τ) => Classical.propDecidable (Eq.{succ u3} τ a b)) f (MvPolynomial.vars.{u1, u2} R σ _inst_1 φ))
+  forall {R : Type.{u1}} {σ : Type.{u2}} {τ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_3 : DecidableEq.{succ u3} τ] (f : σ -> τ) (φ : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u3} (Finset.{u3} τ) (Finset.hasSubset.{u3} τ) (MvPolynomial.vars.{u1, u3} R τ _inst_1 (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) => (MvPolynomial.{u2, u1} σ R _inst_1) -> (MvPolynomial.{u3, u1} τ R _inst_1)) ([anonymous].{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.rename.{u2, u3, u1} σ τ R _inst_1 f) φ)) (Finset.image.{u2, u3} σ τ (fun (a : τ) (b : τ) => _inst_3 a b) f (MvPolynomial.vars.{u1, u2} R σ _inst_1 φ))
 but is expected to have type
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(MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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} 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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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) φ)) (Finset.image.{u2, u1} σ τ (fun (a : τ) (b : τ) => Classical.propDecidable (Eq.{succ u1} τ a b)) f (MvPolynomial.vars.{u3, u2} R σ _inst_1 φ))
+  forall {R : Type.{u3}} {σ : Type.{u2}} {τ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] (_inst_3 : σ -> τ) (f : MvPolynomial.{u2, u3} σ R _inst_1), HasSubset.Subset.{u1} (Finset.{u1} τ) (Finset.instHasSubsetFinset.{u1} τ) (MvPolynomial.vars.{u3, u1} R τ _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) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} 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(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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 _inst_3) f)) (Finset.image.{u2, u1} σ τ (fun (a : τ) (b : τ) => Classical.propDecidable (Eq.{succ u1} τ a b)) _inst_3 (MvPolynomial.vars.{u3, u2} R σ _inst_1 f))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_rename MvPolynomial.vars_renameₓ'. -/
-theorem vars_rename (f : σ → τ) (φ : MvPolynomial σ R) : (rename f φ).vars ⊆ φ.vars.image f :=
-  by
+theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
+    (rename f φ).vars ⊆ φ.vars.image f := by
   intro i hi
   simp only [vars, exists_prop, Multiset.mem_toFinset, Finset.mem_image] at hi⊢
   simpa only [Multiset.mem_map] using degrees_rename _ _ hi
@@ -1330,7 +1360,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_vars_rename MvPolynomial.mem_vars_renameₓ'. -/
 theorem mem_vars_rename (f : σ → τ) (φ : MvPolynomial σ R) {j : τ} (h : j ∈ (rename f φ).vars) :
     ∃ i : σ, i ∈ φ.vars ∧ f i = j := by
-  simpa only [exists_prop, Finset.mem_image] using vars_rename f φ h
+  classical simpa only [exists_prop, Finset.mem_image] using vars_rename f φ h
 #align mv_polynomial.mem_vars_rename MvPolynomial.mem_vars_rename
 
 end EvalVars

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

@@ -219,7 +219,7 @@ theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees +
   by
   refine' Finset.sup_le fun b hb => _
   have := support_mul p q hb
-  simp only [Finset.mem_bunionᵢ, Finset.mem_singleton] at this
+  simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
   rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
   rw [Finsupp.toMultiset_add]
   exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
@@ -548,20 +548,20 @@ theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars
 
 /- warning: mv_polynomial.vars_prod -> MvPolynomial.vars_prod is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} {s : Finset.{u3} ι} (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.prod.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.bunionᵢ.{u3, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) s (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (f i)))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} {s : Finset.{u3} ι} (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.prod.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.biUnion.{u3, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) s (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (f i)))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} {s : Finset.{u2} ι} (f : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u3, u1} R σ _inst_1 (Finset.prod.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.bunionᵢ.{u2, u1} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) s (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (f i)))
+  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} {s : Finset.{u2} ι} (f : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u3, u1} R σ _inst_1 (Finset.prod.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.biUnion.{u2, u1} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) s (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (f i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_prod MvPolynomial.vars_prodₓ'. -/
 /-- The variables of the product of a family of polynomials
 are a subset of the union of the sets of variables of each polynomial.
 -/
 theorem vars_prod {ι : Type _} {s : Finset ι} (f : ι → MvPolynomial σ R) :
-    (∏ i in s, f i).vars ⊆ s.bunionᵢ fun i => (f i).vars :=
+    (∏ i in s, f i).vars ⊆ s.biUnion fun i => (f i).vars :=
   by
   apply s.induction_on
   · simp
   · intro a s hs hsub
-    simp only [hs, Finset.bunionᵢ_insert, Finset.prod_insert, not_false_iff]
+    simp only [hs, Finset.biUnion_insert, Finset.prod_insert, not_false_iff]
     apply Finset.Subset.trans (vars_mul _ _)
     exact Finset.union_subset_union (Finset.Subset.refl _) hsub
 #align mv_polynomial.vars_prod MvPolynomial.vars_prod
@@ -596,16 +596,16 @@ variable {ι : Type _} (t : Finset ι) (φ : ι → MvPolynomial σ R)
 
 /- warning: mv_polynomial.vars_sum_subset -> MvPolynomial.vars_sum_subset is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (t : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) t (fun (i : ι) => φ i))) (Finset.bunionᵢ.{u3, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i)))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (t : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u3, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i)))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u1}} (t : Finset.{u1} ι) (φ : ι -> (MvPolynomial.{u2, u3} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.instHasSubsetFinset.{u2} σ) (MvPolynomial.vars.{u3, u2} R σ _inst_1 (Finset.sum.{max u3 u2, u1} (MvPolynomial.{u2, u3} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))) t (fun (i : ι) => φ i))) (Finset.bunionᵢ.{u1, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u3, u2} R σ _inst_1 (φ i)))
+  forall {R : Type.{u3}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u1}} (t : Finset.{u1} ι) (φ : ι -> (MvPolynomial.{u2, u3} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.instHasSubsetFinset.{u2} σ) (MvPolynomial.vars.{u3, u2} R σ _inst_1 (Finset.sum.{max u3 u2, u1} (MvPolynomial.{u2, u3} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u1, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u3, u2} R σ _inst_1 (φ i)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subsetₓ'. -/
-theorem vars_sum_subset : (∑ i in t, φ i).vars ⊆ Finset.bunionᵢ t fun i => (φ i).vars :=
+theorem vars_sum_subset : (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars :=
   by
   apply t.induction_on
   · simp
   · intro a s has hsum
-    rw [Finset.bunionᵢ_insert, Finset.sum_insert has]
+    rw [Finset.biUnion_insert, Finset.sum_insert has]
     refine'
       Finset.Subset.trans (vars_add_subset _ _) (Finset.union_subset_union (Finset.Subset.refl _) _)
     assumption
@@ -613,22 +613,22 @@ theorem vars_sum_subset : (∑ i in t, φ i).vars ⊆ Finset.bunionᵢ t fun i =
 
 /- warning: mv_polynomial.vars_sum_of_disjoint -> MvPolynomial.vars_sum_of_disjoint is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (t : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), (Pairwise.{u3} ι (Function.onFun.{succ u3, succ u2, 1} ι (Finset.{u2} σ) Prop (Disjoint.{u2} (Finset.{u2} σ) (Finset.partialOrder.{u2} σ) (Finset.orderBot.{u2} σ)) (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i)))) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) t (fun (i : ι) => φ i))) (Finset.bunionᵢ.{u3, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i))))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (t : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), (Pairwise.{u3} ι (Function.onFun.{succ u3, succ u2, 1} ι (Finset.{u2} σ) Prop (Disjoint.{u2} (Finset.{u2} σ) (Finset.partialOrder.{u2} σ) (Finset.orderBot.{u2} σ)) (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i)))) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u3, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i))))
 but is expected to have type
-  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (t : Finset.{u2} ι) (φ : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Finset.{u1} σ) Prop (Disjoint.{u1} (Finset.{u1} σ) (Finset.partialOrder.{u1} σ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} σ)) (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (φ i)))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u3, u1} R σ _inst_1 (Finset.sum.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (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))))) t (fun (i : ι) => φ i))) (Finset.bunionᵢ.{u2, u1} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (φ i))))
+  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (t : Finset.{u2} ι) (φ : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Finset.{u1} σ) Prop (Disjoint.{u1} (Finset.{u1} σ) (Finset.partialOrder.{u1} σ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} σ)) (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (φ i)))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u3, u1} R σ _inst_1 (Finset.sum.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (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))))) t (fun (i : ι) => φ i))) (Finset.biUnion.{u2, u1} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (φ i))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_sum_of_disjoint MvPolynomial.vars_sum_of_disjointₓ'. -/
 theorem vars_sum_of_disjoint (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
-    (∑ i in t, φ i).vars = Finset.bunionᵢ t fun i => (φ i).vars :=
+    (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars :=
   by
   apply t.induction_on
   · simp
   · intro a s has hsum
-    rw [Finset.bunionᵢ_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
+    rw [Finset.biUnion_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
     unfold Pairwise on_fun at h
     rw [hsum]
     simp only [Finset.disjoint_iff_ne] at h⊢
     intro v hv v2 hv2
-    rw [Finset.mem_bunionᵢ] at hv2
+    rw [Finset.mem_biUnion] at hv2
     rcases hv2 with ⟨i, his, hi⟩
     refine' h _ _ hv _ hi
     rintro rfl
@@ -675,17 +675,17 @@ theorem vars_monomial_single (i : σ) {e : ℕ} {r : R} (he : e ≠ 0) (hr : r 
   rw [vars_monomial hr, Finsupp.support_single_ne_zero _ he]
 #align mv_polynomial.vars_monomial_single MvPolynomial.vars_monomial_single
 
-/- warning: mv_polynomial.vars_eq_support_bUnion_support -> MvPolynomial.vars_eq_support_bunionᵢ_support is a dubious translation:
+/- warning: mv_polynomial.vars_eq_support_bUnion_support -> MvPolynomial.vars_eq_support_biUnion_support is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (Finset.bunionᵢ.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) (MvPolynomial.support.{u1, u2} R σ _inst_1 p) (Finsupp.support.{u2, 0} σ Nat Nat.hasZero))
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (Finset.biUnion.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) (MvPolynomial.support.{u1, u2} R σ _inst_1 p) (Finsupp.support.{u2, 0} σ Nat Nat.hasZero))
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (Finset.bunionᵢ.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) (MvPolynomial.support.{u2, u1} R σ _inst_1 p) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_bunionᵢ_supportₓ'. -/
-theorem vars_eq_support_bunionᵢ_support : p.vars = p.support.bunionᵢ Finsupp.support :=
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (Finset.biUnion.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) (MvPolynomial.support.{u2, u1} R σ _inst_1 p) (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_biUnion_supportₓ'. -/
+theorem vars_eq_support_biUnion_support : p.vars = p.support.biUnion Finsupp.support :=
   by
   ext i
-  rw [mem_vars, Finset.mem_bunionᵢ]
-#align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_bunionᵢ_support
+  rw [mem_vars, Finset.mem_biUnion]
+#align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_biUnion_support
 
 end Map
 
@@ -1008,7 +1008,7 @@ theorem totalDegree_mul (a b : MvPolynomial σ R) :
     (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
   Finset.sup_le fun n hn => by
     have := AddMonoidAlgebra.support_mul a b hn
-    simp only [Finset.mem_bunionᵢ, Finset.mem_singleton] at this
+    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
     rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
     rw [Finsupp.sum_add_index']
     · exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)

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

@@ -574,7 +574,7 @@ variable {A : Type _} [CommRing A] [IsDomain A]
 lean 3 declaration is
   forall {σ : Type.{u1}} {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (a : A), (Ne.{succ u2} A a (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))))) -> (forall (φ : MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (instHMul.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))))))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) (fun (_x : RingHom.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) => A -> (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.hasCoeToFun.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) (MvPolynomial.C.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)) a) φ)) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) φ))
 but is expected to have type
-  forall {σ : Type.{u1}} {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (a : A), (Ne.{succ u2} A a (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) _inst_3)))))) -> (forall (φ : MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) (HMul.hMul.{max u2 u1, max u1 u2, max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (Semiring.toNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (CommSemiring.toSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))))))) (MvPolynomial.C.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)) a) φ)) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) φ))
+  forall {σ : Type.{u1}} {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] (a : A), (Ne.{succ u2} A a (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) _inst_3)))))) -> (forall (φ : MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) (HMul.hMul.{max u2 u1, max u1 u2, max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (Semiring.toNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (CommSemiring.toSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))))))) (MvPolynomial.C.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)) a) φ)) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) φ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_C_mul MvPolynomial.vars_C_mulₓ'. -/
 theorem vars_C_mul (a : A) (ha : a ≠ 0) (φ : MvPolynomial σ A) : (C a * φ).vars = φ.vars :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/3905fa80e62c0898131285baab35559fbc4e5cda

@@ -1022,7 +1022,7 @@ theorem totalDegree_mul (a b : MvPolynomial σ R) :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : DistribMulAction.{u1, u2} R S (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))] (a : R) (f : MvPolynomial.{u3, u2} σ S _inst_2), LE.le.{0} Nat Nat.hasLe (MvPolynomial.totalDegree.{u2, u3} S σ _inst_2 (SMul.smul.{u1, max u3 u2} R (MvPolynomial.{u3, u2} σ S _inst_2) (SMulZeroClass.toHasSmul.{u1, max u3 u2} R (MvPolynomial.{u3, u2} σ S _inst_2) (MulZeroClass.toHasZero.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))))) (MvPolynomial.smulZeroClass.{u1, u2, u3} R S σ _inst_2 (DistribSMul.toSmulZeroClass.{u1, u2} R S (AddMonoid.toAddZeroClass.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u1, u2} R S (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) _inst_3)))) a f)) (MvPolynomial.totalDegree.{u2, u3} S σ _inst_2 f)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : DistribMulAction.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))] (a : R) (f : MvPolynomial.{u1, u3} σ S _inst_2), LE.le.{0} Nat instLENat (MvPolynomial.totalDegree.{u3, u1} S σ _inst_2 (HSMul.hSMul.{u2, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u3} σ S _inst_2) (instHSMul.{u2, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (SMulZeroClass.toSMul.{u2, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (CommMonoidWithZero.toZero.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toCommMonoidWithZero.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (DistribSMul.toSMulZeroClass.{u2, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (AddMonoid.toAddZeroClass.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (AddMonoidWithOne.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{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))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{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)))))) (MvPolynomial.distribuMulAction.{u2, u3, u1} R S σ (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) _inst_2 _inst_3))))) a f)) (MvPolynomial.totalDegree.{u3, u1} S σ _inst_2 f)
+  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : DistribMulAction.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))] (a : R) (f : MvPolynomial.{u1, u3} σ S _inst_2), LE.le.{0} Nat instLENat (MvPolynomial.totalDegree.{u3, u1} S σ _inst_2 (HSMul.hSMul.{u2, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u3} σ S _inst_2) (instHSMul.{u2, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (SMulZeroClass.toSMul.{u2, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (CommMonoidWithZero.toZero.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toCommMonoidWithZero.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (MvPolynomial.smulZeroClass.{u2, u3, u1} R S σ _inst_2 (DistribSMul.toSMulZeroClass.{u2, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddMonoidWithOne.toAddMonoid.{u3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))))) _inst_3))))) a f)) (MvPolynomial.totalDegree.{u3, u1} S σ _inst_2 f)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_smul_le MvPolynomial.totalDegree_smul_leₓ'. -/
 theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f : MvPolynomial σ S) :
     (a • f).totalDegree ≤ f.totalDegree :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa

@@ -1020,7 +1020,7 @@ theorem totalDegree_mul (a b : MvPolynomial σ R) :
 
 /- warning: mv_polynomial.total_degree_smul_le -> MvPolynomial.totalDegree_smul_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : DistribMulAction.{u1, u2} R S (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))] (a : R) (f : MvPolynomial.{u3, u2} σ S _inst_2), LE.le.{0} Nat Nat.hasLe (MvPolynomial.totalDegree.{u2, u3} S σ _inst_2 (SMul.smul.{u1, max u3 u2} R (MvPolynomial.{u3, u2} σ S _inst_2) (SMulZeroClass.toHasSmul.{u1, max u3 u2} R (MvPolynomial.{u3, u2} σ S _inst_2) (AddZeroClass.toHasZero.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (AddMonoidWithOne.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))))))) (DistribSMul.toSmulZeroClass.{u1, max u3 u2} R (MvPolynomial.{u3, u2} σ S _inst_2) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (AddMonoidWithOne.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2))))))) (DistribMulAction.toDistribSMul.{u1, max u3 u2} R (MvPolynomial.{u3, u2} σ S _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))))) (MvPolynomial.distribMulAction.{u1, u2, u3} R S σ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_2 _inst_3)))) a f)) (MvPolynomial.totalDegree.{u2, u3} S σ _inst_2 f)
+  forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : DistribMulAction.{u1, u2} R S (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))] (a : R) (f : MvPolynomial.{u3, u2} σ S _inst_2), LE.le.{0} Nat Nat.hasLe (MvPolynomial.totalDegree.{u2, u3} S σ _inst_2 (SMul.smul.{u1, max u3 u2} R (MvPolynomial.{u3, u2} σ S _inst_2) (SMulZeroClass.toHasSmul.{u1, max u3 u2} R (MvPolynomial.{u3, u2} σ S _inst_2) (MulZeroClass.toHasZero.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))))) (MvPolynomial.smulZeroClass.{u1, u2, u3} R S σ _inst_2 (DistribSMul.toSmulZeroClass.{u1, u2} R S (AddMonoid.toAddZeroClass.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u1, u2} R S (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) _inst_3)))) a f)) (MvPolynomial.totalDegree.{u2, u3} S σ _inst_2 f)
 but is expected to have type
   forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] [_inst_3 : DistribMulAction.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))] (a : R) (f : MvPolynomial.{u1, u3} σ S _inst_2), LE.le.{0} Nat instLENat (MvPolynomial.totalDegree.{u3, u1} S σ _inst_2 (HSMul.hSMul.{u2, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u3} σ S _inst_2) (instHSMul.{u2, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (SMulZeroClass.toSMul.{u2, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (CommMonoidWithZero.toZero.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toCommMonoidWithZero.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (DistribSMul.toSMulZeroClass.{u2, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (AddMonoid.toAddZeroClass.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (AddMonoidWithOne.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{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))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u1} R (MvPolynomial.{u1, u3} σ S _inst_2) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{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)))))) (MvPolynomial.distribuMulAction.{u2, u3, u1} R S σ (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) _inst_2 _inst_3))))) a f)) (MvPolynomial.totalDegree.{u3, u1} S σ _inst_2 f)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_smul_le MvPolynomial.totalDegree_smul_leₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ec294687917cbc5c73620b4414ae9b5dd9ae1b4

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.variables
-! leanprover-community/mathlib commit 5120cf49cb659e2499edd7e4d336a04efd598f2f
+! leanprover-community/mathlib commit 1dac236edca9b4b6f5f00b1ad831e35f89472837
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Data.MvPolynomial.Rename
 /-!
 # Degrees and variables of polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file establishes many results about the degree and variable sets of a multivariate polynomial.
 
 The *variable set* of a polynomial $P \in R[X]$ is a `finset` containing each $x \in X$

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

@@ -84,6 +84,7 @@ section Degrees
 /-! ### `degrees` -/
 
 
+#print MvPolynomial.degrees /-
 /-- The maximal degrees of each variable in a multi-variable polynomial, expressed as a multiset.
 
 (For example, `degrees (x^2 * y + y^3)` would be `{x, x, y, y, y}`.)
@@ -91,7 +92,14 @@ section Degrees
 def degrees (p : MvPolynomial σ R) : Multiset σ :=
   p.support.sup fun s : σ →₀ ℕ => s.toMultiset
 #align mv_polynomial.degrees MvPolynomial.degrees
+-/
 
+/- warning: mv_polynomial.degrees_monomial -> MvPolynomial.degrees_monomial 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.degrees_monomial MvPolynomial.degrees_monomialₓ'. -/
 theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ s.toMultiset :=
   Finset.sup_le fun t h => by
     have := Finsupp.support_single_subset h
@@ -99,25 +107,55 @@ theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) 
     rw [this]
 #align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomial
 
+/- warning: mv_polynomial.degrees_monomial_eq -> MvPolynomial.degrees_monomial_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eqₓ'. -/
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
     degrees (monomial s a) = s.toMultiset :=
   le_antisymm (degrees_monomial s a) <|
     Finset.le_sup <| by rw [support_monomial, if_neg ha, Finset.mem_singleton]
 #align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eq
 
-theorem degrees_c (a : R) : degrees (C a : MvPolynomial σ R) = 0 :=
+/- warning: mv_polynomial.degrees_C -> MvPolynomial.degrees_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_C MvPolynomial.degrees_Cₓ'. -/
+theorem degrees_C (a : R) : degrees (C a : MvPolynomial σ R) = 0 :=
   Multiset.le_zero.1 <| degrees_monomial _ _
-#align mv_polynomial.degrees_C MvPolynomial.degrees_c
-
+#align mv_polynomial.degrees_C MvPolynomial.degrees_C
+
+/- warning: mv_polynomial.degrees_X' -> MvPolynomial.degrees_X' 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.degrees_X' MvPolynomial.degrees_X'ₓ'. -/
 theorem degrees_X' (n : σ) : degrees (X n : MvPolynomial σ R) ≤ {n} :=
   le_trans (degrees_monomial _ _) <| le_of_eq <| toMultiset_single _ _
 #align mv_polynomial.degrees_X' MvPolynomial.degrees_X'
 
+/- warning: mv_polynomial.degrees_X -> MvPolynomial.degrees_X 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.degrees_X MvPolynomial.degrees_Xₓ'. -/
 @[simp]
-theorem degrees_x [Nontrivial R] (n : σ) : degrees (X n : MvPolynomial σ R) = {n} :=
+theorem degrees_X [Nontrivial R] (n : σ) : degrees (X n : MvPolynomial σ R) = {n} :=
   (degrees_monomial_eq _ (1 : R) one_ne_zero).trans (toMultiset_single _ _)
-#align mv_polynomial.degrees_X MvPolynomial.degrees_x
-
+#align mv_polynomial.degrees_X MvPolynomial.degrees_X
+
+/- warning: mv_polynomial.degrees_zero -> MvPolynomial.degrees_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_zero MvPolynomial.degrees_zeroₓ'. -/
 @[simp]
 theorem degrees_zero : degrees (0 : MvPolynomial σ R) = 0 :=
   by
@@ -125,11 +163,23 @@ theorem degrees_zero : degrees (0 : MvPolynomial σ R) = 0 :=
   exact degrees_C 0
 #align mv_polynomial.degrees_zero MvPolynomial.degrees_zero
 
+/- warning: mv_polynomial.degrees_one -> MvPolynomial.degrees_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_one MvPolynomial.degrees_oneₓ'. -/
 @[simp]
 theorem degrees_one : degrees (1 : MvPolynomial σ R) = 0 :=
-  degrees_c 1
+  degrees_C 1
 #align mv_polynomial.degrees_one MvPolynomial.degrees_one
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_add MvPolynomial.degrees_addₓ'. -/
 theorem degrees_add (p q : MvPolynomial σ R) : (p + q).degrees ≤ p.degrees ⊔ q.degrees :=
   by
   refine' Finset.sup_le fun b hb => _
@@ -139,6 +189,12 @@ theorem degrees_add (p q : MvPolynomial σ R) : (p + q).degrees ≤ p.degrees 
   · exact le_sup_of_le_right (Finset.le_sup this)
 #align mv_polynomial.degrees_add MvPolynomial.degrees_add
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_sum MvPolynomial.degrees_sumₓ'. -/
 theorem degrees_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees :=
   by
@@ -150,6 +206,12 @@ theorem degrees_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R)
     exact le_trans (degrees_add _ _) (sup_le_sup_left ih _)
 #align mv_polynomial.degrees_sum MvPolynomial.degrees_sum
 
+/- warning: mv_polynomial.degrees_mul -> MvPolynomial.degrees_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_mul MvPolynomial.degrees_mulₓ'. -/
 theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees :=
   by
   refine' Finset.sup_le fun b hb => _
@@ -160,6 +222,12 @@ theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees +
   exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
 #align mv_polynomial.degrees_mul MvPolynomial.degrees_mul
 
+/- warning: mv_polynomial.degrees_prod -> MvPolynomial.degrees_prod 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.degrees_prod MvPolynomial.degrees_prodₓ'. -/
 theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees :=
   by
@@ -170,6 +238,12 @@ theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R
     exact le_trans (degrees_mul _ _) (add_le_add_left ih _)
 #align mv_polynomial.degrees_prod MvPolynomial.degrees_prod
 
+/- warning: mv_polynomial.degrees_pow -> MvPolynomial.degrees_pow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_pow MvPolynomial.degrees_powₓ'. -/
 theorem degrees_pow (p : MvPolynomial σ R) : ∀ n : ℕ, (p ^ n).degrees ≤ n • p.degrees
   | 0 => by rw [pow_zero, degrees_one]; exact Multiset.zero_le _
   | n + 1 => by
@@ -177,11 +251,23 @@ theorem degrees_pow (p : MvPolynomial σ R) : ∀ n : ℕ, (p ^ n).degrees ≤ n
     exact le_trans (degrees_mul _ _) (add_le_add_left (degrees_pow n) _)
 #align mv_polynomial.degrees_pow MvPolynomial.degrees_pow
 
+/- warning: mv_polynomial.mem_degrees -> MvPolynomial.mem_degrees 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.mem_degrees MvPolynomial.mem_degreesₓ'. -/
 theorem mem_degrees {p : MvPolynomial σ R} {i : σ} :
     i ∈ p.degrees ↔ ∃ d, p.coeff d ≠ 0 ∧ i ∈ d.support := by
   simp only [degrees, Multiset.mem_sup, ← mem_support_iff, Finsupp.mem_toMultiset, exists_prop]
 #align mv_polynomial.mem_degrees MvPolynomial.mem_degrees
 
+/- warning: mv_polynomial.le_degrees_add -> MvPolynomial.le_degrees_add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_addₓ'. -/
 theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degrees) :
     p.degrees ≤ (p + q).degrees := by
   apply Finset.sup_le
@@ -204,6 +290,12 @@ theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degre
     all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
 #align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_add
 
+/- warning: mv_polynomial.degrees_add_of_disjoint -> MvPolynomial.degrees_add_of_disjoint is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_add_of_disjoint MvPolynomial.degrees_add_of_disjointₓ'. -/
 theorem degrees_add_of_disjoint {p q : MvPolynomial σ R}
     (h : Multiset.Disjoint p.degrees q.degrees) : (p + q).degrees = p.degrees ∪ q.degrees :=
   by
@@ -215,6 +307,12 @@ theorem degrees_add_of_disjoint {p q : MvPolynomial σ R}
       apply le_degrees_add h.symm
 #align mv_polynomial.degrees_add_of_disjoint MvPolynomial.degrees_add_of_disjoint
 
+/- warning: mv_polynomial.degrees_map -> MvPolynomial.degrees_map is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_map MvPolynomial.degrees_mapₓ'. -/
 theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
     (map f p).degrees ⊆ p.degrees := by
   dsimp only [degrees]
@@ -223,6 +321,12 @@ theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
   apply MvPolynomial.support_map_subset
 #align mv_polynomial.degrees_map MvPolynomial.degrees_map
 
+/- warning: mv_polynomial.degrees_rename -> MvPolynomial.degrees_rename is a dubious translation:
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(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))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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))))))) (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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) φ)) (Multiset.map.{u2, u1} σ τ f (MvPolynomial.degrees.{u3, u2} R σ _inst_1 φ))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_rename MvPolynomial.degrees_renameₓ'. -/
 theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).degrees ⊆ φ.degrees.map f := by
   intro i
@@ -239,11 +343,23 @@ theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
   rw [single_apply, if_neg hi]
 #align mv_polynomial.degrees_rename MvPolynomial.degrees_rename
 
+/- warning: mv_polynomial.degrees_map_of_injective -> MvPolynomial.degrees_map_of_injective is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_map_of_injective MvPolynomial.degrees_map_of_injectiveₓ'. -/
 theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R →+* S}
     (hf : Injective f) : (map f p).degrees = p.degrees := by
   simp only [degrees, MvPolynomial.support_map_of_injective _ hf]
 #align mv_polynomial.degrees_map_of_injective MvPolynomial.degrees_map_of_injective
 
+/- warning: mv_polynomial.degrees_rename_of_injective -> MvPolynomial.degrees_rename_of_injective is a dubious translation:
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(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))))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u2, u3} σ 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))))))) (DistribMulAction.toDistribSMul.{u3, max u2 u3} R (MvPolynomial.{u2, u3} σ 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)))))) (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))))))) (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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) p)) (Multiset.map.{u2, u1} σ τ f (MvPolynomial.degrees.{u3, u2} R σ _inst_1 p)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degrees_rename_of_injective MvPolynomial.degrees_rename_of_injectiveₓ'. -/
 theorem degrees_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f) :
     degrees (rename f p) = (degrees p).map f :=
   by
@@ -260,35 +376,73 @@ section Vars
 /-! ### `vars` -/
 
 
+#print MvPolynomial.vars /-
 /-- `vars p` is the set of variables appearing in the polynomial `p` -/
 def vars (p : MvPolynomial σ R) : Finset σ :=
   p.degrees.toFinset
 #align mv_polynomial.vars MvPolynomial.vars
+-/
 
+/- warning: mv_polynomial.vars_0 -> MvPolynomial.vars_0 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.vars_0 MvPolynomial.vars_0ₓ'. -/
 @[simp]
 theorem vars_0 : (0 : MvPolynomial σ R).vars = ∅ := by
   rw [vars, degrees_zero, Multiset.toFinset_zero]
 #align mv_polynomial.vars_0 MvPolynomial.vars_0
 
+/- warning: mv_polynomial.vars_monomial -> MvPolynomial.vars_monomial is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_monomial MvPolynomial.vars_monomialₓ'. -/
 @[simp]
 theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by
   rw [vars, degrees_monomial_eq _ _ h, Finsupp.toFinset_toMultiset]
 #align mv_polynomial.vars_monomial MvPolynomial.vars_monomial
 
+/- warning: mv_polynomial.vars_C -> MvPolynomial.vars_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.vars_C MvPolynomial.vars_Cₓ'. -/
 @[simp]
-theorem vars_c : (C r : MvPolynomial σ R).vars = ∅ := by
+theorem vars_C : (C r : MvPolynomial σ R).vars = ∅ := by
   rw [vars, degrees_C, Multiset.toFinset_zero]
-#align mv_polynomial.vars_C MvPolynomial.vars_c
-
+#align mv_polynomial.vars_C MvPolynomial.vars_C
+
+/- warning: mv_polynomial.vars_X -> MvPolynomial.vars_X is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} {n : σ} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (MvPolynomial.X.{u1, u2} R σ _inst_1 n)) (Singleton.singleton.{u2, u2} σ (Finset.{u2} σ) (Finset.hasSingleton.{u2} σ) n)
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} {n : σ} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Nontrivial.{u2} R], Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (MvPolynomial.X.{u2, u1} R σ _inst_1 n)) (Singleton.singleton.{u1, u1} σ (Finset.{u1} σ) (Finset.instSingletonFinset.{u1} σ) n)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_X MvPolynomial.vars_Xₓ'. -/
 @[simp]
-theorem vars_x [Nontrivial R] : (X n : MvPolynomial σ R).vars = {n} := by
+theorem vars_X [Nontrivial R] : (X n : MvPolynomial σ R).vars = {n} := by
   rw [X, vars_monomial (one_ne_zero' R), Finsupp.support_single_ne_zero _ (one_ne_zero' ℕ)]
-#align mv_polynomial.vars_X MvPolynomial.vars_x
-
+#align mv_polynomial.vars_X MvPolynomial.vars_X
+
+/- warning: mv_polynomial.mem_vars -> MvPolynomial.mem_vars is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {p : MvPolynomial.{u2, u1} σ R _inst_1} (i : σ), Iff (Membership.Mem.{u2, u2} σ (Finset.{u2} σ) (Finset.hasMem.{u2} σ) i (MvPolynomial.vars.{u1, u2} R σ _inst_1 p)) (Exists.{succ u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (fun (d : Finsupp.{u2, 0} σ Nat Nat.hasZero) => Exists.{0} (Membership.Mem.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Finset.{u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero)) (Finset.hasMem.{u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero)) d (MvPolynomial.support.{u1, u2} R σ _inst_1 p)) (fun (H : Membership.Mem.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Finset.{u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero)) (Finset.hasMem.{u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero)) d (MvPolynomial.support.{u1, u2} R σ _inst_1 p)) => Membership.Mem.{u2, u2} σ (Finset.{u2} σ) (Finset.hasMem.{u2} σ) i (Finsupp.support.{u2, 0} σ Nat Nat.hasZero d))))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {p : MvPolynomial.{u1, u2} σ R _inst_1} (i : σ), Iff (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (MvPolynomial.vars.{u2, u1} R σ _inst_1 p)) (Exists.{succ u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (d : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Exists.{0} (Membership.mem.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finset.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finset.instMembershipFinset.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) d (MvPolynomial.support.{u2, u1} R σ _inst_1 p)) (fun (H : Membership.mem.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finset.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finset.instMembershipFinset.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) d (MvPolynomial.support.{u2, u1} R σ _inst_1 p)) => Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) i (Finsupp.support.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d))))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_vars MvPolynomial.mem_varsₓ'. -/
 theorem mem_vars (i : σ) : i ∈ p.vars ↔ ∃ (d : σ →₀ ℕ)(H : d ∈ p.support), i ∈ d.support := by
   simp only [vars, Multiset.mem_toFinset, mem_degrees, mem_support_iff, exists_prop]
 #align mv_polynomial.mem_vars MvPolynomial.mem_vars
 
+/- warning: mv_polynomial.mem_support_not_mem_vars_zero -> MvPolynomial.mem_support_not_mem_vars_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {f : MvPolynomial.{u2, u1} σ R _inst_1} {x : Finsupp.{u2, 0} σ Nat Nat.hasZero}, (Membership.Mem.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Finset.{u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero)) (Finset.hasMem.{u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero)) x (MvPolynomial.support.{u1, u2} R σ _inst_1 f)) -> (forall {v : σ}, (Not (Membership.Mem.{u2, u2} σ (Finset.{u2} σ) (Finset.hasMem.{u2} σ) v (MvPolynomial.vars.{u1, u2} R σ _inst_1 f))) -> (Eq.{1} Nat (coeFn.{succ u2, succ u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u2, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u2, 0} σ Nat Nat.hasZero) x v) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {f : MvPolynomial.{u1, u2} σ R _inst_1} {x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)}, (Membership.mem.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finset.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finset.instMembershipFinset.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) x (MvPolynomial.support.{u2, u1} R σ _inst_1 f)) -> (forall {v : σ}, (Not (Membership.mem.{u1, u1} σ (Finset.{u1} σ) (Finset.instMembershipFinset.{u1} σ) v (MvPolynomial.vars.{u2, u1} R σ _inst_1 f))) -> (Eq.{1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) v) (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)) x v) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) v) 0 (instOfNatNat 0))))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_support_not_mem_vars_zero MvPolynomial.mem_support_not_mem_vars_zeroₓ'. -/
 theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ} (H : x ∈ f.support)
     {v : σ} (h : v ∉ vars f) : x v = 0 :=
   by
@@ -303,6 +457,12 @@ theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ
   rwa [← to_finset_to_multiset, Multiset.mem_toFinset] at h
 #align mv_polynomial.mem_support_not_mem_vars_zero MvPolynomial.mem_support_not_mem_vars_zero
 
+/- warning: mv_polynomial.vars_add_subset -> MvPolynomial.vars_add_subset is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u2, u1} σ R _inst_1) (q : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Union.union.{u2} (Finset.{u2} σ) (Finset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b))) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (MvPolynomial.vars.{u1, u2} R σ _inst_1 q))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) (q : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (MvPolynomial.vars.{u2, u1} R σ _inst_1 q))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_add_subset MvPolynomial.vars_add_subsetₓ'. -/
 theorem vars_add_subset (p q : MvPolynomial σ R) : (p + q).vars ⊆ p.vars ∪ q.vars :=
   by
   intro x hx
@@ -310,6 +470,12 @@ theorem vars_add_subset (p q : MvPolynomial σ R) : (p + q).vars ⊆ p.vars ∪
   simpa using Multiset.mem_of_le (degrees_add _ _) hx
 #align mv_polynomial.vars_add_subset MvPolynomial.vars_add_subset
 
+/- warning: mv_polynomial.vars_add_of_disjoint -> MvPolynomial.vars_add_of_disjoint is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {p : MvPolynomial.{u2, u1} σ R _inst_1} {q : MvPolynomial.{u2, u1} σ R _inst_1}, (Disjoint.{u2} (Finset.{u2} σ) (Finset.partialOrder.{u2} σ) (Finset.orderBot.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (MvPolynomial.vars.{u1, u2} R σ _inst_1 q)) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (Union.union.{u2} (Finset.{u2} σ) (Finset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b))) (MvPolynomial.vars.{u1, u2} R σ _inst_1 p) (MvPolynomial.vars.{u1, u2} R σ _inst_1 q)))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {p : MvPolynomial.{u1, u2} σ R _inst_1} {q : MvPolynomial.{u1, u2} σ R _inst_1}, (Disjoint.{u1} (Finset.{u1} σ) (Finset.partialOrder.{u1} σ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (MvPolynomial.vars.{u2, u1} R σ _inst_1 q)) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p) (MvPolynomial.vars.{u2, u1} R σ _inst_1 q)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_add_of_disjoint MvPolynomial.vars_add_of_disjointₓ'. -/
 theorem vars_add_of_disjoint (h : Disjoint p.vars q.vars) : (p + q).vars = p.vars ∪ q.vars :=
   by
   apply Finset.Subset.antisymm (vars_add_subset p q)
@@ -321,6 +487,12 @@ theorem vars_add_of_disjoint (h : Disjoint p.vars q.vars) : (p + q).vars = p.var
 
 section Mul
 
+/- warning: mv_polynomial.vars_mul -> MvPolynomial.vars_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (φ : MvPolynomial.{u2, u1} σ R _inst_1) (ψ : MvPolynomial.{u2, u1} σ R _inst_1), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) φ ψ)) (Union.union.{u2} (Finset.{u2} σ) (Finset.hasUnion.{u2} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b))) (MvPolynomial.vars.{u1, u2} R σ _inst_1 φ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 ψ))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{u1, u2} σ R _inst_1) (ψ : MvPolynomial.{u1, u2} σ R _inst_1), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{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)))))) φ ψ)) (Union.union.{u1} (Finset.{u1} σ) (Finset.instUnionFinset.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b))) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 ψ))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_mul MvPolynomial.vars_mulₓ'. -/
 theorem vars_mul (φ ψ : MvPolynomial σ R) : (φ * ψ).vars ⊆ φ.vars ∪ ψ.vars :=
   by
   intro i
@@ -345,11 +517,23 @@ theorem vars_mul (φ ψ : MvPolynomial σ R) : (φ * ψ).vars ⊆ φ.vars ∪ ψ
     solve_by_elim
 #align mv_polynomial.vars_mul MvPolynomial.vars_mul
 
+/- warning: mv_polynomial.vars_one -> MvPolynomial.vars_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R], Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 1 (OfNat.mk.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 1 (One.one.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{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)))))))))) (EmptyCollection.emptyCollection.{u2} (Finset.{u2} σ) (Finset.hasEmptyc.{u2} σ))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R], Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) 1 (One.toOfNat1.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toOne.{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)))))) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} σ) (Finset.instEmptyCollectionFinset.{u1} σ))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_one MvPolynomial.vars_oneₓ'. -/
 @[simp]
 theorem vars_one : (1 : MvPolynomial σ R).vars = ∅ :=
-  vars_c
+  vars_C
 #align mv_polynomial.vars_one MvPolynomial.vars_one
 
+/- warning: mv_polynomial.vars_pow -> MvPolynomial.vars_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (φ : MvPolynomial.{u2, u1} σ R _inst_1) (n : Nat), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (MvPolynomial.{u2, u1} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (Monoid.Pow.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toMonoidWithZero.{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)))))) φ n)) (MvPolynomial.vars.{u1, u2} R σ _inst_1 φ)
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{u1, u2} σ R _inst_1) (n : Nat), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u2, u1} R σ _inst_1 (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (Monoid.Pow.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toMonoidWithZero.{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)))))) φ n)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 φ)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_pow MvPolynomial.vars_powₓ'. -/
 theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars :=
   by
   induction' n with n ih
@@ -359,6 +543,12 @@ theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars
     exact Finset.union_subset (Finset.Subset.refl _) ih
 #align mv_polynomial.vars_pow MvPolynomial.vars_pow
 
+/- warning: mv_polynomial.vars_prod -> MvPolynomial.vars_prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} {s : Finset.{u3} ι} (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.prod.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.bunionᵢ.{u3, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) s (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (f i)))
+but is expected to have type
+  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} {s : Finset.{u2} ι} (f : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u3, u1} R σ _inst_1 (Finset.prod.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) s (fun (i : ι) => f i))) (Finset.bunionᵢ.{u2, u1} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) s (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (f i)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_prod MvPolynomial.vars_prodₓ'. -/
 /-- The variables of the product of a family of polynomials
 are a subset of the union of the sets of variables of each polynomial.
 -/
@@ -377,7 +567,13 @@ section IsDomain
 
 variable {A : Type _} [CommRing A] [IsDomain A]
 
-theorem vars_c_mul (a : A) (ha : a ≠ 0) (φ : MvPolynomial σ A) : (C a * φ).vars = φ.vars :=
+/- warning: mv_polynomial.vars_C_mul -> MvPolynomial.vars_C_mul is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (a : A), (Ne.{succ u2} A a (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))))) -> (forall (φ : MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (instHMul.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))))))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) (fun (_x : RingHom.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) => A -> (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.hasCoeToFun.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) (MvPolynomial.C.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)) a) φ)) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) φ))
+but is expected to have type
+  forall {σ : Type.{u1}} {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (a : A), (Ne.{succ u2} A a (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) _inst_3)))))) -> (forall (φ : MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)), Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) (HMul.hMul.{max u2 u1, max u1 u2, max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) a) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => 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A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u2 u1} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2))))) A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} A (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.commSemiring.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)))))))) (MvPolynomial.C.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2)) a) φ)) (MvPolynomial.vars.{u2, u1} A σ (CommRing.toCommSemiring.{u2} A _inst_2) φ))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_C_mul MvPolynomial.vars_C_mulₓ'. -/
+theorem vars_C_mul (a : A) (ha : a ≠ 0) (φ : MvPolynomial σ A) : (C a * φ).vars = φ.vars :=
   by
   ext1 i
   simp only [mem_vars, exists_prop, mem_support_iff]
@@ -385,7 +581,7 @@ theorem vars_c_mul (a : A) (ha : a ≠ 0) (φ : MvPolynomial σ A) : (C a * φ).
   intro d
   apply and_congr _ Iff.rfl
   rw [coeff_C_mul, mul_ne_zero_iff, eq_true ha, true_and_iff]
-#align mv_polynomial.vars_C_mul MvPolynomial.vars_c_mul
+#align mv_polynomial.vars_C_mul MvPolynomial.vars_C_mul
 
 end IsDomain
 
@@ -395,6 +591,12 @@ section Sum
 
 variable {ι : Type _} (t : Finset ι) (φ : ι → MvPolynomial σ R)
 
+/- warning: mv_polynomial.vars_sum_subset -> MvPolynomial.vars_sum_subset is a dubious translation:
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+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (t : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.hasSubset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) t (fun (i : ι) => φ i))) (Finset.bunionᵢ.{u3, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i)))
+but is expected to have type
+  forall {R : Type.{u3}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u1}} (t : Finset.{u1} ι) (φ : ι -> (MvPolynomial.{u2, u3} σ R _inst_1)), HasSubset.Subset.{u2} (Finset.{u2} σ) (Finset.instHasSubsetFinset.{u2} σ) (MvPolynomial.vars.{u3, u2} R σ _inst_1 (Finset.sum.{max u3 u2, u1} (MvPolynomial.{u2, u3} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1))))) t (fun (i : ι) => φ i))) (Finset.bunionᵢ.{u1, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u3, u2} R σ _inst_1 (φ i)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subsetₓ'. -/
 theorem vars_sum_subset : (∑ i in t, φ i).vars ⊆ Finset.bunionᵢ t fun i => (φ i).vars :=
   by
   apply t.induction_on
@@ -406,6 +608,12 @@ theorem vars_sum_subset : (∑ i in t, φ i).vars ⊆ Finset.bunionᵢ t fun i =
     assumption
 #align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subset
 
+/- warning: mv_polynomial.vars_sum_of_disjoint -> MvPolynomial.vars_sum_of_disjoint is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (t : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), (Pairwise.{u3} ι (Function.onFun.{succ u3, succ u2, 1} ι (Finset.{u2} σ) Prop (Disjoint.{u2} (Finset.{u2} σ) (Finset.partialOrder.{u2} σ) (Finset.orderBot.{u2} σ)) (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i)))) -> (Eq.{succ u2} (Finset.{u2} σ) (MvPolynomial.vars.{u1, u2} R σ _inst_1 (Finset.sum.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (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))))) t (fun (i : ι) => φ i))) (Finset.bunionᵢ.{u3, u2} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u2} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u1, u2} R σ _inst_1 (φ i))))
+but is expected to have type
+  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (t : Finset.{u2} ι) (φ : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Finset.{u1} σ) Prop (Disjoint.{u1} (Finset.{u1} σ) (Finset.partialOrder.{u1} σ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} σ)) (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (φ i)))) -> (Eq.{succ u1} (Finset.{u1} σ) (MvPolynomial.vars.{u3, u1} R σ _inst_1 (Finset.sum.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (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))))) t (fun (i : ι) => φ i))) (Finset.bunionᵢ.{u2, u1} ι σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) t (fun (i : ι) => MvPolynomial.vars.{u3, u1} R σ _inst_1 (φ i))))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_sum_of_disjoint MvPolynomial.vars_sum_of_disjointₓ'. -/
 theorem vars_sum_of_disjoint (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
     (∑ i in t, φ i).vars = Finset.bunionᵢ t fun i => (φ i).vars :=
   by
@@ -432,20 +640,44 @@ variable [CommSemiring S] (f : R →+* S)
 
 variable (p)
 
+/- warning: mv_polynomial.vars_map -> MvPolynomial.vars_map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] (p : MvPolynomial.{u3, u1} σ R _inst_1) [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), HasSubset.Subset.{u3} (Finset.{u3} σ) (Finset.hasSubset.{u3} σ) (MvPolynomial.vars.{u2, u3} S σ _inst_2 (coeFn.{max (succ (max u3 u1)) (succ (max u3 u2)), max (succ (max u3 u1)) (succ (max u3 u2))} (RingHom.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) (fun (_x : RingHom.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> (MvPolynomial.{u3, u2} σ S _inst_2)) (RingHom.hasCoeToFun.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u3} S σ _inst_2)))) (MvPolynomial.map.{u1, u2, u3} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.vars.{u1, u3} R σ _inst_1 p)
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (p : MvPolynomial.{u1, u2} σ R _inst_1) [_inst_2 : CommSemiring.{u3} S] (f : 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))), HasSubset.Subset.{u1} (Finset.{u1} σ) (Finset.instHasSubsetFinset.{u1} σ) (MvPolynomial.vars.{u3, u1} S σ _inst_2 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{max u3 u1} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u3 u1} 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S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u2 u1, max u3 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (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.{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.{u2, u3, u1} R S σ _inst_1 _inst_2 f) p)) (MvPolynomial.vars.{u2, u1} R σ _inst_1 p)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_map MvPolynomial.vars_mapₓ'. -/
 theorem vars_map : (map f p).vars ⊆ p.vars := by simp [vars, degrees_map]
 #align mv_polynomial.vars_map MvPolynomial.vars_map
 
 variable {f}
 
+/- warning: mv_polynomial.vars_map_of_injective -> MvPolynomial.vars_map_of_injective is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_map_of_injective MvPolynomial.vars_map_of_injectiveₓ'. -/
 theorem vars_map_of_injective (hf : Injective f) : (map f p).vars = p.vars := by
   simp [vars, degrees_map_of_injective _ hf]
 #align mv_polynomial.vars_map_of_injective MvPolynomial.vars_map_of_injective
 
+/- warning: mv_polynomial.vars_monomial_single -> MvPolynomial.vars_monomial_single is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_monomial_single MvPolynomial.vars_monomial_singleₓ'. -/
 theorem vars_monomial_single (i : σ) {e : ℕ} {r : R} (he : e ≠ 0) (hr : r ≠ 0) :
     (monomial (Finsupp.single i e) r).vars = {i} := by
   rw [vars_monomial hr, Finsupp.support_single_ne_zero _ he]
 #align mv_polynomial.vars_monomial_single MvPolynomial.vars_monomial_single
 
+/- warning: mv_polynomial.vars_eq_support_bUnion_support -> MvPolynomial.vars_eq_support_bunionᵢ_support is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_bunionᵢ_supportₓ'. -/
 theorem vars_eq_support_bunionᵢ_support : p.vars = p.support.bunionᵢ Finsupp.support :=
   by
   ext i
@@ -461,11 +693,19 @@ section DegreeOf
 /-! ### `degree_of` -/
 
 
+#print MvPolynomial.degreeOf /-
 /-- `degree_of n p` gives the highest power of X_n that appears in `p` -/
 def degreeOf (n : σ) (p : MvPolynomial σ R) : ℕ :=
   p.degrees.count n
 #align mv_polynomial.degree_of MvPolynomial.degreeOf
+-/
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_eq_sup MvPolynomial.degreeOf_eq_supₓ'. -/
 theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
     degreeOf n f = f.support.sup fun m => m n :=
   by
@@ -475,29 +715,59 @@ theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
   simp
 #align mv_polynomial.degree_of_eq_sup MvPolynomial.degreeOf_eq_sup
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_lt_iff MvPolynomial.degreeOf_lt_iffₓ'. -/
 theorem degreeOf_lt_iff {n : σ} {f : MvPolynomial σ R} {d : ℕ} (h : 0 < d) :
     degreeOf n f < d ↔ ∀ m : σ →₀ ℕ, m ∈ f.support → m n < d := by
   rwa [degree_of_eq_sup n f, Finset.sup_lt_iff]
 #align mv_polynomial.degree_of_lt_iff MvPolynomial.degreeOf_lt_iff
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_zero MvPolynomial.degreeOf_zeroₓ'. -/
 @[simp]
 theorem degreeOf_zero (n : σ) : degreeOf n (0 : MvPolynomial σ R) = 0 := by
   simp only [degree_of, degrees_zero, Multiset.count_zero]
 #align mv_polynomial.degree_of_zero MvPolynomial.degreeOf_zero
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_C MvPolynomial.degreeOf_Cₓ'. -/
 @[simp]
-theorem degreeOf_c (a : R) (x : σ) : degreeOf x (C a : MvPolynomial σ R) = 0 := by
+theorem degreeOf_C (a : R) (x : σ) : degreeOf x (C a : MvPolynomial σ R) = 0 := by
   simp [degree_of, degrees_C]
-#align mv_polynomial.degree_of_C MvPolynomial.degreeOf_c
-
-theorem degreeOf_x (i j : σ) [Nontrivial R] :
+#align mv_polynomial.degree_of_C MvPolynomial.degreeOf_C
+
+/- warning: mv_polynomial.degree_of_X -> MvPolynomial.degreeOf_X is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (i : σ) (j : σ) [_inst_2 : Nontrivial.{u1} R], Eq.{1} Nat (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 i (MvPolynomial.X.{u1, u2} R σ _inst_1 j)) (ite.{1} Nat (Eq.{succ u2} σ i j) (Classical.propDecidable (Eq.{succ u2} σ i j)) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (i : σ) (j : σ) [_inst_2 : Nontrivial.{u2} R], Eq.{1} Nat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 i (MvPolynomial.X.{u2, u1} R σ _inst_1 j)) (ite.{1} Nat (Eq.{succ u1} σ i j) (Classical.propDecidable (Eq.{succ u1} σ i j)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_X MvPolynomial.degreeOf_Xₓ'. -/
+theorem degreeOf_X (i j : σ) [Nontrivial R] :
     degreeOf i (X j : MvPolynomial σ R) = if i = j then 1 else 0 :=
   by
   by_cases c : i = j
   · simp only [c, if_true, eq_self_iff_true, degree_of, degrees_X, Multiset.count_singleton]
   simp [c, if_false, degree_of, degrees_X]
-#align mv_polynomial.degree_of_X MvPolynomial.degreeOf_x
-
+#align mv_polynomial.degree_of_X MvPolynomial.degreeOf_X
+
+/- warning: mv_polynomial.degree_of_add_le -> MvPolynomial.degreeOf_add_le 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.degree_of_add_le MvPolynomial.degreeOf_add_leₓ'. -/
 theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
     degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) :=
   by
@@ -507,12 +777,24 @@ theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
   rw [Multiset.count_union]
 #align mv_polynomial.degree_of_add_le MvPolynomial.degreeOf_add_le
 
+/- warning: mv_polynomial.monomial_le_degree_of -> MvPolynomial.monomial_le_degreeOf is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (i : σ) {f : MvPolynomial.{u2, u1} σ R _inst_1} {m : Finsupp.{u2, 0} σ Nat Nat.hasZero}, (Membership.Mem.{u2, u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (Finset.{u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero)) (Finset.hasMem.{u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero)) m (MvPolynomial.support.{u1, u2} R σ _inst_1 f)) -> (LE.le.{0} Nat Nat.hasLe (coeFn.{succ u2, succ u2} (Finsupp.{u2, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u2, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u2, 0} σ Nat Nat.hasZero) m i) (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 i f))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (i : σ) {f : MvPolynomial.{u1, u2} σ R _inst_1} {m : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)}, (Membership.mem.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finset.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finset.instMembershipFinset.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) m (MvPolynomial.support.{u2, u1} R σ _inst_1 f)) -> (LE.le.{0} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) i) instLENat (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)) m i) (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 i f))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.monomial_le_degree_of MvPolynomial.monomial_le_degreeOfₓ'. -/
 theorem monomial_le_degreeOf (i : σ) {f : MvPolynomial σ R} {m : σ →₀ ℕ} (h_m : m ∈ f.support) :
     m i ≤ degreeOf i f := by
   rw [degree_of_eq_sup i]
   apply Finset.le_sup h_m
 #align mv_polynomial.monomial_le_degree_of MvPolynomial.monomial_le_degreeOf
 
+/- warning: mv_polynomial.degree_of_mul_le -> MvPolynomial.degreeOf_mul_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (i : σ) (f : MvPolynomial.{u2, u1} σ R _inst_1) (g : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{0} Nat Nat.hasLe (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 i (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) f g)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 i f) (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 i g))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (i : σ) (f : MvPolynomial.{u1, u2} σ R _inst_1) (g : MvPolynomial.{u1, u2} σ R _inst_1), LE.le.{0} Nat instLENat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 i (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{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)))))) f g)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 i f) (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 i g))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_mul_le MvPolynomial.degreeOf_mul_leₓ'. -/
 -- TODO we can prove equality here if R is a domain
 theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
     degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g :=
@@ -522,7 +804,13 @@ theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
   rw [Multiset.count_add]
 #align mv_polynomial.degree_of_mul_le MvPolynomial.degreeOf_mul_le
 
-theorem degreeOf_mul_x_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
+/- warning: mv_polynomial.degree_of_mul_X_ne -> MvPolynomial.degreeOf_mul_X_ne is a dubious translation:
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+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {i : σ} {j : σ} (f : MvPolynomial.{u2, u1} σ R _inst_1), (Ne.{succ u2} σ i j) -> (Eq.{1} Nat (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 i (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) f (MvPolynomial.X.{u1, u2} R σ _inst_1 j))) (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 i f))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {i : σ} {j : σ} (f : MvPolynomial.{u1, u2} σ R _inst_1), (Ne.{succ u1} σ i j) -> (Eq.{1} Nat (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 i (HMul.hMul.{max u2 u1, max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{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)))))) f (MvPolynomial.X.{u2, u1} R σ _inst_1 j))) (MvPolynomial.degreeOf.{u2, u1} R σ _inst_1 i f))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_mul_X_ne MvPolynomial.degreeOf_mul_X_neₓ'. -/
+theorem degreeOf_mul_X_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
     degreeOf i (f * X j) = degreeOf i f :=
   by
   repeat' rw [degree_of_eq_sup i]
@@ -532,10 +820,16 @@ theorem degreeOf_mul_x_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
   ext
   simp only [single, Nat.one_ne_zero, add_right_eq_self, addRightEmbedding_apply, coe_mk,
     Pi.add_apply, comp_app, ite_eq_right_iff, Finsupp.coe_add, Pi.single_eq_of_ne h]
-#align mv_polynomial.degree_of_mul_X_ne MvPolynomial.degreeOf_mul_x_ne
-
+#align mv_polynomial.degree_of_mul_X_ne MvPolynomial.degreeOf_mul_X_ne
+
+/- warning: mv_polynomial.degree_of_mul_X_eq -> MvPolynomial.degreeOf_mul_X_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (j : σ) (f : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{0} Nat Nat.hasLe (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 j (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) f (MvPolynomial.X.{u1, u2} R σ _inst_1 j))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (MvPolynomial.degreeOf.{u1, u2} R σ _inst_1 j f) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eqₓ'. -/
 -- TODO in the following we have equality iff f ≠ 0
-theorem degreeOf_mul_x_eq (j : σ) (f : MvPolynomial σ R) :
+theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
     degreeOf j (f * X j) ≤ degreeOf j f + 1 :=
   by
   repeat' rw [degree_of]
@@ -543,8 +837,14 @@ theorem degreeOf_mul_x_eq (j : σ) (f : MvPolynomial σ R) :
   simp only [Multiset.count_add, add_le_add_iff_left]
   convert Multiset.count_le_of_le j (degrees_X' j)
   rw [Multiset.count_singleton_self]
-#align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_x_eq
-
+#align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eq
+
+/- warning: mv_polynomial.degree_of_rename_of_injective -> MvPolynomial.degreeOf_rename_of_injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_rename_of_injective MvPolynomial.degreeOf_rename_of_injectiveₓ'. -/
 theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
     (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by
   simp only [degree_of, degrees_rename_of_injective h, Multiset.count_map_eq_count' f p.degrees h]
@@ -557,11 +857,19 @@ section TotalDegree
 /-! ### `total_degree` -/
 
 
+#print MvPolynomial.totalDegree /-
 /-- `total_degree p` gives the maximum |s| over the monomials X^s in `p` -/
 def totalDegree (p : MvPolynomial σ R) : ℕ :=
   p.support.sup fun s => s.Sum fun n e => e
 #align mv_polynomial.total_degree MvPolynomial.totalDegree
+-/
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_eq MvPolynomial.totalDegree_eqₓ'. -/
 theorem totalDegree_eq (p : MvPolynomial σ R) :
     p.totalDegree = p.support.sup fun m => m.toMultiset.card :=
   by
@@ -570,40 +878,72 @@ theorem totalDegree_eq (p : MvPolynomial σ R) :
   exact (Finsupp.card_toMultiset _).symm
 #align mv_polynomial.total_degree_eq MvPolynomial.totalDegree_eq
 
+/- warning: mv_polynomial.total_degree_le_degrees_card -> MvPolynomial.totalDegree_le_degrees_card 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.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_cardₓ'. -/
 theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) : p.totalDegree ≤ p.degrees.card :=
   by
   rw [total_degree_eq]
   exact Finset.sup_le fun s hs => Multiset.card_le_of_le <| Finset.le_sup hs
 #align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
 
+/- warning: mv_polynomial.total_degree_C -> MvPolynomial.totalDegree_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_C MvPolynomial.totalDegree_Cₓ'. -/
 @[simp]
-theorem totalDegree_c (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
+theorem totalDegree_C (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
   Nat.eq_zero_of_le_zero <|
     Finset.sup_le fun n hn => by
       have := Finsupp.support_single_subset hn
       rw [Finset.mem_singleton] at this
       subst this
       exact le_rfl
-#align mv_polynomial.total_degree_C MvPolynomial.totalDegree_c
-
+#align mv_polynomial.total_degree_C MvPolynomial.totalDegree_C
+
+/- warning: mv_polynomial.total_degree_zero -> MvPolynomial.totalDegree_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R], Eq.{1} Nat (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 0 (OfNat.mk.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 0 (Zero.zero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MulZeroClass.toHasZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (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)))))))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R], Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (Zero.toOfNat0.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommMonoidWithZero.toZero.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toCommMonoidWithZero.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_zero MvPolynomial.totalDegree_zeroₓ'. -/
 @[simp]
 theorem totalDegree_zero : (0 : MvPolynomial σ R).totalDegree = 0 := by
   rw [← C_0] <;> exact total_degree_C (0 : R)
 #align mv_polynomial.total_degree_zero MvPolynomial.totalDegree_zero
 
+/- warning: mv_polynomial.total_degree_one -> MvPolynomial.totalDegree_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R], Eq.{1} Nat (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 1 (OfNat.mk.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 1 (One.one.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoidWithOne.toOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{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)))))))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R], Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) 1 (One.toOfNat1.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toOne.{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)))))) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_one MvPolynomial.totalDegree_oneₓ'. -/
 @[simp]
 theorem totalDegree_one : (1 : MvPolynomial σ R).totalDegree = 0 :=
-  totalDegree_c (1 : R)
+  totalDegree_C (1 : R)
 #align mv_polynomial.total_degree_one MvPolynomial.totalDegree_one
 
+#print MvPolynomial.totalDegree_X /-
 @[simp]
-theorem totalDegree_x {R} [CommSemiring R] [Nontrivial R] (s : σ) :
+theorem totalDegree_X {R} [CommSemiring R] [Nontrivial R] (s : σ) :
     (X s : MvPolynomial σ R).totalDegree = 1 :=
   by
   rw [total_degree, support_X]
   simp only [Finset.sup, sum_single_index, Finset.fold_singleton, sup_bot_eq]
-#align mv_polynomial.total_degree_X MvPolynomial.totalDegree_x
+#align mv_polynomial.total_degree_X MvPolynomial.totalDegree_X
+-/
 
+/- warning: mv_polynomial.total_degree_add -> MvPolynomial.totalDegree_add is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (a : MvPolynomial.{u2, u1} σ R _inst_1) (b : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{0} Nat Nat.hasLe (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) a b)) (LinearOrder.max.{0} Nat Nat.linearOrder (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 a) (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 b))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (a : MvPolynomial.{u1, u2} σ R _inst_1) (b : MvPolynomial.{u1, u2} σ R _inst_1), LE.le.{0} Nat instLENat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) a b)) (Max.max.{0} Nat Nat.instMaxNat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 a) (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 b))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_add MvPolynomial.totalDegree_addₓ'. -/
 theorem totalDegree_add (a b : MvPolynomial σ R) :
     (a + b).totalDegree ≤ max a.totalDegree b.totalDegree :=
   Finset.sup_le fun n hn => by
@@ -614,6 +954,12 @@ theorem totalDegree_add (a b : MvPolynomial σ R) :
     · exact le_max_of_le_right (Finset.le_sup this)
 #align mv_polynomial.total_degree_add MvPolynomial.totalDegree_add
 
+/- warning: mv_polynomial.total_degree_add_eq_left_of_total_degree_lt -> MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {p : MvPolynomial.{u2, u1} σ R _inst_1} {q : MvPolynomial.{u2, u1} σ R _inst_1}, (LT.lt.{0} Nat Nat.hasLt (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 q) (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 p)) -> (Eq.{1} Nat (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) p q)) (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 p))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {p : MvPolynomial.{u1, u2} σ R _inst_1} {q : MvPolynomial.{u1, u2} σ R _inst_1}, (LT.lt.{0} Nat instLTNat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 q) (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 p)) -> (Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) p q)) (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_add_eq_left_of_total_degree_lt MvPolynomial.totalDegree_add_eq_left_of_totalDegree_ltₓ'. -/
 theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
     (h : q.totalDegree < p.totalDegree) : (p + q).totalDegree = p.totalDegree := by
   classical
@@ -638,11 +984,23 @@ theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
     exact Finset.le_sup hbb
 #align mv_polynomial.total_degree_add_eq_left_of_total_degree_lt MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt
 
+/- warning: mv_polynomial.total_degree_add_eq_right_of_total_degree_lt -> MvPolynomial.totalDegree_add_eq_right_of_totalDegree_lt is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {p : MvPolynomial.{u2, u1} σ R _inst_1} {q : MvPolynomial.{u2, u1} σ R _inst_1}, (LT.lt.{0} Nat Nat.hasLt (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 q) (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 p)) -> (Eq.{1} Nat (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) q p)) (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 p))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] {p : MvPolynomial.{u1, u2} σ R _inst_1} {q : MvPolynomial.{u1, u2} σ R _inst_1}, (LT.lt.{0} Nat instLTNat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 q) (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 p)) -> (Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toAdd.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{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))))))) q p)) (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_add_eq_right_of_total_degree_lt MvPolynomial.totalDegree_add_eq_right_of_totalDegree_ltₓ'. -/
 theorem totalDegree_add_eq_right_of_totalDegree_lt {p q : MvPolynomial σ R}
     (h : q.totalDegree < p.totalDegree) : (q + p).totalDegree = p.totalDegree := by
   rw [add_comm, total_degree_add_eq_left_of_total_degree_lt h]
 #align mv_polynomial.total_degree_add_eq_right_of_total_degree_lt MvPolynomial.totalDegree_add_eq_right_of_totalDegree_lt
 
+/- warning: mv_polynomial.total_degree_mul -> MvPolynomial.totalDegree_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (a : MvPolynomial.{u2, u1} σ R _inst_1) (b : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{0} Nat Nat.hasLe (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Distrib.toHasMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (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))))))) a b)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 a) (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 b))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (a : MvPolynomial.{u1, u2} σ R _inst_1) (b : MvPolynomial.{u1, u2} σ R _inst_1), LE.le.{0} Nat instLENat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{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)))))) a b)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 a) (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 b))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_mul MvPolynomial.totalDegree_mulₓ'. -/
 theorem totalDegree_mul (a b : MvPolynomial σ R) :
     (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
   Finset.sup_le fun n hn => by
@@ -657,11 +1015,23 @@ theorem totalDegree_mul (a b : MvPolynomial σ R) :
       rfl
 #align mv_polynomial.total_degree_mul MvPolynomial.totalDegree_mul
 
+/- warning: mv_polynomial.total_degree_smul_le -> MvPolynomial.totalDegree_smul_le is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_smul_le MvPolynomial.totalDegree_smul_leₓ'. -/
 theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f : MvPolynomial σ S) :
     (a • f).totalDegree ≤ f.totalDegree :=
   Finset.sup_mono support_smul
 #align mv_polynomial.total_degree_smul_le MvPolynomial.totalDegree_smul_le
 
+/- warning: mv_polynomial.total_degree_pow -> MvPolynomial.totalDegree_pow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_pow MvPolynomial.totalDegree_powₓ'. -/
 theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree ≤ n * a.totalDegree :=
   by
   induction' n with n ih
@@ -674,17 +1044,35 @@ theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree
     
 #align mv_polynomial.total_degree_pow MvPolynomial.totalDegree_pow
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_monomial MvPolynomial.totalDegree_monomialₓ'. -/
 @[simp]
 theorem totalDegree_monomial (s : σ →₀ ℕ) {c : R} (hc : c ≠ 0) :
     (monomial s c : MvPolynomial σ R).totalDegree = s.Sum fun _ e => e := by
   simp [total_degree, support_monomial, if_neg hc]
 #align mv_polynomial.total_degree_monomial MvPolynomial.totalDegree_monomial
 
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+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Nontrivial.{u2} R] (s : σ) (n : Nat), Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 (HPow.hPow.{max u1 u2, 0, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (instHPow.{max u1 u2, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (Monoid.Pow.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toMonoidWithZero.{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 s) n)) n
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_X_pow MvPolynomial.totalDegree_X_powₓ'. -/
 @[simp]
-theorem totalDegree_x_pow [Nontrivial R] (s : σ) (n : ℕ) :
+theorem totalDegree_X_pow [Nontrivial R] (s : σ) (n : ℕ) :
     (X s ^ n : MvPolynomial σ R).totalDegree = n := by simp [X_pow_eq_monomial, one_ne_zero]
-#align mv_polynomial.total_degree_X_pow MvPolynomial.totalDegree_x_pow
-
+#align mv_polynomial.total_degree_X_pow MvPolynomial.totalDegree_X_pow
+
+/- warning: mv_polynomial.total_degree_list_prod -> MvPolynomial.totalDegree_list_prod is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : List.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1)), LE.le.{0} Nat instLENat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 (List.prod.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{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.toOne.{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))) s)) (List.sum.{0} Nat instAddNat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (List.map.{max u1 u2, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_list_prod MvPolynomial.totalDegree_list_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem totalDegree_list_prod :
     ∀ s : List (MvPolynomial σ R), s.Prod.totalDegree ≤ (s.map MvPolynomial.totalDegree).Sum
@@ -694,6 +1082,12 @@ theorem totalDegree_list_prod :
     exact le_trans (total_degree_mul _ _) (add_le_add_left (total_degree_list_prod ps) _)
 #align mv_polynomial.total_degree_list_prod MvPolynomial.totalDegree_list_prod
 
+/- warning: mv_polynomial.total_degree_multiset_prod -> MvPolynomial.totalDegree_multiset_prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1)), LE.le.{0} Nat Nat.hasLe (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 (Multiset.prod.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) s)) (Multiset.sum.{0} Nat Nat.addCommMonoid (Multiset.map.{max u2 u1, 0} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1) s))
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] (s : Multiset.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1)), LE.le.{0} Nat instLENat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 (Multiset.prod.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) s)) (Multiset.sum.{0} Nat Nat.addCommMonoid (Multiset.map.{max u1 u2, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_multiset_prod MvPolynomial.totalDegree_multiset_prodₓ'. -/
 theorem totalDegree_multiset_prod (s : Multiset (MvPolynomial σ R)) :
     s.Prod.totalDegree ≤ (s.map MvPolynomial.totalDegree).Sum :=
   by
@@ -702,6 +1096,12 @@ theorem totalDegree_multiset_prod (s : Multiset (MvPolynomial σ R)) :
   exact total_degree_list_prod l
 #align mv_polynomial.total_degree_multiset_prod MvPolynomial.totalDegree_multiset_prod
 
+/- warning: mv_polynomial.total_degree_finset_prod -> MvPolynomial.totalDegree_finset_prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (s : Finset.{u3} ι) (f : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)), LE.le.{0} Nat Nat.hasLe (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 (Finset.prod.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) s f)) (Finset.sum.{0, u3} Nat ι Nat.addCommMonoid s (fun (i : ι) => MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 (f i)))
+but is expected to have type
+  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (s : Finset.{u2} ι) (f : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), LE.le.{0} Nat instLENat (MvPolynomial.totalDegree.{u3, u1} R σ _inst_1 (Finset.prod.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) s f)) (Finset.sum.{0, u2} Nat ι Nat.addCommMonoid s (fun (i : ι) => MvPolynomial.totalDegree.{u3, u1} R σ _inst_1 (f i)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_finset_prod MvPolynomial.totalDegree_finset_prodₓ'. -/
 theorem totalDegree_finset_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (s.Prod f).totalDegree ≤ ∑ i in s, (f i).totalDegree :=
   by
@@ -710,6 +1110,12 @@ theorem totalDegree_finset_prod {ι : Type _} (s : Finset ι) (f : ι → MvPoly
   rfl
 #align mv_polynomial.total_degree_finset_prod MvPolynomial.totalDegree_finset_prod
 
+/- warning: mv_polynomial.total_degree_finset_sum -> MvPolynomial.totalDegree_finset_sum is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u3}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] {ι : Type.{u2}} (s : Finset.{u2} ι) (f : ι -> (MvPolynomial.{u1, u3} σ R _inst_1)), LE.le.{0} Nat instLENat (MvPolynomial.totalDegree.{u3, u1} R σ _inst_1 (Finset.sum.{max u3 u1, u2} (MvPolynomial.{u1, u3} σ R _inst_1) ι (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))))) s f)) (Finset.sup.{0, u2} Nat ι (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) Nat.orderBot s (fun (i : ι) => MvPolynomial.totalDegree.{u3, u1} R σ _inst_1 (f i)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_finset_sum MvPolynomial.totalDegree_finset_sumₓ'. -/
 theorem totalDegree_finset_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (s.Sum f).totalDegree ≤ Finset.sup s fun i => (f i).totalDegree :=
   by
@@ -719,6 +1125,12 @@ theorem totalDegree_finset_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolyn
     exact (MvPolynomial.totalDegree_add _ _).trans (max_le_max le_rfl hind)
 #align mv_polynomial.total_degree_finset_sum MvPolynomial.totalDegree_finset_sum
 
+/- warning: mv_polynomial.exists_degree_lt -> MvPolynomial.exists_degree_lt is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Fintype.{u1} σ] (f : MvPolynomial.{u1, u2} σ R _inst_1) (n : Nat), (LT.lt.{0} Nat instLTNat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 f) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) n (Fintype.card.{u1} σ _inst_2))) -> (forall {d : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)}, (Membership.mem.{u1, u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finset.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finset.instMembershipFinset.{u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) d (MvPolynomial.support.{u2, u1} R σ _inst_1 f)) -> (Exists.{succ u1} σ (fun (i : σ) => LT.lt.{0} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) i) instLTNat (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) n)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.exists_degree_lt MvPolynomial.exists_degree_ltₓ'. -/
 theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
     (h : f.totalDegree < n * Fintype.card σ) {d : σ →₀ ℕ} (hd : d ∈ f.support) : ∃ i, d i < n :=
   by
@@ -735,6 +1147,12 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
     
 #align mv_polynomial.exists_degree_lt MvPolynomial.exists_degree_lt
 
+/- warning: mv_polynomial.coeff_eq_zero_of_total_degree_lt -> MvPolynomial.coeff_eq_zero_of_totalDegree_lt 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.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_ltₓ'. -/
 theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ ℕ}
     (h : f.totalDegree < ∑ i in d.support, d i) : coeff d f = 0 := by
   classical
@@ -746,6 +1164,12 @@ theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ 
     · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_lt
 
+/- warning: mv_polynomial.total_degree_rename_le -> MvPolynomial.totalDegree_rename_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} {τ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] (f : σ -> τ) (p : MvPolynomial.{u2, u1} σ R _inst_1), LE.le.{0} Nat Nat.hasLe (MvPolynomial.totalDegree.{u1, u3} R τ _inst_1 (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgHom.{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) => (MvPolynomial.{u2, u1} σ R _inst_1) -> (MvPolynomial.{u3, u1} τ R _inst_1)) ([anonymous].{u1, max u2 u1, max u3 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u3, u1} τ 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 u3 u1} (MvPolynomial.{u3, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.rename.{u2, u3, u1} σ τ R _inst_1 f) p)) (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 p)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.total_degree_rename_le MvPolynomial.totalDegree_rename_leₓ'. -/
 theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     (rename f p).totalDegree ≤ p.totalDegree :=
   Finset.sup_le fun b => by
@@ -769,6 +1193,12 @@ section EvalVars
 
 variable [CommSemiring S]
 
+/- warning: mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars -> MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) {g : σ -> S} {p : MvPolynomial.{u3, u1} σ R _inst_1}, (forall (i : σ), (Membership.Mem.{u3, u3} σ (Finset.{u3} σ) (Finset.hasMem.{u3} σ) i (MvPolynomial.vars.{u1, u3} R σ _inst_1 p)) -> (Eq.{succ u2} S (g i) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))))))) -> (Eq.{succ u2} S (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (RingHom.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> S) (RingHom.hasCoeToFun.{max u3 u1, u2} (MvPolynomial.{u3, u1} σ R _inst_1) S (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (MvPolynomial.eval₂Hom.{u1, u2, u3} R S σ _inst_1 _inst_2 f g) p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f (coeFn.{max (succ (max u3 u1)) (succ u1), max (succ (max u3 u1)) (succ u1)} (RingHom.{max u3 u1, u1} (MvPolynomial.{u3, u1} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{max u3 u1, u1} (MvPolynomial.{u3, u1} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (MvPolynomial.{u3, u1} σ R _inst_1) -> R) (RingHom.hasCoeToFun.{max u3 u1, u1} (MvPolynomial.{u3, u1} σ R _inst_1) R (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.constantCoeff.{u1, u3} R σ _inst_1) p)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars MvPolynomial.eval₂Hom_eq_constantCoeff_of_varsₓ'. -/
 theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p : MvPolynomial σ R}
     (hp : ∀ i ∈ p.vars, g i = 0) : eval₂Hom f g p = f (constantCoeff p) :=
   by
@@ -799,11 +1229,23 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
     contradiction
 #align mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars
 
+/- warning: mv_polynomial.aeval_eq_constant_coeff_of_vars -> MvPolynomial.aeval_eq_constantCoeff_of_vars is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.aeval_eq_constant_coeff_of_vars MvPolynomial.aeval_eq_constantCoeff_of_varsₓ'. -/
 theorem aeval_eq_constantCoeff_of_vars [Algebra R S] {g : σ → S} {p : MvPolynomial σ R}
     (hp : ∀ i ∈ p.vars, g i = 0) : aeval g p = algebraMap _ _ (constantCoeff p) :=
   eval₂Hom_eq_constantCoeff_of_vars _ hp
 #align mv_polynomial.aeval_eq_constant_coeff_of_vars MvPolynomial.aeval_eq_constantCoeff_of_vars
 
+/- warning: mv_polynomial.eval₂_hom_congr' -> MvPolynomial.eval₂Hom_congr' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval₂_hom_congr' MvPolynomial.eval₂Hom_congr'ₓ'. -/
 theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p₂ : MvPolynomial σ R} :
     f₁ = f₂ →
       (∀ i, i ∈ p₁.vars → i ∈ p₂.vars → g₁ i = g₂ i) →
@@ -825,6 +1267,12 @@ theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p
   rw [h i this this]
 #align mv_polynomial.eval₂_hom_congr' MvPolynomial.eval₂Hom_congr'
 
+/- warning: mv_polynomial.hom_congr_vars -> MvPolynomial.hom_congr_vars is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.hom_congr_vars MvPolynomial.hom_congr_varsₓ'. -/
 /-- If `f₁` and `f₂` are ring homs out of the polynomial ring and `p₁` and `p₂` are polynomials,
   then `f₁ p₁ = f₂ p₂` if `p₁ = p₂` and `f₁` and `f₂` are equal on `R` and on the variables
   of `p₁`.  -/
@@ -838,6 +1286,12 @@ theorem hom_congr_vars {f₁ f₂ : MvPolynomial σ R →+* S} {p₁ p₂ : MvPo
     
 #align mv_polynomial.hom_congr_vars MvPolynomial.hom_congr_vars
 
+/- warning: mv_polynomial.exists_rename_eq_of_vars_subset_range -> MvPolynomial.exists_rename_eq_of_vars_subset_range is a dubious translation:
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(MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)))))) (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)))))) (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)))) (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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u2 u1) u3, u3, max u1 u3, max u2 u3} (AlgHom.{u3, max u3 u1, max u3 u2} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} 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)))) (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)))) (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)))) (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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u1 u3, max u2 u3, max (max u2 u1) u3} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (AlgHom.{u3, max u3 u1, max u3 u2} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (AlgHom.algHomClass.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.{u2, u3} σ 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)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (MvPolynomial.rename.{u1, u2, u3} τ σ R _inst_1 f) q) p))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.exists_rename_eq_of_vars_subset_range MvPolynomial.exists_rename_eq_of_vars_subset_rangeₓ'. -/
 theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ → σ) (hfi : Injective f)
     (hf : ↑p.vars ⊆ Set.range f) : ∃ q : MvPolynomial τ R, rename f q = p :=
   ⟨aeval (fun i : σ => Option.elim' 0 X <| partialInv f i) p,
@@ -852,6 +1306,12 @@ theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ 
     · rfl⟩
 #align mv_polynomial.exists_rename_eq_of_vars_subset_range MvPolynomial.exists_rename_eq_of_vars_subset_range
 
+/- warning: mv_polynomial.vars_rename -> MvPolynomial.vars_rename 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.vars_rename MvPolynomial.vars_renameₓ'. -/
 theorem vars_rename (f : σ → τ) (φ : MvPolynomial σ R) : (rename f φ).vars ⊆ φ.vars.image f :=
   by
   intro i hi
@@ -859,6 +1319,12 @@ theorem vars_rename (f : σ → τ) (φ : MvPolynomial σ R) : (rename f φ).var
   simpa only [Multiset.mem_map] using degrees_rename _ _ hi
 #align mv_polynomial.vars_rename MvPolynomial.vars_rename
 
+/- warning: mv_polynomial.mem_vars_rename -> MvPolynomial.mem_vars_rename is a dubious translation:
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_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} (MvPolynomial.{u1, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R τ _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 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)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{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))) (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 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 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 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)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u2 u3, max u1 u3, max (max u2 u1) u3} 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)) (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))) (AlgHom.algHomClass.{u3, max u2 u3, max u1 u3} 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.rename.{u2, u1, u3} σ τ R _inst_1 f) φ))) -> (Exists.{succ u2} σ (fun (i : σ) => And (Membership.mem.{u2, u2} σ (Finset.{u2} σ) (Finset.instMembershipFinset.{u2} σ) i (MvPolynomial.vars.{u3, u2} R σ _inst_1 φ)) (Eq.{succ u1} τ (f i) j)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_vars_rename MvPolynomial.mem_vars_renameₓ'. -/
 theorem mem_vars_rename (f : σ → τ) (φ : MvPolynomial σ R) {j : τ} (h : j ∈ (rename f φ).vars) :
     ∃ i : σ, i ∈ φ.vars ∧ f i = j := by
   simpa only [exists_prop, Finset.mem_image] using vars_rename f φ h

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

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.variables
-! leanprover-community/mathlib commit 65902a4a1a39ff6fdfb657a35dde2579dbb4a155
+! 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.Algebra.BigOperators.Order
-import Mathbin.Data.MvPolynomial.Monad
+import Mathbin.Data.MvPolynomial.Rename
 
 /-!
 # Degrees and variables of polynomials
@@ -840,7 +840,7 @@ theorem hom_congr_vars {f₁ f₂ : MvPolynomial σ R →+* S} {p₁ p₂ : MvPo
 
 theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ → σ) (hfi : Injective f)
     (hf : ↑p.vars ⊆ Set.range f) : ∃ q : MvPolynomial τ R, rename f q = p :=
-  ⟨bind₁ (fun i : σ => Option.elim' 0 X <| partialInv f i) p,
+  ⟨aeval (fun i : σ => Option.elim' 0 X <| partialInv f i) p,
     by
     show (rename f).toRingHom.comp _ p = RingHom.id _ p
     refine' hom_congr_vars _ _ _
@@ -852,48 +852,6 @@ theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ 
     · rfl⟩
 #align mv_polynomial.exists_rename_eq_of_vars_subset_range MvPolynomial.exists_rename_eq_of_vars_subset_range
 
-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
-
-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
-
 theorem vars_rename (f : σ → τ) (φ : MvPolynomial σ R) : (rename f φ).vars ⊆ φ.vars.image f :=
   by
   intro i hi

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

@@ -105,16 +105,16 @@ theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
     Finset.le_sup <| by rw [support_monomial, if_neg ha, Finset.mem_singleton]
 #align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eq
 
-theorem degrees_c (a : R) : degrees (c a : MvPolynomial σ R) = 0 :=
+theorem degrees_c (a : R) : degrees (C a : MvPolynomial σ R) = 0 :=
   Multiset.le_zero.1 <| degrees_monomial _ _
 #align mv_polynomial.degrees_C MvPolynomial.degrees_c
 
-theorem degrees_X' (n : σ) : degrees (x n : MvPolynomial σ R) ≤ {n} :=
+theorem degrees_X' (n : σ) : degrees (X n : MvPolynomial σ R) ≤ {n} :=
   le_trans (degrees_monomial _ _) <| le_of_eq <| toMultiset_single _ _
 #align mv_polynomial.degrees_X' MvPolynomial.degrees_X'
 
 @[simp]
-theorem degrees_x [Nontrivial R] (n : σ) : degrees (x n : MvPolynomial σ R) = {n} :=
+theorem degrees_x [Nontrivial R] (n : σ) : degrees (X n : MvPolynomial σ R) = {n} :=
   (degrees_monomial_eq _ (1 : R) one_ne_zero).trans (toMultiset_single _ _)
 #align mv_polynomial.degrees_X MvPolynomial.degrees_x
 
@@ -276,12 +276,12 @@ theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by
 #align mv_polynomial.vars_monomial MvPolynomial.vars_monomial
 
 @[simp]
-theorem vars_c : (c r : MvPolynomial σ R).vars = ∅ := by
+theorem vars_c : (C r : MvPolynomial σ R).vars = ∅ := by
   rw [vars, degrees_C, Multiset.toFinset_zero]
 #align mv_polynomial.vars_C MvPolynomial.vars_c
 
 @[simp]
-theorem vars_x [Nontrivial R] : (x n : MvPolynomial σ R).vars = {n} := by
+theorem vars_x [Nontrivial R] : (X n : MvPolynomial σ R).vars = {n} := by
   rw [X, vars_monomial (one_ne_zero' R), Finsupp.support_single_ne_zero _ (one_ne_zero' ℕ)]
 #align mv_polynomial.vars_X MvPolynomial.vars_x
 
@@ -377,7 +377,7 @@ section IsDomain
 
 variable {A : Type _} [CommRing A] [IsDomain A]
 
-theorem vars_c_mul (a : A) (ha : a ≠ 0) (φ : MvPolynomial σ A) : (c a * φ).vars = φ.vars :=
+theorem vars_c_mul (a : A) (ha : a ≠ 0) (φ : MvPolynomial σ A) : (C a * φ).vars = φ.vars :=
   by
   ext1 i
   simp only [mem_vars, exists_prop, mem_support_iff]
@@ -486,12 +486,12 @@ theorem degreeOf_zero (n : σ) : degreeOf n (0 : MvPolynomial σ R) = 0 := by
 #align mv_polynomial.degree_of_zero MvPolynomial.degreeOf_zero
 
 @[simp]
-theorem degreeOf_c (a : R) (x : σ) : degreeOf x (c a : MvPolynomial σ R) = 0 := by
+theorem degreeOf_c (a : R) (x : σ) : degreeOf x (C a : MvPolynomial σ R) = 0 := by
   simp [degree_of, degrees_C]
 #align mv_polynomial.degree_of_C MvPolynomial.degreeOf_c
 
 theorem degreeOf_x (i j : σ) [Nontrivial R] :
-    degreeOf i (x j : MvPolynomial σ R) = if i = j then 1 else 0 :=
+    degreeOf i (X j : MvPolynomial σ R) = if i = j then 1 else 0 :=
   by
   by_cases c : i = j
   · simp only [c, if_true, eq_self_iff_true, degree_of, degrees_X, Multiset.count_singleton]
@@ -523,7 +523,7 @@ theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
 #align mv_polynomial.degree_of_mul_le MvPolynomial.degreeOf_mul_le
 
 theorem degreeOf_mul_x_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
-    degreeOf i (f * x j) = degreeOf i f :=
+    degreeOf i (f * X j) = degreeOf i f :=
   by
   repeat' rw [degree_of_eq_sup i]
   rw [support_mul_X]
@@ -536,7 +536,7 @@ theorem degreeOf_mul_x_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
 
 -- TODO in the following we have equality iff f ≠ 0
 theorem degreeOf_mul_x_eq (j : σ) (f : MvPolynomial σ R) :
-    degreeOf j (f * x j) ≤ degreeOf j f + 1 :=
+    degreeOf j (f * X j) ≤ degreeOf j f + 1 :=
   by
   repeat' rw [degree_of]
   apply (Multiset.count_le_of_le j (degrees_mul f (X j))).trans
@@ -577,7 +577,7 @@ theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) : p.totalDegree ≤
 #align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
 
 @[simp]
-theorem totalDegree_c (a : R) : (c a : MvPolynomial σ R).totalDegree = 0 :=
+theorem totalDegree_c (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
   Nat.eq_zero_of_le_zero <|
     Finset.sup_le fun n hn => by
       have := Finsupp.support_single_subset hn
@@ -598,7 +598,7 @@ theorem totalDegree_one : (1 : MvPolynomial σ R).totalDegree = 0 :=
 
 @[simp]
 theorem totalDegree_x {R} [CommSemiring R] [Nontrivial R] (s : σ) :
-    (x s : MvPolynomial σ R).totalDegree = 1 :=
+    (X s : MvPolynomial σ R).totalDegree = 1 :=
   by
   rw [total_degree, support_X]
   simp only [Finset.sup, sum_single_index, Finset.fold_singleton, sup_bot_eq]
@@ -682,7 +682,7 @@ theorem totalDegree_monomial (s : σ →₀ ℕ) {c : R} (hc : c ≠ 0) :
 
 @[simp]
 theorem totalDegree_x_pow [Nontrivial R] (s : σ) (n : ℕ) :
-    (x s ^ n : MvPolynomial σ R).totalDegree = n := by simp [X_pow_eq_monomial, one_ne_zero]
+    (X s ^ n : MvPolynomial σ R).totalDegree = n := by simp [X_pow_eq_monomial, one_ne_zero]
 #align mv_polynomial.total_degree_X_pow MvPolynomial.totalDegree_x_pow
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -829,18 +829,18 @@ theorem eval₂Hom_congr' {f₁ f₂ : R →+* S} {g₁ g₂ : σ → S} {p₁ p
   then `f₁ p₁ = f₂ p₂` if `p₁ = p₂` and `f₁` and `f₂` are equal on `R` and on the variables
   of `p₁`.  -/
 theorem hom_congr_vars {f₁ f₂ : MvPolynomial σ R →+* S} {p₁ p₂ : MvPolynomial σ R}
-    (hC : f₁.comp c = f₂.comp c) (hv : ∀ i, i ∈ p₁.vars → i ∈ p₂.vars → f₁ (x i) = f₂ (x i))
+    (hC : f₁.comp C = f₂.comp C) (hv : ∀ i, i ∈ p₁.vars → i ∈ p₂.vars → f₁ (X i) = f₂ (X i))
     (hp : p₁ = p₂) : f₁ p₁ = f₂ p₂ :=
   calc
-    f₁ p₁ = eval₂Hom (f₁.comp c) (f₁ ∘ x) p₁ := RingHom.congr_fun (by ext <;> simp) _
-    _ = eval₂Hom (f₂.comp c) (f₂ ∘ x) p₂ := (eval₂Hom_congr' hC hv hp)
+    f₁ p₁ = eval₂Hom (f₁.comp C) (f₁ ∘ X) p₁ := RingHom.congr_fun (by ext <;> simp) _
+    _ = eval₂Hom (f₂.comp C) (f₂ ∘ X) p₂ := (eval₂Hom_congr' hC hv hp)
     _ = f₂ p₂ := RingHom.congr_fun (by ext <;> simp) _
     
 #align mv_polynomial.hom_congr_vars MvPolynomial.hom_congr_vars
 
 theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ → σ) (hfi : Injective f)
     (hf : ↑p.vars ⊆ Set.range f) : ∃ q : MvPolynomial τ R, rename f q = p :=
-  ⟨bind₁ (fun i : σ => Option.elim' 0 x <| partialInv f i) p,
+  ⟨bind₁ (fun i : σ => Option.elim' 0 X <| partialInv f i) p,
     by
     show (rename f).toRingHom.comp _ p = RingHom.id _ p
     refine' hom_congr_vars _ _ _

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

@@ -665,7 +665,7 @@ theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f :
 theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree ≤ n * a.totalDegree :=
   by
   induction' n with n ih
-  · simp only [Nat.zero_eq, zero_mul, pow_zero, total_degree_one]
+  · simp only [Nat.zero_eq, MulZeroClass.zero_mul, pow_zero, total_degree_one]
   rw [pow_succ]
   calc
     total_degree (a * a ^ n) ≤ a.total_degree + (a ^ n).totalDegree := total_degree_mul _ _
@@ -790,7 +790,7 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
       rw [Finset.nonempty_iff_ne_empty, Ne.def, Finsupp.support_eq_empty]
       rintro rfl
       contradiction
-    rw [Finsupp.prod, Finset.prod_eq_zero hi, mul_zero]
+    rw [Finsupp.prod, Finset.prod_eq_zero hi, MulZeroClass.mul_zero]
     rw [hp, zero_pow (Nat.pos_of_ne_zero <| finsupp.mem_support_iff.mp hi)]
     rw [mem_vars]
     exact ⟨d, hd, hi⟩

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

@@ -669,7 +669,7 @@ theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree
   rw [pow_succ]
   calc
     total_degree (a * a ^ n) ≤ a.total_degree + (a ^ n).totalDegree := total_degree_mul _ _
-    _ ≤ a.total_degree + n * a.total_degree := add_le_add_left ih _
+    _ ≤ a.total_degree + n * a.total_degree := (add_le_add_left ih _)
     _ = (n + 1) * a.total_degree := by rw [add_mul, one_mul, add_comm]
     
 #align mv_polynomial.total_degree_pow MvPolynomial.totalDegree_pow
@@ -726,7 +726,7 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
   calc
     n * Fintype.card σ = ∑ s : σ, n := by
       rw [Finset.sum_const, Nat.nsmul_eq_mul, mul_comm, Finset.card_univ]
-    _ ≤ ∑ s, d s := Finset.sum_le_sum fun s _ => h s
+    _ ≤ ∑ s, d s := (Finset.sum_le_sum fun s _ => h s)
     _ ≤ d.sum fun i e => e := by
       rw [Finsupp.sum_fintype]
       intros
@@ -833,7 +833,7 @@ theorem hom_congr_vars {f₁ f₂ : MvPolynomial σ R →+* S} {p₁ p₂ : MvPo
     (hp : p₁ = p₂) : f₁ p₁ = f₂ p₂ :=
   calc
     f₁ p₁ = eval₂Hom (f₁.comp c) (f₁ ∘ x) p₁ := RingHom.congr_fun (by ext <;> simp) _
-    _ = eval₂Hom (f₂.comp c) (f₂ ∘ x) p₂ := eval₂Hom_congr' hC hv hp
+    _ = eval₂Hom (f₂.comp c) (f₂ ∘ x) p₂ := (eval₂Hom_congr' hC hv hp)
     _ = f₂ p₂ := RingHom.congr_fun (by ext <;> simp) _
     
 #align mv_polynomial.hom_congr_vars MvPolynomial.hom_congr_vars
@@ -859,7 +859,7 @@ theorem vars_bind₁ (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
     (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 _ _
+      (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 := _
@@ -877,7 +877,7 @@ 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.bUnion fun i : σ => (f i ^ d i).vars := vars_prod _
+      _ ≤ 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

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

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -259,7 +259,7 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
     rw [Finset.sum_eq_single (0 : σ →₀ ℕ)]
     · rw [Finsupp.prod_zero_index, mul_one]
       rfl
-    intro d hd hd0
+    on_goal 1 => intro d hd hd0
   on_goal 3 =>
     rw [constantCoeff_eq, coeff, ← Ne, ← Finsupp.mem_support_iff] at h0
     intro

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

@@ -459,6 +459,14 @@ theorem totalDegree_monomial (s : σ →₀ ℕ) {c : R} (hc : c ≠ 0) :
   classical simp [totalDegree, support_monomial, if_neg hc]
 #align mv_polynomial.total_degree_monomial MvPolynomial.totalDegree_monomial
 
+theorem totalDegree_monomial_le (s : σ →₀ ℕ) (c : R) :
+    (monomial s c).totalDegree ≤ s.sum fun _ ↦ id := by
+  if hc : c = 0 then
+    simp only [hc, map_zero, totalDegree_zero, zero_le]
+  else
+    rw [totalDegree_monomial _ hc]
+    exact le_rfl
+
 @[simp]
 theorem totalDegree_X_pow [Nontrivial R] (s : σ) (n : ℕ) :
     (X s ^ n : MvPolynomial σ R).totalDegree = n := by simp [X_pow_eq_monomial, one_ne_zero]

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

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

@@ -261,7 +261,7 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
       rfl
     intro d hd hd0
   on_goal 3 =>
-    rw [constantCoeff_eq, coeff, ← Ne.def, ← Finsupp.mem_support_iff] at h0
+    rw [constantCoeff_eq, coeff, ← Ne, ← Finsupp.mem_support_iff] at h0
     intro
     contradiction
   repeat'

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

@@ -308,7 +308,7 @@ theorem hom_congr_vars {f₁ f₂ : MvPolynomial σ R →+* S} {p₁ p₂ : MvPo
     (hp : p₁ = p₂) : f₁ p₁ = f₂ p₂ :=
   calc
     f₁ p₁ = eval₂Hom (f₁.comp C) (f₁ ∘ X) p₁ := RingHom.congr_fun (by ext <;> simp) _
-    _ = eval₂Hom (f₂.comp C) (f₂ ∘ X) p₂ := (eval₂Hom_congr' hC hv hp)
+    _ = eval₂Hom (f₂.comp C) (f₂ ∘ X) p₂ := eval₂Hom_congr' hC hv hp
     _ = f₂ p₂ := RingHom.congr_fun (by ext <;> simp) _
 #align mv_polynomial.hom_congr_vars MvPolynomial.hom_congr_vars
 

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

@@ -507,7 +507,7 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
   calc
     n * Fintype.card σ = ∑ _s : σ, n := by
       rw [Finset.sum_const, Nat.nsmul_eq_mul, mul_comm, Finset.card_univ]
-    _ ≤ ∑ s, d s := (Finset.sum_le_sum fun s _ => h s)
+    _ ≤ ∑ s, d s := Finset.sum_le_sum fun s _ => h s
     _ ≤ d.sum fun _ e => e := by
       rw [Finsupp.sum_fintype]
       intros

Take the content of

• some of Algebra.BigOperators.List.Basic
• some of Algebra.BigOperators.List.Lemmas
• some of Algebra.BigOperators.Multiset.Basic
• some of Algebra.BigOperators.Multiset.Lemmas
• Algebra.BigOperators.Multiset.Order
• Algebra.BigOperators.Order

and sort it into six files:

• Algebra.Order.BigOperators.Group.List. I credit Yakov for https://github.com/leanprover-community/mathlib/pull/8543.
• Algebra.Order.BigOperators.Group.Multiset. Copyright inherited from Algebra.BigOperators.Multiset.Order.
• Algebra.Order.BigOperators.Group.Finset. Copyright inherited from Algebra.BigOperators.Order.
• Algebra.Order.BigOperators.Ring.List. I credit Stuart for https://github.com/leanprover-community/mathlib/pull/10184.
• Algebra.Order.BigOperators.Ring.Multiset. I credit Ruben for https://github.com/leanprover-community/mathlib/pull/8787.
• Algebra.Order.BigOperators.Ring.Finset. I credit Floris for https://github.com/leanprover-community/mathlib/pull/1294.

Here are the design decisions at play:

• Pure algebra and big operators algebra shouldn't import (algebraic) order theory. This PR makes that better, but not perfect because we still import Data.Nat.Order.Basic in a few List files.
• It's Algebra.Order.BigOperators instead of Algebra.BigOperators.Order because algebraic order theory is more of a theory than big operators algebra. Another reason is that algebraic order theory is the only way to mix pure order and pure algebra, while there are more ways to mix pure finiteness and pure algebra than just big operators.
• There are separate files for group/monoid lemmas vs ring lemmas. Groups/monoids are the natural setup for big operators, so their lemmas shouldn't be mixed with ring lemmas that involves both addition and multiplication. As a result, everything under Algebra.Order.BigOperators.Group should be additivisable (except a few Nat- or Int-specific lemmas). In contrast, things under Algebra.Order.BigOperators.Ring are more prone to having heavy imports.
• Lemmas are separated according to List vs Multiset vs Finset. This is not strictly necessary, and can be relaxed in cases where there aren't that many lemmas to be had. As an example, I could split out the AbsoluteValue lemmas from Algebra.Order.BigOperators.Ring.Finset to a file Algebra.Order.BigOperators.Ring.AbsoluteValue and it could stay this way until too many lemmas are in this file (or a split is needed for import reasons), in which case we would need files Algebra.Order.BigOperators.Ring.AbsoluteValue.Finset, Algebra.Order.BigOperators.Ring.AbsoluteValue.Multiset, etc...
• Finsupp big operator and finprod/finsum order lemmas also belong in Algebra.Order.BigOperators. I haven't done so in this PR because the diff is big enough like that.

@@ -3,9 +3,9 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 -/
-import Mathlib.Algebra.BigOperators.Order
 import Mathlib.Algebra.MonoidAlgebra.Degree
 import Mathlib.Algebra.MvPolynomial.Rename
+import Mathlib.Algebra.Order.BigOperators.Ring.Finset
 
 #align_import data.mv_polynomial.variables from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 

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

@@ -3,7 +3,7 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 -/
-import Mathlib.Data.MvPolynomial.Degrees
+import Mathlib.Algebra.MvPolynomial.Degrees
 
 #align_import data.mv_polynomial.variables from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 -/
-import Mathlib.Algebra.MonoidAlgebra.Degree
 import Mathlib.Algebra.BigOperators.Order
-import Mathlib.Data.MvPolynomial.Rename
+import Mathlib.Algebra.MonoidAlgebra.Degree
+import Mathlib.Algebra.MvPolynomial.Rename
 
 #align_import data.mv_polynomial.variables from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 

@@ -267,7 +267,7 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
   repeat'
     obtain ⟨i, hi⟩ : Finset.Nonempty (Finsupp.support d) := by
       rw [constantCoeff_eq, coeff, ← Finsupp.not_mem_support_iff] at h0
-      rw [Finset.nonempty_iff_ne_empty, Ne.def, Finsupp.support_eq_empty]
+      rw [Finset.nonempty_iff_ne_empty, Ne, Finsupp.support_eq_empty]
       rintro rfl
       contradiction
     rw [Finsupp.prod, Finset.prod_eq_zero hi, mul_zero]

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

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

where the latter is more natural

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

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

but it seems to no longer apply.

Remarks on the PR :

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

@@ -137,7 +137,7 @@ theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars
   classical
   induction' n with n ih
   · simp
-  · rw [pow_succ]
+  · rw [pow_succ']
     apply Finset.Subset.trans (vars_mul _ _)
     exact Finset.union_subset (Finset.Subset.refl _) ih
 #align mv_polynomial.vars_pow MvPolynomial.vars_pow

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)

@@ -214,7 +214,6 @@ end Sum
 section Map
 
 variable [CommSemiring S] (f : R →+* S)
-
 variable (p)
 
 theorem vars_map : (map f p).vars ⊆ p.vars := by classical simp [vars_def, degrees_map]

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

@@ -103,16 +103,8 @@ theorem mem_vars (i : σ) : i ∈ p.vars ↔ ∃ d ∈ p.support, i ∈ d.suppor
 
 theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ} (H : x ∈ f.support)
     {v : σ} (h : v ∉ vars f) : x v = 0 := by
-  classical
-  rw [vars_def, Multiset.mem_toFinset] at h
-  rw [← Finsupp.not_mem_support_iff]
   contrapose! h
-  rw [degrees_def]
-  rw [show f.support = insert x f.support from Eq.symm <| Finset.insert_eq_of_mem H]
-  rw [Finset.sup_insert]
-  simp only [Multiset.mem_union, Multiset.sup_eq_union]
-  left
-  rwa [← toFinset_toMultiset, Multiset.mem_toFinset] at h
+  exact (mem_vars v).mpr ⟨x, H, Finsupp.mem_support_iff.mpr h⟩
 #align mv_polynomial.mem_support_not_mem_vars_zero MvPolynomial.mem_support_not_mem_vars_zero
 
 theorem vars_add_subset [DecidableEq σ] (p q : MvPolynomial σ R) :
@@ -124,36 +116,16 @@ theorem vars_add_subset [DecidableEq σ] (p q : MvPolynomial σ R) :
 
 theorem vars_add_of_disjoint [DecidableEq σ] (h : Disjoint p.vars q.vars) :
     (p + q).vars = p.vars ∪ q.vars := by
-  apply Finset.Subset.antisymm (vars_add_subset p q)
-  intro x hx
+  refine (vars_add_subset p q).antisymm fun x hx => ?_
   simp only [vars_def, Multiset.disjoint_toFinset] at h hx ⊢
-  rw [degrees_add_of_disjoint h, Multiset.toFinset_union]
-  exact hx
+  rwa [degrees_add_of_disjoint h, Multiset.toFinset_union]
 #align mv_polynomial.vars_add_of_disjoint MvPolynomial.vars_add_of_disjoint
 
 section Mul
 
 theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars ⊆ φ.vars ∪ ψ.vars := by
-  intro i
-  simp only [mem_vars, Finset.mem_union]
-  rintro ⟨d, hd, hi⟩
-  rw [mem_support_iff, coeff_mul] at hd
-  contrapose! hd
-  cases hd
-  rw [Finset.sum_eq_zero]
-  rintro ⟨d₁, d₂⟩ H
-  rw [Finset.mem_antidiagonal] at H
-  subst H
-  obtain H | H : i ∈ d₁.support ∨ i ∈ d₂.support := by
-    simpa only [Finset.mem_union] using Finsupp.support_add hi
-  · suffices coeff d₁ φ = 0 by simp [this]
-    rw [coeff, ← Finsupp.not_mem_support_iff]
-    intro
-    solve_by_elim
-  · suffices coeff d₂ ψ = 0 by simp [this]
-    rw [coeff, ← Finsupp.not_mem_support_iff]
-    intro
-    solve_by_elim
+  simp_rw [vars_def, ← Multiset.toFinset_add, Multiset.toFinset_subset]
+  exact Multiset.subset_of_le (degrees_mul φ ψ)
 #align mv_polynomial.vars_mul MvPolynomial.vars_mul
 
 @[simp]

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

@@ -89,17 +89,15 @@ theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
 
 theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ toMultiset s := by
   classical
-    refine' Finset.sup_le fun t h => _
-    have := Finsupp.support_single_subset h
-    rw [Finset.mem_singleton] at this
-    rw [this]
+    refine (supDegree_single s a).trans_le ?_
+    split_ifs
+    exacts [bot_le, le_rfl]
 #align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomial
 
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
     degrees (monomial s a) = toMultiset s := by
   classical
-    refine' le_antisymm (degrees_monomial s a) <| Finset.le_sup <| _
-    rw [support_monomial, if_neg ha, Finset.mem_singleton]
+    exact (supDegree_single s a).trans (if_neg ha)
 #align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eq
 
 theorem degrees_C (a : R) : degrees (C a : MvPolynomial σ R) = 0 :=
@@ -131,36 +129,23 @@ theorem degrees_one : degrees (1 : MvPolynomial σ R) = 0 :=
 
 theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
     (p + q).degrees ≤ p.degrees ⊔ q.degrees := by
-  classical
-  simp_rw [degrees_def]
-  refine' Finset.sup_le fun b hb => _
-  have := Finsupp.support_add hb; rw [Finset.mem_union] at this
-  cases' this with h h
-  · exact le_sup_of_le_left (Finset.le_sup h)
-  · exact le_sup_of_le_right (Finset.le_sup h)
+  simp_rw [degrees_def]; exact supDegree_add_le
 #align mv_polynomial.degrees_add MvPolynomial.degrees_add
 
 theorem degrees_sum {ι : Type*} [DecidableEq σ] (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by
-  classical
-  refine' s.induction _ _
-  · simp only [Finset.sum_empty, Finset.sup_empty, degrees_zero]
-    exact le_rfl
-  · intro i s his ih
-    rw [Finset.sup_insert, Finset.sum_insert his]
-    exact le_trans (degrees_add _ _) (sup_le_sup_left ih _)
+  simp_rw [degrees_def]; exact supDegree_sum_le
 #align mv_polynomial.degrees_sum MvPolynomial.degrees_sum
 
 theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees := by
   classical
-  refine (Finset.sup_mono <| support_mul p q).trans <| Finset.sup_add_le.2 fun a ha b hb ↦ ?_
-  rw [Finsupp.toMultiset_add]
-  exact add_le_add (Finset.le_sup ha) (Finset.le_sup hb)
+  simp_rw [degrees_def]
+  exact supDegree_mul_le (map_add _)
 #align mv_polynomial.degrees_mul MvPolynomial.degrees_mul
 
 theorem degrees_prod {ι : Type*} (s : Finset ι) (f : ι → MvPolynomial σ R) :
-    (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees :=
-  Finset.le_prod_of_submultiplicative (Multiplicative.ofAdd ∘ degrees) degrees_one degrees_mul _ _
+    (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees := by
+  classical exact supDegree_prod_le (map_zero _) (map_add _)
 #align mv_polynomial.degrees_prod MvPolynomial.degrees_prod
 
 theorem degrees_pow (p : MvPolynomial σ R) (n : ℕ) : (p ^ n).degrees ≤ n • p.degrees := by
@@ -179,16 +164,12 @@ theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degre
   apply Finset.sup_le
   intro d hd
   rw [Multiset.disjoint_iff_ne] at h
-  rw [Multiset.le_iff_count]
-  intro i
-  rw [degrees, Multiset.count_finset_sup]
-  simp only [Finsupp.count_toMultiset]
-  by_cases h0 : d = 0
-  · simp only [h0, zero_le, Finsupp.zero_apply]
-  · refine' @Finset.le_sup _ _ _ _ (p + q).support (fun a => a i) d _
+  obtain rfl | h0 := eq_or_ne d 0
+  · rw [toMultiset_zero]; apply Multiset.zero_le
+  · refine Finset.le_sup_of_le (b := d) ?_ le_rfl
     rw [mem_support_iff, coeff_add]
     suffices q.coeff d = 0 by rwa [this, add_zero, coeff, ← Finsupp.mem_support_iff]
-    rw [← Finsupp.support_eq_empty, ← Ne.def, ← Finset.nonempty_iff_ne_empty] at h0
+    rw [Ne, ← Finsupp.support_eq_empty, ← Ne, ← Finset.nonempty_iff_ne_empty] at h0
     obtain ⟨j, hj⟩ := h0
     contrapose! h
     rw [mem_support_iff] at hd
@@ -303,11 +284,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
     degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) := by
-  letI := Classical.decEq σ
-  repeat' rw [degreeOf]
-  apply (Multiset.count_le_of_le n (degrees_add f g)).trans
-  dsimp
-  rw [Multiset.count_union]
+  simp_rw [degreeOf_eq_sup]; exact supDegree_add_le
 #align mv_polynomial.degree_of_add_le MvPolynomial.degreeOf_add_le
 
 theorem monomial_le_degreeOf (i : σ) {f : MvPolynomial σ R} {m : σ →₀ ℕ} (h_m : m ∈ f.support) :
@@ -404,12 +381,7 @@ theorem totalDegree_le_of_support_subset (h : p.support ⊆ q.support) :
 
 @[simp]
 theorem totalDegree_C (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
-  Nat.eq_zero_of_le_zero <|
-    Finset.sup_le fun n hn => by
-      have := Finsupp.support_single_subset hn
-      rw [Finset.mem_singleton] at this
-      subst this
-      exact le_rfl
+  (supDegree_single 0 a).trans <| by rw [sum_zero_index, bot_eq_zero', ite_self]
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.total_degree_C MvPolynomial.totalDegree_C
 
@@ -433,7 +405,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem totalDegree_add (a b : MvPolynomial σ R) :
     (a + b).totalDegree ≤ max a.totalDegree b.totalDegree :=
-  AddMonoidAlgebra.sup_support_add_le _ _ _
+  sup_support_add_le _ _ _
 #align mv_polynomial.total_degree_add MvPolynomial.totalDegree_add
 
 theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
@@ -466,8 +438,7 @@ theorem totalDegree_add_eq_right_of_totalDegree_lt {p q : MvPolynomial σ R}
 
 theorem totalDegree_mul (a b : MvPolynomial σ R) :
     (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
-  AddMonoidAlgebra.sup_support_mul_le
-    (by exact (Finsupp.sum_add_index' (fun _ => rfl) (fun _ _ _ => rfl)).le) _ _
+  sup_support_mul_le (by exact (Finsupp.sum_add_index' (fun _ => rfl) (fun _ _ _ => rfl)).le) _ _
 #align mv_polynomial.total_degree_mul MvPolynomial.totalDegree_mul
 
 theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f : MvPolynomial σ S) :
@@ -477,13 +448,9 @@ theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f :
 
 theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) :
     (a ^ n).totalDegree ≤ n * a.totalDegree := by
-  induction' n with n ih
-  · simp only [Nat.zero_eq, pow_zero, totalDegree_one, zero_mul, le_refl]
-  rw [pow_succ]
-  calc
-    totalDegree (a * a ^ n) ≤ a.totalDegree + (a ^ n).totalDegree := totalDegree_mul _ _
-    _ ≤ a.totalDegree + n * a.totalDegree := (add_le_add_left ih _)
-    _ = (n + 1) * a.totalDegree := by rw [add_mul, one_mul, add_comm]
+  rw [Finset.pow_eq_prod_const, ← Nat.nsmul_eq_mul, Finset.nsmul_eq_sum_const]
+  refine supDegree_prod_le rfl (fun _ _ => ?_)
+  exact Finsupp.sum_add_index' (fun _ => rfl) (fun _ _ _ => rfl)
 #align mv_polynomial.total_degree_pow MvPolynomial.totalDegree_pow
 
 @[simp]
@@ -568,10 +535,7 @@ theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     have h' := Finsupp.mapDomain_support h
     rw [Finset.mem_image] at h'
     rcases h' with ⟨s, hs, rfl⟩
-    rw [Finsupp.sum_mapDomain_index]
-    exact le_trans le_rfl (le_totalDegree hs)
-    exact fun _ => rfl
-    exact fun _ _ _ => rfl
+    exact (sum_mapDomain_index (fun _ => rfl) (fun _ _ _ => rfl)).trans_le (le_totalDegree hs)
 #align mv_polynomial.total_degree_rename_le MvPolynomial.totalDegree_rename_le
 
 end TotalDegree

Splits this file into two. The sections about degree related concepts are totally independent of the vars related concepts so this was a clean split.

@@ -3,40 +3,24 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 -/
-import Mathlib.Algebra.MonoidAlgebra.Degree
-import Mathlib.Algebra.BigOperators.Order
-import Mathlib.Data.MvPolynomial.Rename
+import Mathlib.Data.MvPolynomial.Degrees
 
 #align_import data.mv_polynomial.variables from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 
 /-!
-# Degrees and variables of polynomials
+# Variables of polynomials
 
-This file establishes many results about the degree and variable sets of a multivariate polynomial.
+This file establishes many results about the variable sets of a multivariate polynomial.
 
 The *variable set* of a polynomial $P \in R[X]$ is a `Finset` containing each $x \in X$
 that appears in a monomial in $P$.
 
-The *degree set* of a polynomial $P \in R[X]$ is a `Multiset` containing, for each $x$ in the
-variable set, $n$ copies of $x$, where $n$ is the maximum number of copies of $x$ appearing in a
-monomial of $P$.
 
 ## Main declarations
 
-* `MvPolynomial.degrees p` : the multiset of variables representing the union of the multisets
-  corresponding to each non-zero monomial in `p`.
-  For example if `7 ≠ 0` in `R` and `p = x²y+7y³` then `degrees p = {x, x, y, y, y}`
-
 * `MvPolynomial.vars p` : the finset of variables occurring in `p`.
   For example if `p = x⁴y+yz` then `vars p = {x, y, z}`
 
-* `MvPolynomial.degreeOf n p : ℕ` : the total degree of `p` with respect to the variable `n`.
-  For example if `p = x⁴y+yz` then `degreeOf y p = 1`.
-
-* `MvPolynomial.totalDegree p : ℕ` :
-  the max of the sizes of the multisets `s` whose monomials `X^s` occur in `p`.
-  For example if `p = x⁴y+yz` then `totalDegree p = 5`.
-
 ## Notation
 
 As in other polynomial files, we typically use the notation:
@@ -75,185 +59,6 @@ section CommSemiring
 
 variable [CommSemiring R] {p q : MvPolynomial σ R}
 
-section Degrees
-
-/-! ### `degrees` -/
-
-
-/-- The maximal degrees of each variable in a multi-variable polynomial, expressed as a multiset.
-
-(For example, `degrees (x^2 * y + y^3)` would be `{x, x, y, y, y}`.)
--/
-def degrees (p : MvPolynomial σ R) : Multiset σ :=
-  letI := Classical.decEq σ
-  p.support.sup fun s : σ →₀ ℕ => toMultiset s
-#align mv_polynomial.degrees MvPolynomial.degrees
-
-theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
-    p.degrees = p.support.sup fun s : σ →₀ ℕ => Finsupp.toMultiset s := by rw [degrees]; convert rfl
-#align mv_polynomial.degrees_def MvPolynomial.degrees_def
-
-theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ toMultiset s := by
-  classical
-    refine' Finset.sup_le fun t h => _
-    have := Finsupp.support_single_subset h
-    rw [Finset.mem_singleton] at this
-    rw [this]
-#align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomial
-
-theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
-    degrees (monomial s a) = toMultiset s := by
-  classical
-    refine' le_antisymm (degrees_monomial s a) <| Finset.le_sup <| _
-    rw [support_monomial, if_neg ha, Finset.mem_singleton]
-#align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eq
-
-theorem degrees_C (a : R) : degrees (C a : MvPolynomial σ R) = 0 :=
-  Multiset.le_zero.1 <| degrees_monomial _ _
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.degrees_C MvPolynomial.degrees_C
-
-theorem degrees_X' (n : σ) : degrees (X n : MvPolynomial σ R) ≤ {n} :=
-  le_trans (degrees_monomial _ _) <| le_of_eq <| toMultiset_single _ _
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.degrees_X' MvPolynomial.degrees_X'
-
-@[simp]
-theorem degrees_X [Nontrivial R] (n : σ) : degrees (X n : MvPolynomial σ R) = {n} :=
-  (degrees_monomial_eq _ (1 : R) one_ne_zero).trans (toMultiset_single _ _)
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.degrees_X MvPolynomial.degrees_X
-
-@[simp]
-theorem degrees_zero : degrees (0 : MvPolynomial σ R) = 0 := by
-  rw [← C_0]
-  exact degrees_C 0
-#align mv_polynomial.degrees_zero MvPolynomial.degrees_zero
-
-@[simp]
-theorem degrees_one : degrees (1 : MvPolynomial σ R) = 0 :=
-  degrees_C 1
-#align mv_polynomial.degrees_one MvPolynomial.degrees_one
-
-theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
-    (p + q).degrees ≤ p.degrees ⊔ q.degrees := by
-  classical
-  simp_rw [degrees_def]
-  refine' Finset.sup_le fun b hb => _
-  have := Finsupp.support_add hb; rw [Finset.mem_union] at this
-  cases' this with h h
-  · exact le_sup_of_le_left (Finset.le_sup h)
-  · exact le_sup_of_le_right (Finset.le_sup h)
-#align mv_polynomial.degrees_add MvPolynomial.degrees_add
-
-theorem degrees_sum {ι : Type*} [DecidableEq σ] (s : Finset ι) (f : ι → MvPolynomial σ R) :
-    (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by
-  classical
-  refine' s.induction _ _
-  · simp only [Finset.sum_empty, Finset.sup_empty, degrees_zero]
-    exact le_rfl
-  · intro i s his ih
-    rw [Finset.sup_insert, Finset.sum_insert his]
-    exact le_trans (degrees_add _ _) (sup_le_sup_left ih _)
-#align mv_polynomial.degrees_sum MvPolynomial.degrees_sum
-
-theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees := by
-  classical
-  refine (Finset.sup_mono <| support_mul p q).trans <| Finset.sup_add_le.2 fun a ha b hb ↦ ?_
-  rw [Finsupp.toMultiset_add]
-  exact add_le_add (Finset.le_sup ha) (Finset.le_sup hb)
-#align mv_polynomial.degrees_mul MvPolynomial.degrees_mul
-
-theorem degrees_prod {ι : Type*} (s : Finset ι) (f : ι → MvPolynomial σ R) :
-    (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees :=
-  Finset.le_prod_of_submultiplicative (Multiplicative.ofAdd ∘ degrees) degrees_one degrees_mul _ _
-#align mv_polynomial.degrees_prod MvPolynomial.degrees_prod
-
-theorem degrees_pow (p : MvPolynomial σ R) (n : ℕ) : (p ^ n).degrees ≤ n • p.degrees := by
-  simpa using degrees_prod (Finset.range n) fun _ ↦ p
-#align mv_polynomial.degrees_pow MvPolynomial.degrees_pow
-
-theorem mem_degrees {p : MvPolynomial σ R} {i : σ} :
-    i ∈ p.degrees ↔ ∃ d, p.coeff d ≠ 0 ∧ i ∈ d.support := by
-  classical
-  simp only [degrees_def, Multiset.mem_sup, ← mem_support_iff, Finsupp.mem_toMultiset, exists_prop]
-#align mv_polynomial.mem_degrees MvPolynomial.mem_degrees
-
-theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degrees) :
-    p.degrees ≤ (p + q).degrees := by
-  classical
-  apply Finset.sup_le
-  intro d hd
-  rw [Multiset.disjoint_iff_ne] at h
-  rw [Multiset.le_iff_count]
-  intro i
-  rw [degrees, Multiset.count_finset_sup]
-  simp only [Finsupp.count_toMultiset]
-  by_cases h0 : d = 0
-  · simp only [h0, zero_le, Finsupp.zero_apply]
-  · refine' @Finset.le_sup _ _ _ _ (p + q).support (fun a => a i) d _
-    rw [mem_support_iff, coeff_add]
-    suffices q.coeff d = 0 by rwa [this, add_zero, coeff, ← Finsupp.mem_support_iff]
-    rw [← Finsupp.support_eq_empty, ← Ne.def, ← Finset.nonempty_iff_ne_empty] at h0
-    obtain ⟨j, hj⟩ := h0
-    contrapose! h
-    rw [mem_support_iff] at hd
-    refine' ⟨j, _, j, _, rfl⟩
-    all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
-#align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_add
-
-theorem degrees_add_of_disjoint [DecidableEq σ] {p q : MvPolynomial σ R}
-    (h : Multiset.Disjoint p.degrees q.degrees) : (p + q).degrees = p.degrees ∪ q.degrees := by
-  apply le_antisymm
-  · apply degrees_add
-  · apply Multiset.union_le
-    · apply le_degrees_add h
-    · rw [add_comm]
-      apply le_degrees_add h.symm
-#align mv_polynomial.degrees_add_of_disjoint MvPolynomial.degrees_add_of_disjoint
-
-theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
-    (map f p).degrees ⊆ p.degrees := by
-  classical
-  dsimp only [degrees]
-  apply Multiset.subset_of_le
-  apply Finset.sup_mono
-  apply MvPolynomial.support_map_subset
-#align mv_polynomial.degrees_map MvPolynomial.degrees_map
-
-theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
-    (rename f φ).degrees ⊆ φ.degrees.map f := by
-  classical
-  intro i
-  rw [mem_degrees, Multiset.mem_map]
-  rintro ⟨d, hd, hi⟩
-  obtain ⟨x, rfl, hx⟩ := coeff_rename_ne_zero _ _ _ hd
-  simp only [Finsupp.mapDomain, Finsupp.mem_support_iff] at hi
-  rw [sum_apply, Finsupp.sum] at hi
-  contrapose! hi
-  rw [Finset.sum_eq_zero]
-  intro j hj
-  simp only [exists_prop, mem_degrees] at hi
-  specialize hi j ⟨x, hx, hj⟩
-  rw [Finsupp.single_apply, if_neg hi]
-#align mv_polynomial.degrees_rename MvPolynomial.degrees_rename
-
-theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R →+* S}
-    (hf : Injective f) : (map f p).degrees = p.degrees := by
-  simp only [degrees, MvPolynomial.support_map_of_injective _ hf]
-#align mv_polynomial.degrees_map_of_injective MvPolynomial.degrees_map_of_injective
-
-theorem degrees_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f) :
-    degrees (rename f p) = (degrees p).map f := by
-  classical
-  simp only [degrees, Multiset.map_finset_sup p.support Finsupp.toMultiset f h,
-    support_rename_of_injective h, Finset.sup_image]
-  refine' Finset.sup_congr rfl fun x _ => _
-  exact (Finsupp.toMultiset_map _ _).symm
-#align mv_polynomial.degrees_rename_of_injective MvPolynomial.degrees_rename_of_injective
-
-end Degrees
-
 section Vars
 
 /-! ### `vars` -/
@@ -464,334 +269,6 @@ end Map
 
 end Vars
 
-section DegreeOf
-
-/-! ### `degreeOf` -/
-
-
-/-- `degreeOf n p` gives the highest power of X_n that appears in `p` -/
-def degreeOf (n : σ) (p : MvPolynomial σ R) : ℕ :=
-  letI := Classical.decEq σ
-  p.degrees.count n
-#align mv_polynomial.degree_of MvPolynomial.degreeOf
-
-theorem degreeOf_def [DecidableEq σ] (n : σ) (p : MvPolynomial σ R) :
-    p.degreeOf n = p.degrees.count n := by rw [degreeOf]; convert rfl
-#align mv_polynomial.degree_of_def MvPolynomial.degreeOf_def
-
-theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
-    degreeOf n f = f.support.sup fun m => m n := by
-  classical
-  rw [degreeOf_def, degrees, Multiset.count_finset_sup]
-  congr
-  ext
-  simp
-#align mv_polynomial.degree_of_eq_sup MvPolynomial.degreeOf_eq_sup
-
-theorem degreeOf_lt_iff {n : σ} {f : MvPolynomial σ R} {d : ℕ} (h : 0 < d) :
-    degreeOf n f < d ↔ ∀ m : σ →₀ ℕ, m ∈ f.support → m n < d := by
-  rwa [degreeOf_eq_sup, Finset.sup_lt_iff]
-#align mv_polynomial.degree_of_lt_iff MvPolynomial.degreeOf_lt_iff
-
-lemma degreeOf_le_iff {n : σ} {f : MvPolynomial σ R} {d : ℕ} :
-    degreeOf n f ≤ d ↔ ∀ m ∈ support f, m n ≤ d := by
-  rw [degreeOf_eq_sup, Finset.sup_le_iff]
-
-@[simp]
-theorem degreeOf_zero (n : σ) : degreeOf n (0 : MvPolynomial σ R) = 0 := by
-  classical simp only [degreeOf_def, degrees_zero, Multiset.count_zero]
-#align mv_polynomial.degree_of_zero MvPolynomial.degreeOf_zero
-
-@[simp]
-theorem degreeOf_C (a : R) (x : σ) : degreeOf x (C a : MvPolynomial σ R) = 0 := by
-  classical simp [degreeOf_def, degrees_C]
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.degree_of_C MvPolynomial.degreeOf_C
-
-theorem degreeOf_X [DecidableEq σ] (i j : σ) [Nontrivial R] :
-    degreeOf i (X j : MvPolynomial σ R) = if i = j then 1 else 0 := by
-  classical
-  by_cases c : i = j
-  · simp only [c, if_true, eq_self_iff_true, degreeOf_def, degrees_X, Multiset.count_singleton]
-  simp [c, if_false, degreeOf_def, degrees_X]
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.degree_of_X MvPolynomial.degreeOf_X
-
-theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
-    degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) := by
-  letI := Classical.decEq σ
-  repeat' rw [degreeOf]
-  apply (Multiset.count_le_of_le n (degrees_add f g)).trans
-  dsimp
-  rw [Multiset.count_union]
-#align mv_polynomial.degree_of_add_le MvPolynomial.degreeOf_add_le
-
-theorem monomial_le_degreeOf (i : σ) {f : MvPolynomial σ R} {m : σ →₀ ℕ} (h_m : m ∈ f.support) :
-    m i ≤ degreeOf i f := by
-  rw [degreeOf_eq_sup i]
-  apply Finset.le_sup h_m
-#align mv_polynomial.monomial_le_degree_of MvPolynomial.monomial_le_degreeOf
-
--- TODO we can prove equality here if R is a domain
-theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
-    degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g := by
-  classical
-  repeat' rw [degreeOf]
-  convert Multiset.count_le_of_le i (degrees_mul f g)
-  rw [Multiset.count_add]
-#align mv_polynomial.degree_of_mul_le MvPolynomial.degreeOf_mul_le
-
-theorem degreeOf_mul_X_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
-    degreeOf i (f * X j) = degreeOf i f := by
-  classical
-  repeat' rw [degreeOf_eq_sup (R := R) i]
-  rw [support_mul_X]
-  simp only [Finset.sup_map]
-  congr
-  ext
-  simp only [Finsupp.single, Nat.one_ne_zero, add_right_eq_self, addRightEmbedding_apply, coe_mk,
-    Pi.add_apply, comp_apply, ite_eq_right_iff, Finsupp.coe_add, Pi.single_eq_of_ne h]
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.degree_of_mul_X_ne MvPolynomial.degreeOf_mul_X_ne
-
--- TODO in the following we have equality iff f ≠ 0
-theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
-    degreeOf j (f * X j) ≤ degreeOf j f + 1 := by
-  classical
-  repeat' rw [degreeOf]
-  apply (Multiset.count_le_of_le j (degrees_mul f (X j))).trans
-  simp only [Multiset.count_add, add_le_add_iff_left]
-  convert Multiset.count_le_of_le j (degrees_X' (R := R) j)
-  rw [Multiset.count_singleton_self]
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eq
-
-theorem degreeOf_C_mul_le (p : MvPolynomial σ R) (i : σ) (c : R) :
-    (C c * p).degreeOf i ≤ p.degreeOf i := by
-  unfold degreeOf
-  convert Multiset.count_le_of_le i <| degrees_mul (C c) p
-  simp [degrees_C]
-
-theorem degreeOf_mul_C_le (p : MvPolynomial σ R) (i : σ) (c : R) :
-    (p * C c).degreeOf i ≤ p.degreeOf i := by
-  unfold degreeOf
-  convert Multiset.count_le_of_le i <| degrees_mul p (C c)
-  simp [degrees_C]
-
-theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
-    (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by
-  classical
-  simp only [degreeOf, degrees_rename_of_injective h, Multiset.count_map_eq_count' f p.degrees h]
-#align mv_polynomial.degree_of_rename_of_injective MvPolynomial.degreeOf_rename_of_injective
-
-end DegreeOf
-
-section TotalDegree
-
-/-! ### `totalDegree` -/
-
-
-/-- `totalDegree p` gives the maximum |s| over the monomials X^s in `p` -/
-def totalDegree (p : MvPolynomial σ R) : ℕ :=
-  p.support.sup fun s => s.sum fun _ e => e
-#align mv_polynomial.total_degree MvPolynomial.totalDegree
-
-theorem totalDegree_eq (p : MvPolynomial σ R) :
-    p.totalDegree = p.support.sup fun m => Multiset.card (toMultiset m) := by
-  rw [totalDegree]
-  congr; funext m
-  exact (Finsupp.card_toMultiset _).symm
-#align mv_polynomial.total_degree_eq MvPolynomial.totalDegree_eq
-
-theorem le_totalDegree {p : MvPolynomial σ R} {s : σ →₀ ℕ} (h : s ∈ p.support) :
-    (s.sum fun _ e => e) ≤ totalDegree p :=
-  Finset.le_sup (α := ℕ) (f := fun s => sum s fun _ e => e) h
-
-theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) :
-    p.totalDegree ≤ Multiset.card p.degrees := by
-  classical
-  rw [totalDegree_eq]
-  exact Finset.sup_le fun s hs => Multiset.card_le_card <| Finset.le_sup hs
-#align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
-
-theorem totalDegree_le_of_support_subset (h : p.support ⊆ q.support) :
-    totalDegree p ≤ totalDegree q :=
-  Finset.sup_mono h
-
-@[simp]
-theorem totalDegree_C (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
-  Nat.eq_zero_of_le_zero <|
-    Finset.sup_le fun n hn => by
-      have := Finsupp.support_single_subset hn
-      rw [Finset.mem_singleton] at this
-      subst this
-      exact le_rfl
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.total_degree_C MvPolynomial.totalDegree_C
-
-@[simp]
-theorem totalDegree_zero : (0 : MvPolynomial σ R).totalDegree = 0 := by
-  rw [← C_0]; exact totalDegree_C (0 : R)
-#align mv_polynomial.total_degree_zero MvPolynomial.totalDegree_zero
-
-@[simp]
-theorem totalDegree_one : (1 : MvPolynomial σ R).totalDegree = 0 :=
-  totalDegree_C (1 : R)
-#align mv_polynomial.total_degree_one MvPolynomial.totalDegree_one
-
-@[simp]
-theorem totalDegree_X {R} [CommSemiring R] [Nontrivial R] (s : σ) :
-    (X s : MvPolynomial σ R).totalDegree = 1 := by
-  rw [totalDegree, support_X]
-  simp only [Finset.sup, Finsupp.sum_single_index, Finset.fold_singleton, sup_bot_eq]
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.total_degree_X MvPolynomial.totalDegree_X
-
-theorem totalDegree_add (a b : MvPolynomial σ R) :
-    (a + b).totalDegree ≤ max a.totalDegree b.totalDegree :=
-  AddMonoidAlgebra.sup_support_add_le _ _ _
-#align mv_polynomial.total_degree_add MvPolynomial.totalDegree_add
-
-theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
-    (h : q.totalDegree < p.totalDegree) : (p + q).totalDegree = p.totalDegree := by
-  classical
-    apply le_antisymm
-    · rw [← max_eq_left_of_lt h]
-      exact totalDegree_add p q
-    by_cases hp : p = 0
-    · simp [hp]
-    obtain ⟨b, hb₁, hb₂⟩ :=
-      p.support.exists_mem_eq_sup (Finsupp.support_nonempty_iff.mpr hp) fun m : σ →₀ ℕ =>
-        Multiset.card (toMultiset m)
-    have hb : ¬b ∈ q.support := by
-      contrapose! h
-      rw [totalDegree_eq p, hb₂, totalDegree_eq]
-      apply Finset.le_sup h
-    have hbb : b ∈ (p + q).support := by
-      apply support_sdiff_support_subset_support_add
-      rw [Finset.mem_sdiff]
-      exact ⟨hb₁, hb⟩
-    rw [totalDegree_eq, hb₂, totalDegree_eq]
-    exact Finset.le_sup (f := fun m => Multiset.card (Finsupp.toMultiset m)) hbb
-#align mv_polynomial.total_degree_add_eq_left_of_total_degree_lt MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt
-
-theorem totalDegree_add_eq_right_of_totalDegree_lt {p q : MvPolynomial σ R}
-    (h : q.totalDegree < p.totalDegree) : (q + p).totalDegree = p.totalDegree := by
-  rw [add_comm, totalDegree_add_eq_left_of_totalDegree_lt h]
-#align mv_polynomial.total_degree_add_eq_right_of_total_degree_lt MvPolynomial.totalDegree_add_eq_right_of_totalDegree_lt
-
-theorem totalDegree_mul (a b : MvPolynomial σ R) :
-    (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
-  AddMonoidAlgebra.sup_support_mul_le
-    (by exact (Finsupp.sum_add_index' (fun _ => rfl) (fun _ _ _ => rfl)).le) _ _
-#align mv_polynomial.total_degree_mul MvPolynomial.totalDegree_mul
-
-theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f : MvPolynomial σ S) :
-    (a • f).totalDegree ≤ f.totalDegree :=
-  Finset.sup_mono support_smul
-#align mv_polynomial.total_degree_smul_le MvPolynomial.totalDegree_smul_le
-
-theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) :
-    (a ^ n).totalDegree ≤ n * a.totalDegree := by
-  induction' n with n ih
-  · simp only [Nat.zero_eq, pow_zero, totalDegree_one, zero_mul, le_refl]
-  rw [pow_succ]
-  calc
-    totalDegree (a * a ^ n) ≤ a.totalDegree + (a ^ n).totalDegree := totalDegree_mul _ _
-    _ ≤ a.totalDegree + n * a.totalDegree := (add_le_add_left ih _)
-    _ = (n + 1) * a.totalDegree := by rw [add_mul, one_mul, add_comm]
-#align mv_polynomial.total_degree_pow MvPolynomial.totalDegree_pow
-
-@[simp]
-theorem totalDegree_monomial (s : σ →₀ ℕ) {c : R} (hc : c ≠ 0) :
-    (monomial s c : MvPolynomial σ R).totalDegree = s.sum fun _ e => e := by
-  classical simp [totalDegree, support_monomial, if_neg hc]
-#align mv_polynomial.total_degree_monomial MvPolynomial.totalDegree_monomial
-
-@[simp]
-theorem totalDegree_X_pow [Nontrivial R] (s : σ) (n : ℕ) :
-    (X s ^ n : MvPolynomial σ R).totalDegree = n := by simp [X_pow_eq_monomial, one_ne_zero]
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.total_degree_X_pow MvPolynomial.totalDegree_X_pow
-
-/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-theorem totalDegree_list_prod :
-    ∀ s : List (MvPolynomial σ R), s.prod.totalDegree ≤ (s.map MvPolynomial.totalDegree).sum
-  | [] => by rw [@List.prod_nil (MvPolynomial σ R) _, totalDegree_one]; rfl
-  | p::ps => by
-    rw [@List.prod_cons (MvPolynomial σ R) _, List.map, List.sum_cons]
-    exact le_trans (totalDegree_mul _ _) (add_le_add_left (totalDegree_list_prod ps) _)
-#align mv_polynomial.total_degree_list_prod MvPolynomial.totalDegree_list_prod
-
-theorem totalDegree_multiset_prod (s : Multiset (MvPolynomial σ R)) :
-    s.prod.totalDegree ≤ (s.map MvPolynomial.totalDegree).sum := by
-  refine' Quotient.inductionOn s fun l => _
-  rw [Multiset.quot_mk_to_coe, Multiset.prod_coe, Multiset.map_coe, Multiset.sum_coe]
-  exact totalDegree_list_prod l
-#align mv_polynomial.total_degree_multiset_prod MvPolynomial.totalDegree_multiset_prod
-
-theorem totalDegree_finset_prod {ι : Type*} (s : Finset ι) (f : ι → MvPolynomial σ R) :
-    (s.prod f).totalDegree ≤ ∑ i in s, (f i).totalDegree := by
-  refine' le_trans (totalDegree_multiset_prod _) _
-  rw [Multiset.map_map]
-  rfl
-#align mv_polynomial.total_degree_finset_prod MvPolynomial.totalDegree_finset_prod
-
-theorem totalDegree_finset_sum {ι : Type*} (s : Finset ι) (f : ι → MvPolynomial σ R) :
-    (s.sum f).totalDegree ≤ Finset.sup s fun i => (f i).totalDegree := by
-  induction' s using Finset.cons_induction with a s has hind
-  · exact zero_le _
-  · rw [Finset.sum_cons, Finset.sup_cons, sup_eq_max]
-    exact (MvPolynomial.totalDegree_add _ _).trans (max_le_max le_rfl hind)
-#align mv_polynomial.total_degree_finset_sum MvPolynomial.totalDegree_finset_sum
-
-lemma degreeOf_le_totalDegree (f : MvPolynomial σ R) (i : σ) : f.degreeOf i ≤ f.totalDegree :=
-  degreeOf_le_iff.mpr fun d hd ↦ (eq_or_ne (d i) 0).elim (·.trans_le zero_le') fun h ↦
-    (Finset.single_le_sum (fun _ _ ↦ zero_le') <| Finsupp.mem_support_iff.mpr h).trans
-    (le_totalDegree hd)
-
-theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
-    (h : f.totalDegree < n * Fintype.card σ) {d : σ →₀ ℕ} (hd : d ∈ f.support) : ∃ i, d i < n := by
-  contrapose! h
-  calc
-    n * Fintype.card σ = ∑ _s : σ, n := by
-      rw [Finset.sum_const, Nat.nsmul_eq_mul, mul_comm, Finset.card_univ]
-    _ ≤ ∑ s, d s := (Finset.sum_le_sum fun s _ => h s)
-    _ ≤ d.sum fun _ e => e := by
-      rw [Finsupp.sum_fintype]
-      intros
-      rfl
-    _ ≤ f.totalDegree := le_totalDegree hd
-#align mv_polynomial.exists_degree_lt MvPolynomial.exists_degree_lt
-
-theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ ℕ}
-    (h : f.totalDegree < ∑ i in d.support, d i) : coeff d f = 0 := by
-  classical
-    rw [totalDegree, Finset.sup_lt_iff] at h
-    · specialize h d
-      rw [mem_support_iff] at h
-      refine' not_not.mp (mt h _)
-      exact lt_irrefl _
-    · exact lt_of_le_of_lt (Nat.zero_le _) h
-#align mv_polynomial.coeff_eq_zero_of_total_degree_lt MvPolynomial.coeff_eq_zero_of_totalDegree_lt
-
-theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
-    (rename f p).totalDegree ≤ p.totalDegree :=
-  Finset.sup_le fun b => by
-    classical
-    intro h
-    rw [rename_eq] at h
-    have h' := Finsupp.mapDomain_support h
-    rw [Finset.mem_image] at h'
-    rcases h' with ⟨s, hs, rfl⟩
-    rw [Finsupp.sum_mapDomain_index]
-    exact le_trans le_rfl (le_totalDegree hs)
-    exact fun _ => rfl
-    exact fun _ _ _ => rfl
-#align mv_polynomial.total_degree_rename_le MvPolynomial.totalDegree_rename_le
-
-end TotalDegree
-
 section EvalVars
 
 /-! ### `vars` and `eval` -/

Splits this file into two. The sections about degree related concepts are totally independent of the vars related concepts so this was a clean split.

These did not respect the naming convention by having the coe as a prefix instead of a suffix, or vice-versa. Also add a bunch of norm_cast

@@ -726,7 +726,7 @@ theorem totalDegree_list_prod :
 theorem totalDegree_multiset_prod (s : Multiset (MvPolynomial σ R)) :
     s.prod.totalDegree ≤ (s.map MvPolynomial.totalDegree).sum := by
   refine' Quotient.inductionOn s fun l => _
-  rw [Multiset.quot_mk_to_coe, Multiset.coe_prod, Multiset.coe_map, Multiset.coe_sum]
+  rw [Multiset.quot_mk_to_coe, Multiset.prod_coe, Multiset.map_coe, Multiset.sum_coe]
   exact totalDegree_list_prod l
 #align mv_polynomial.total_degree_multiset_prod MvPolynomial.totalDegree_multiset_prod
 

Adds lemma about the degree of a polynomial multiplied by a constant.

@@ -566,6 +566,18 @@ theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eq
 
+theorem degreeOf_C_mul_le (p : MvPolynomial σ R) (i : σ) (c : R) :
+    (C c * p).degreeOf i ≤ p.degreeOf i := by
+  unfold degreeOf
+  convert Multiset.count_le_of_le i <| degrees_mul (C c) p
+  simp [degrees_C]
+
+theorem degreeOf_mul_C_le (p : MvPolynomial σ R) (i : σ) (c : R) :
+    (p * C c).degreeOf i ≤ p.degreeOf i := by
+  unfold degreeOf
+  convert Multiset.count_le_of_le i <| degrees_mul p (C c)
+  simp [degrees_C]
+
 theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
     (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by
   classical

• add rename_isHomogeneous without Injective assumption, and rename rename_isHomogeneous to rename_isHomogeneous_iff.

• refactor degreeOf_le_totalDegree through restrictTotalDegree_le_restrictDegree

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

@@ -490,12 +490,12 @@ theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
 
 theorem degreeOf_lt_iff {n : σ} {f : MvPolynomial σ R} {d : ℕ} (h : 0 < d) :
     degreeOf n f < d ↔ ∀ m : σ →₀ ℕ, m ∈ f.support → m n < d := by
-  rwa [degreeOf_eq_sup n f, Finset.sup_lt_iff]
+  rwa [degreeOf_eq_sup, Finset.sup_lt_iff]
 #align mv_polynomial.degree_of_lt_iff MvPolynomial.degreeOf_lt_iff
 
 lemma degreeOf_le_iff {n : σ} {f : MvPolynomial σ R} {d : ℕ} :
     degreeOf n f ≤ d ↔ ∀ m ∈ support f, m n ≤ d := by
-  simp only [← Nat.lt_succ_iff, degreeOf_lt_iff (Nat.succ_pos _)]
+  rw [degreeOf_eq_sup, Finset.sup_le_iff]
 
 @[simp]
 theorem degreeOf_zero (n : σ) : degreeOf n (0 : MvPolynomial σ R) = 0 := by
@@ -733,13 +733,10 @@ theorem totalDegree_finset_sum {ι : Type*} (s : Finset ι) (f : ι → MvPolyno
     exact (MvPolynomial.totalDegree_add _ _).trans (max_le_max le_rfl hind)
 #align mv_polynomial.total_degree_finset_sum MvPolynomial.totalDegree_finset_sum
 
-lemma degreeOf_le_totalDegree (f : MvPolynomial σ R) (i : σ) : f.degreeOf i ≤ f.totalDegree := by
-  rw [degreeOf_le_iff]
-  intro d hd
-  refine le_trans ?_ (le_totalDegree hd)
-  if hi : i ∈ d.support
-  then exact Finset.single_le_sum (fun _ _ ↦ zero_le') hi
-  else rw [Finsupp.not_mem_support_iff] at hi; simp only [hi, zero_le]
+lemma degreeOf_le_totalDegree (f : MvPolynomial σ R) (i : σ) : f.degreeOf i ≤ f.totalDegree :=
+  degreeOf_le_iff.mpr fun d hd ↦ (eq_or_ne (d i) 0).elim (·.trans_le zero_le') fun h ↦
+    (Finset.single_le_sum (fun _ _ ↦ zero_le') <| Finsupp.mem_support_iff.mpr h).trans
+    (le_totalDegree hd)
 
 theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
     (h : f.totalDegree < n * Fintype.card σ) {d : σ →₀ ℕ} (hd : d ∈ f.support) : ∃ i, d i < n := by

@@ -493,6 +493,10 @@ theorem degreeOf_lt_iff {n : σ} {f : MvPolynomial σ R} {d : ℕ} (h : 0 < d) :
   rwa [degreeOf_eq_sup n f, Finset.sup_lt_iff]
 #align mv_polynomial.degree_of_lt_iff MvPolynomial.degreeOf_lt_iff
 
+lemma degreeOf_le_iff {n : σ} {f : MvPolynomial σ R} {d : ℕ} :
+    degreeOf n f ≤ d ↔ ∀ m ∈ support f, m n ≤ d := by
+  simp only [← Nat.lt_succ_iff, degreeOf_lt_iff (Nat.succ_pos _)]
+
 @[simp]
 theorem degreeOf_zero (n : σ) : degreeOf n (0 : MvPolynomial σ R) = 0 := by
   classical simp only [degreeOf_def, degrees_zero, Multiset.count_zero]
@@ -729,6 +733,14 @@ theorem totalDegree_finset_sum {ι : Type*} (s : Finset ι) (f : ι → MvPolyno
     exact (MvPolynomial.totalDegree_add _ _).trans (max_le_max le_rfl hind)
 #align mv_polynomial.total_degree_finset_sum MvPolynomial.totalDegree_finset_sum
 
+lemma degreeOf_le_totalDegree (f : MvPolynomial σ R) (i : σ) : f.degreeOf i ≤ f.totalDegree := by
+  rw [degreeOf_le_iff]
+  intro d hd
+  refine le_trans ?_ (le_totalDegree hd)
+  if hi : i ∈ d.support
+  then exact Finset.single_le_sum (fun _ _ ↦ zero_le') hi
+  else rw [Finsupp.not_mem_support_iff] at hi; simp only [hi, zero_le]
+
 theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
     (h : f.totalDegree < n * Fintype.card σ) {d : σ →₀ ℕ} (hd : d ∈ f.support) : ∃ i, d i < n := by
   contrapose! h

This involves moving lemmas from Algebra.GroupPower.Ring to Algebra.GroupWithZero.Basic and changing some 0 < n assumptions to n ≠ 0.

From LeanAPAP

@@ -802,7 +802,7 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
       rintro rfl
       contradiction
     rw [Finsupp.prod, Finset.prod_eq_zero hi, mul_zero]
-    rw [hp, zero_pow (Nat.pos_of_ne_zero <| Finsupp.mem_support_iff.mp hi)]
+    rw [hp, zero_pow (Finsupp.mem_support_iff.1 hi)]
     rw [mem_vars]
     exact ⟨d, hd, hi⟩
 #align mv_polynomial.eval₂_hom_eq_constant_coeff_of_vars MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars

Use pointwise multiplication/addition of Finsets in MonoidAlgebra.support_mul and AddMonoidAlgebra.support_mul.

@@ -159,29 +159,18 @@ theorem degrees_sum {ι : Type*} [DecidableEq σ] (s : Finset ι) (f : ι → Mv
 
 theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees := by
   classical
-  refine' Finset.sup_le fun b hb => _
-  have := support_mul p q hb
-  simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
-  rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
+  refine (Finset.sup_mono <| support_mul p q).trans <| Finset.sup_add_le.2 fun a ha b hb ↦ ?_
   rw [Finsupp.toMultiset_add]
-  exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
+  exact add_le_add (Finset.le_sup ha) (Finset.le_sup hb)
 #align mv_polynomial.degrees_mul MvPolynomial.degrees_mul
 
 theorem degrees_prod {ι : Type*} (s : Finset ι) (f : ι → MvPolynomial σ R) :
-    (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees := by
-  classical
-  refine' s.induction _ _
-  · simp only [Finset.prod_empty, Finset.sum_empty, degrees_one, le_refl]
-  · intro i s his ih
-    rw [Finset.prod_insert his, Finset.sum_insert his]
-    exact le_trans (degrees_mul _ _) (add_le_add_left ih _)
+    (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees :=
+  Finset.le_prod_of_submultiplicative (Multiplicative.ofAdd ∘ degrees) degrees_one degrees_mul _ _
 #align mv_polynomial.degrees_prod MvPolynomial.degrees_prod
 
-theorem degrees_pow (p : MvPolynomial σ R) : ∀ n : ℕ, (p ^ n).degrees ≤ n • p.degrees
-  | 0 => by rw [pow_zero, degrees_one]; exact Multiset.zero_le _
-  | n + 1 => by
-    rw [pow_succ, add_smul, add_comm, one_smul]
-    exact le_trans (degrees_mul _ _) (add_le_add_left (degrees_pow _ n) _)
+theorem degrees_pow (p : MvPolynomial σ R) (n : ℕ) : (p ^ n).degrees ≤ n • p.degrees := by
+  simpa using degrees_prod (Finset.range n) fun _ ↦ p
 #align mv_polynomial.degrees_pow MvPolynomial.degrees_pow
 
 theorem mem_degrees {p : MvPolynomial σ R} {i : σ} :

Change a few lemma names that have historically bothered me.

• Finset.card_le_of_subset → Finset.card_le_card
• Multiset.card_le_of_le → Multiset.card_le_card
• Multiset.card_lt_of_lt → Multiset.card_lt_card
• Set.ncard_le_of_subset → Set.ncard_le_ncard
• Finset.image_filter → Finset.filter_image
• CompleteLattice.finset_sup_compact_of_compact → CompleteLattice.isCompactElement_finset_sup

@@ -606,7 +606,7 @@ theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) :
     p.totalDegree ≤ Multiset.card p.degrees := by
   classical
   rw [totalDegree_eq]
-  exact Finset.sup_le fun s hs => Multiset.card_le_of_le <| Finset.le_sup hs
+  exact Finset.sup_le fun s hs => Multiset.card_le_card <| Finset.le_sup hs
 #align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
 
 theorem totalDegree_le_of_support_subset (h : p.support ⊆ q.support) :

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

@@ -303,7 +303,7 @@ theorem vars_X [Nontrivial R] : (X n : MvPolynomial σ R).vars = {n} := by
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.vars_X MvPolynomial.vars_X
 
-theorem mem_vars (i : σ) : i ∈ p.vars ↔ ∃ (d : σ →₀ ℕ) (_ : d ∈ p.support), i ∈ d.support := by
+theorem mem_vars (i : σ) : i ∈ p.vars ↔ ∃ d ∈ p.support, i ∈ d.support := by
   classical simp only [vars_def, Multiset.mem_toFinset, mem_degrees, mem_support_iff, exists_prop]
 #align mv_polynomial.mem_vars MvPolynomial.mem_vars
 
@@ -469,7 +469,6 @@ theorem vars_eq_support_biUnion_support [DecidableEq σ] :
     p.vars = p.support.biUnion Finsupp.support := by
   ext i
   rw [mem_vars, Finset.mem_biUnion]
-  simp
 #align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_biUnion_support
 
 end Map

From hairer.

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

@@ -610,6 +610,10 @@ theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) :
   exact Finset.sup_le fun s hs => Multiset.card_le_of_le <| Finset.le_sup hs
 #align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
 
+theorem totalDegree_le_of_support_subset (h : p.support ⊆ q.support) :
+    totalDegree p ≤ totalDegree q :=
+  Finset.sup_mono h
+
 @[simp]
 theorem totalDegree_C (a : R) : (C a : MvPolynomial σ R).totalDegree = 0 :=
   Nat.eq_zero_of_le_zero <|

PR contents

This is the supremum of

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

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

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

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

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

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

leanprover/lean4#2778

We can get rid of all the

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

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

leanprover/lean4#2722

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

leanprover/lean4#2783

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

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

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

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

@@ -686,7 +686,7 @@ theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f :
 theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) :
     (a ^ n).totalDegree ≤ n * a.totalDegree := by
   induction' n with n ih
-  · simp only [Nat.zero_eq, zero_mul, pow_zero, totalDegree_one]
+  · simp only [Nat.zero_eq, pow_zero, totalDegree_one, zero_mul, le_refl]
   rw [pow_succ]
   calc
     totalDegree (a * a ^ n) ≤ a.totalDegree + (a ^ n).totalDegree := totalDegree_mul _ _

We define a type class Finset.HasAntidiagonal A which contains a function antidiagonal : A → Finset (A × A) such that antidiagonal n is the Finset of all pairs adding to n, as witnessed by mem_antidiagonal.

When A is a canonically ordered add monoid with locally finite order this typeclass can be instantiated with Finset.antidiagonalOfLocallyFinite. This applies in particular when A is ℕ, more generally or σ →₀ ℕ, or even ι →₀ A under the additional assumption OrderedSub A that make it a canonically ordered add monoid. (In fact, we would just need an AddMonoid with a compatible order, finite Iic, such that if a + b = n, then a, b ≤ n, and any finiteness condition would be OK.)

For computational reasons it is better to manually provide instances for ℕ and σ →₀ ℕ, to avoid quadratic runtime performance. These instances are provided as Finset.Nat.instHasAntidiagonal and Finsupp.instHasAntidiagonal. This is why Finset.antidiagonalOfLocallyFinite is an abbrev and not an instance.

This definition does not exactly match with that of Multiset.antidiagonal defined in Mathlib.Data.Multiset.Antidiagonal, because of the multiplicities. Indeed, by counting multiplicities, Multiset α is equivalent to α →₀ ℕ, but Finset.antidiagonal and Multiset.antidiagonal will return different objects. For example, for s : Multiset ℕ := {0,0,0}, Multiset.antidiagonal s has 8 elements but Finset.antidiagonal s has only 4.

def s : Multiset ℕ := {0, 0, 0}
#eval (Finset.antidiagonal s).card -- 4
#eval Multiset.card (Multiset.antidiagonal s) -- 8

TODO

• Define HasMulAntidiagonal (for monoids). For PNat, we will recover the set of divisors of a strictly positive integer.

This closes #7917

Co-authored by: María Inés de Frutos-Fernández <mariaines.dff@gmail.com> and Eric Wieser <efw27@cam.ac.uk>

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -348,7 +348,7 @@ theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars 
   cases hd
   rw [Finset.sum_eq_zero]
   rintro ⟨d₁, d₂⟩ H
-  rw [Finsupp.mem_antidiagonal] at H
+  rw [Finset.mem_antidiagonal] at H
   subst H
   obtain H | H : i ∈ d₁.support ∨ i ∈ d₂.support := by
     simpa only [Finset.mem_union] using Finsupp.support_add hi

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -686,7 +686,7 @@ theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f :
 theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) :
     (a ^ n).totalDegree ≤ n * a.totalDegree := by
   induction' n with n ih
-  · simp only [Nat.zero_eq, MulZeroClass.zero_mul, pow_zero, totalDegree_one]
+  · simp only [Nat.zero_eq, zero_mul, pow_zero, totalDegree_one]
   rw [pow_succ]
   calc
     totalDegree (a * a ^ n) ≤ a.totalDegree + (a ^ n).totalDegree := totalDegree_mul _ _
@@ -809,7 +809,7 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
       rw [Finset.nonempty_iff_ne_empty, Ne.def, Finsupp.support_eq_empty]
       rintro rfl
       contradiction
-    rw [Finsupp.prod, Finset.prod_eq_zero hi, MulZeroClass.mul_zero]
+    rw [Finsupp.prod, Finset.prod_eq_zero hi, mul_zero]
     rw [hp, zero_pow (Nat.pos_of_ne_zero <| Finsupp.mem_support_iff.mp hi)]
     rw [mem_vars]
     exact ⟨d, hd, hi⟩

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

This has nice performance benefits.

@@ -41,9 +41,9 @@ monomial of $P$.
 
 As in other polynomial files, we typically use the notation:
 
-+ `σ τ : Type _` (indexing the variables)
++ `σ τ : Type*` (indexing the variables)
 
-+ `R : Type _` `[CommSemiring R]` (the coefficients)
++ `R : Type*` `[CommSemiring R]` (the coefficients)
 
 + `s : σ →₀ ℕ`, a function from `σ` to `ℕ` which is zero away from a finite set.
 This will give rise to a monomial in `MvPolynomial σ R` which mathematicians might call `X^s`
@@ -69,7 +69,7 @@ variable {R : Type u} {S : Type v}
 
 namespace MvPolynomial
 
-variable {σ τ : Type _} {r : R} {e : ℕ} {n m : σ} {s : σ →₀ ℕ}
+variable {σ τ : Type*} {r : R} {e : ℕ} {n m : σ} {s : σ →₀ ℕ}
 
 section CommSemiring
 
@@ -146,7 +146,7 @@ theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
   · exact le_sup_of_le_right (Finset.le_sup h)
 #align mv_polynomial.degrees_add MvPolynomial.degrees_add
 
-theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → MvPolynomial σ R) :
+theorem degrees_sum {ι : Type*} [DecidableEq σ] (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by
   classical
   refine' s.induction _ _
@@ -167,7 +167,7 @@ theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees +
   exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
 #align mv_polynomial.degrees_mul MvPolynomial.degrees_mul
 
-theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
+theorem degrees_prod {ι : Type*} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees := by
   classical
   refine' s.induction _ _
@@ -379,7 +379,7 @@ theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars
 /-- The variables of the product of a family of polynomials
 are a subset of the union of the sets of variables of each polynomial.
 -/
-theorem vars_prod {ι : Type _} [DecidableEq σ] {s : Finset ι} (f : ι → MvPolynomial σ R) :
+theorem vars_prod {ι : Type*} [DecidableEq σ] {s : Finset ι} (f : ι → MvPolynomial σ R) :
     (∏ i in s, f i).vars ⊆ s.biUnion fun i => (f i).vars := by
   classical
   induction s using Finset.induction_on with
@@ -392,7 +392,7 @@ theorem vars_prod {ι : Type _} [DecidableEq σ] {s : Finset ι} (f : ι → MvP
 
 section IsDomain
 
-variable {A : Type _} [CommRing A] [IsDomain A]
+variable {A : Type*} [CommRing A] [IsDomain A]
 
 theorem vars_C_mul (a : A) (ha : a ≠ 0) (φ : MvPolynomial σ A) :
     (C a * φ : MvPolynomial σ A).vars = φ.vars := by
@@ -411,7 +411,7 @@ end Mul
 
 section Sum
 
-variable {ι : Type _} (t : Finset ι) (φ : ι → MvPolynomial σ R)
+variable {ι : Type*} (t : Finset ι) (φ : ι → MvPolynomial σ R)
 
 theorem vars_sum_subset [DecidableEq σ] :
     (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by
@@ -722,14 +722,14 @@ theorem totalDegree_multiset_prod (s : Multiset (MvPolynomial σ R)) :
   exact totalDegree_list_prod l
 #align mv_polynomial.total_degree_multiset_prod MvPolynomial.totalDegree_multiset_prod
 
-theorem totalDegree_finset_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
+theorem totalDegree_finset_prod {ι : Type*} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (s.prod f).totalDegree ≤ ∑ i in s, (f i).totalDegree := by
   refine' le_trans (totalDegree_multiset_prod _) _
   rw [Multiset.map_map]
   rfl
 #align mv_polynomial.total_degree_finset_prod MvPolynomial.totalDegree_finset_prod
 
-theorem totalDegree_finset_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
+theorem totalDegree_finset_sum {ι : Type*} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (s.sum f).totalDegree ≤ Finset.sup s fun i => (f i).totalDegree := by
   induction' s using Finset.cons_induction with a s has hind
   · exact zero_le _

And other similar lemmas

With thanks to @adomani for adding these lemmas.

@@ -3,6 +3,7 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 -/
+import Mathlib.Algebra.MonoidAlgebra.Degree
 import Mathlib.Algebra.BigOperators.Order
 import Mathlib.Data.MvPolynomial.Rename
 
@@ -640,13 +641,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem totalDegree_add (a b : MvPolynomial σ R) :
     (a + b).totalDegree ≤ max a.totalDegree b.totalDegree :=
-  Finset.sup_le fun n hn => by
-    classical
-    have := Finsupp.support_add hn
-    rw [Finset.mem_union] at this
-    cases' this with h h
-    · exact le_max_of_le_left (le_totalDegree h)
-    · exact le_max_of_le_right (le_totalDegree h)
+  AddMonoidAlgebra.sup_support_add_le _ _ _
 #align mv_polynomial.total_degree_add MvPolynomial.totalDegree_add
 
 theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
@@ -679,18 +674,8 @@ theorem totalDegree_add_eq_right_of_totalDegree_lt {p q : MvPolynomial σ R}
 
 theorem totalDegree_mul (a b : MvPolynomial σ R) :
     (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
-  Finset.sup_le fun n hn => by
-    classical
-    have := AddMonoidAlgebra.support_mul a b hn
-    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
-    rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
-    rw [Finsupp.sum_add_index']
-    · dsimp [totalDegree]
-      exact add_le_add (le_totalDegree h₁) (le_totalDegree h₂)
-    · intro _
-      rfl
-    · intro _ b₁ b₂
-      rfl
+  AddMonoidAlgebra.sup_support_mul_le
+    (by exact (Finsupp.sum_add_index' (fun _ => rfl) (fun _ _ _ => rfl)).le) _ _
 #align mv_polynomial.total_degree_mul MvPolynomial.totalDegree_mul
 
 theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f : MvPolynomial σ S) :

• 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) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-
-! This file was ported from Lean 3 source module data.mv_polynomial.variables
-! 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.Algebra.BigOperators.Order
 import Mathlib.Data.MvPolynomial.Rename
 
+#align_import data.mv_polynomial.variables from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
+
 /-!
 # Degrees and variables of polynomials
 

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

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

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

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

@@ -597,7 +597,7 @@ def totalDegree (p : MvPolynomial σ R) : ℕ :=
 theorem totalDegree_eq (p : MvPolynomial σ R) :
     p.totalDegree = p.support.sup fun m => Multiset.card (toMultiset m) := by
   rw [totalDegree]
-  congr ; funext m
+  congr; funext m
   exact (Finsupp.card_toMultiset _).symm
 #align mv_polynomial.total_degree_eq MvPolynomial.totalDegree_eq
 

Changes are of the form

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

@@ -326,7 +326,7 @@ theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ
 theorem vars_add_subset [DecidableEq σ] (p q : MvPolynomial σ R) :
     (p + q).vars ⊆ p.vars ∪ q.vars := by
   intro x hx
-  simp only [vars_def, Finset.mem_union, Multiset.mem_toFinset] at hx⊢
+  simp only [vars_def, Finset.mem_union, Multiset.mem_toFinset] at hx ⊢
   simpa using Multiset.mem_of_le (degrees_add _ _) hx
 #align mv_polynomial.vars_add_subset MvPolynomial.vars_add_subset
 
@@ -334,7 +334,7 @@ theorem vars_add_of_disjoint [DecidableEq σ] (h : Disjoint p.vars q.vars) :
     (p + q).vars = p.vars ∪ q.vars := by
   apply Finset.Subset.antisymm (vars_add_subset p q)
   intro x hx
-  simp only [vars_def, Multiset.disjoint_toFinset] at h hx⊢
+  simp only [vars_def, Multiset.disjoint_toFinset] at h hx ⊢
   rw [degrees_add_of_disjoint h, Multiset.toFinset_union]
   exact hx
 #align mv_polynomial.vars_add_of_disjoint MvPolynomial.vars_add_of_disjoint
@@ -436,7 +436,7 @@ theorem vars_sum_of_disjoint [DecidableEq σ] (h : Pairwise <| (Disjoint on fun
     rw [Finset.biUnion_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
     unfold Pairwise onFun at h
     rw [hsum]
-    simp only [Finset.disjoint_iff_ne] at h⊢
+    simp only [Finset.disjoint_iff_ne] at h ⊢
     intro v hv v2 hv2
     rw [Finset.mem_biUnion] at hv2
     rcases hv2 with ⟨i, his, hi⟩
@@ -887,7 +887,7 @@ theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).vars ⊆ φ.vars.image f := by
   classical
   intro i hi
-  simp only [vars_def, exists_prop, Multiset.mem_toFinset, Finset.mem_image] at hi⊢
+  simp only [vars_def, exists_prop, Multiset.mem_toFinset, Finset.mem_image] at hi ⊢
   simpa only [Multiset.mem_map] using degrees_rename _ _ hi
 #align mv_polynomial.vars_rename MvPolynomial.vars_rename
 

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

@@ -554,7 +554,7 @@ theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
 theorem degreeOf_mul_X_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
     degreeOf i (f * X j) = degreeOf i f := by
   classical
-  repeat' rw [degreeOf_eq_sup (R:=R) i]
+  repeat' rw [degreeOf_eq_sup (R := R) i]
   rw [support_mul_X]
   simp only [Finset.sup_map]
   congr
@@ -571,7 +571,7 @@ theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
   repeat' rw [degreeOf]
   apply (Multiset.count_le_of_le j (degrees_mul f (X j))).trans
   simp only [Multiset.count_add, add_le_add_iff_left]
-  convert Multiset.count_le_of_le j (degrees_X' (R:=R) j)
+  convert Multiset.count_le_of_le j (degrees_X' (R := R) j)
   rw [Multiset.count_singleton_self]
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.degree_of_mul_X_eq MvPolynomial.degreeOf_mul_X_eq

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: Johannes Hölzl, Johan Commelin, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.variables
-! 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.
 -/
@@ -61,8 +61,6 @@ This will give rise to a monomial in `MvPolynomial σ R` which mathematicians mi
 
 noncomputable section
 
-open Classical BigOperators
-
 open Set Function Finsupp AddMonoidAlgebra
 
 open BigOperators
@@ -89,20 +87,27 @@ section Degrees
 (For example, `degrees (x^2 * y + y^3)` would be `{x, x, y, y, y}`.)
 -/
 def degrees (p : MvPolynomial σ R) : Multiset σ :=
+  letI := Classical.decEq σ
   p.support.sup fun s : σ →₀ ℕ => toMultiset s
 #align mv_polynomial.degrees MvPolynomial.degrees
 
-theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ toMultiset s :=
-  Finset.sup_le fun t h => by
+theorem degrees_def [DecidableEq σ] (p : MvPolynomial σ R) :
+    p.degrees = p.support.sup fun s : σ →₀ ℕ => Finsupp.toMultiset s := by rw [degrees]; convert rfl
+#align mv_polynomial.degrees_def MvPolynomial.degrees_def
+
+theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) ≤ toMultiset s := by
+  classical
+    refine' Finset.sup_le fun t h => _
     have := Finsupp.support_single_subset h
     rw [Finset.mem_singleton] at this
     rw [this]
 #align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomial
 
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :
-    degrees (monomial s a) = toMultiset s :=
-  le_antisymm (degrees_monomial s a) <|
-    Finset.le_sup <| by rw [support_monomial, if_neg ha, Finset.mem_singleton]
+    degrees (monomial s a) = toMultiset s := by
+  classical
+    refine' le_antisymm (degrees_monomial s a) <| Finset.le_sup <| _
+    rw [support_monomial, if_neg ha, Finset.mem_singleton]
 #align mv_polynomial.degrees_monomial_eq MvPolynomial.degrees_monomial_eq
 
 theorem degrees_C (a : R) : degrees (C a : MvPolynomial σ R) = 0 :=
@@ -132,7 +137,10 @@ theorem degrees_one : degrees (1 : MvPolynomial σ R) = 0 :=
   degrees_C 1
 #align mv_polynomial.degrees_one MvPolynomial.degrees_one
 
-theorem degrees_add (p q : MvPolynomial σ R) : (p + q).degrees ≤ p.degrees ⊔ q.degrees := by
+theorem degrees_add [DecidableEq σ] (p q : MvPolynomial σ R) :
+    (p + q).degrees ≤ p.degrees ⊔ q.degrees := by
+  classical
+  simp_rw [degrees_def]
   refine' Finset.sup_le fun b hb => _
   have := Finsupp.support_add hb; rw [Finset.mem_union] at this
   cases' this with h h
@@ -140,8 +148,9 @@ theorem degrees_add (p q : MvPolynomial σ R) : (p + q).degrees ≤ p.degrees 
   · exact le_sup_of_le_right (Finset.le_sup h)
 #align mv_polynomial.degrees_add MvPolynomial.degrees_add
 
-theorem degrees_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
+theorem degrees_sum {ι : Type _} [DecidableEq σ] (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∑ i in s, f i).degrees ≤ s.sup fun i => (f i).degrees := by
+  classical
   refine' s.induction _ _
   · simp only [Finset.sum_empty, Finset.sup_empty, degrees_zero]
     exact le_rfl
@@ -151,6 +160,7 @@ theorem degrees_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R)
 #align mv_polynomial.degrees_sum MvPolynomial.degrees_sum
 
 theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees := by
+  classical
   refine' Finset.sup_le fun b hb => _
   have := support_mul p q hb
   simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
@@ -161,6 +171,7 @@ theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees +
 
 theorem degrees_prod {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R) :
     (∏ i in s, f i).degrees ≤ ∑ i in s, (f i).degrees := by
+  classical
   refine' s.induction _ _
   · simp only [Finset.prod_empty, Finset.sum_empty, degrees_one, le_refl]
   · intro i s his ih
@@ -177,11 +188,13 @@ theorem degrees_pow (p : MvPolynomial σ R) : ∀ n : ℕ, (p ^ n).degrees ≤ n
 
 theorem mem_degrees {p : MvPolynomial σ R} {i : σ} :
     i ∈ p.degrees ↔ ∃ d, p.coeff d ≠ 0 ∧ i ∈ d.support := by
-  simp only [degrees, Multiset.mem_sup, ← mem_support_iff, Finsupp.mem_toMultiset, exists_prop]
+  classical
+  simp only [degrees_def, Multiset.mem_sup, ← mem_support_iff, Finsupp.mem_toMultiset, exists_prop]
 #align mv_polynomial.mem_degrees MvPolynomial.mem_degrees
 
 theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degrees) :
     p.degrees ≤ (p + q).degrees := by
+  classical
   apply Finset.sup_le
   intro d hd
   rw [Multiset.disjoint_iff_ne] at h
@@ -202,7 +215,7 @@ theorem le_degrees_add {p q : MvPolynomial σ R} (h : p.degrees.Disjoint q.degre
     all_goals rw [mem_degrees]; refine' ⟨d, _, hj⟩; assumption
 #align mv_polynomial.le_degrees_add MvPolynomial.le_degrees_add
 
-theorem degrees_add_of_disjoint {p q : MvPolynomial σ R}
+theorem degrees_add_of_disjoint [DecidableEq σ] {p q : MvPolynomial σ R}
     (h : Multiset.Disjoint p.degrees q.degrees) : (p + q).degrees = p.degrees ∪ q.degrees := by
   apply le_antisymm
   · apply degrees_add
@@ -214,6 +227,7 @@ theorem degrees_add_of_disjoint {p q : MvPolynomial σ R}
 
 theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
     (map f p).degrees ⊆ p.degrees := by
+  classical
   dsimp only [degrees]
   apply Multiset.subset_of_le
   apply Finset.sup_mono
@@ -222,6 +236,7 @@ theorem degrees_map [CommSemiring S] (p : MvPolynomial σ R) (f : R →+* S) :
 
 theorem degrees_rename (f : σ → τ) (φ : MvPolynomial σ R) :
     (rename f φ).degrees ⊆ φ.degrees.map f := by
+  classical
   intro i
   rw [mem_degrees, Multiset.mem_map]
   rintro ⟨d, hd, hi⟩
@@ -243,6 +258,7 @@ theorem degrees_map_of_injective [CommSemiring S] (p : MvPolynomial σ R) {f : R
 
 theorem degrees_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f) :
     degrees (rename f p) = (degrees p).map f := by
+  classical
   simp only [degrees, Multiset.map_finset_sup p.support Finsupp.toMultiset f h,
     support_rename_of_injective h, Finset.sup_image]
   refine' Finset.sup_congr rfl fun x _ => _
@@ -258,22 +274,28 @@ section Vars
 
 /-- `vars p` is the set of variables appearing in the polynomial `p` -/
 def vars (p : MvPolynomial σ R) : Finset σ :=
+  letI := Classical.decEq σ
   p.degrees.toFinset
 #align mv_polynomial.vars MvPolynomial.vars
 
+theorem vars_def [DecidableEq σ] (p : MvPolynomial σ R) : p.vars = p.degrees.toFinset := by
+  rw [vars]
+  convert rfl
+#align mv_polynomial.vars_def MvPolynomial.vars_def
+
 @[simp]
 theorem vars_0 : (0 : MvPolynomial σ R).vars = ∅ := by
-  rw [vars, degrees_zero, Multiset.toFinset_zero]
+  classical rw [vars_def, degrees_zero, Multiset.toFinset_zero]
 #align mv_polynomial.vars_0 MvPolynomial.vars_0
 
 @[simp]
 theorem vars_monomial (h : r ≠ 0) : (monomial s r).vars = s.support := by
-  rw [vars, degrees_monomial_eq _ _ h, Finsupp.toFinset_toMultiset]
+  classical rw [vars_def, degrees_monomial_eq _ _ h, Finsupp.toFinset_toMultiset]
 #align mv_polynomial.vars_monomial MvPolynomial.vars_monomial
 
 @[simp]
 theorem vars_C : (C r : MvPolynomial σ R).vars = ∅ := by
-  rw [vars, degrees_C, Multiset.toFinset_zero]
+  classical rw [vars_def, degrees_C, Multiset.toFinset_zero]
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.vars_C MvPolynomial.vars_C
 
@@ -284,15 +306,16 @@ set_option linter.uppercaseLean3 false in
 #align mv_polynomial.vars_X MvPolynomial.vars_X
 
 theorem mem_vars (i : σ) : i ∈ p.vars ↔ ∃ (d : σ →₀ ℕ) (_ : d ∈ p.support), i ∈ d.support := by
-  simp only [vars, Multiset.mem_toFinset, mem_degrees, mem_support_iff, exists_prop]
+  classical simp only [vars_def, Multiset.mem_toFinset, mem_degrees, mem_support_iff, exists_prop]
 #align mv_polynomial.mem_vars MvPolynomial.mem_vars
 
 theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ} (H : x ∈ f.support)
     {v : σ} (h : v ∉ vars f) : x v = 0 := by
-  rw [vars, Multiset.mem_toFinset] at h
+  classical
+  rw [vars_def, Multiset.mem_toFinset] at h
   rw [← Finsupp.not_mem_support_iff]
   contrapose! h
-  unfold degrees
+  rw [degrees_def]
   rw [show f.support = insert x f.support from Eq.symm <| Finset.insert_eq_of_mem H]
   rw [Finset.sup_insert]
   simp only [Multiset.mem_union, Multiset.sup_eq_union]
@@ -300,23 +323,25 @@ theorem mem_support_not_mem_vars_zero {f : MvPolynomial σ R} {x : σ →₀ ℕ
   rwa [← toFinset_toMultiset, Multiset.mem_toFinset] at h
 #align mv_polynomial.mem_support_not_mem_vars_zero MvPolynomial.mem_support_not_mem_vars_zero
 
-theorem vars_add_subset (p q : MvPolynomial σ R) : (p + q).vars ⊆ p.vars ∪ q.vars := by
+theorem vars_add_subset [DecidableEq σ] (p q : MvPolynomial σ R) :
+    (p + q).vars ⊆ p.vars ∪ q.vars := by
   intro x hx
-  simp only [vars, Finset.mem_union, Multiset.mem_toFinset] at hx⊢
+  simp only [vars_def, Finset.mem_union, Multiset.mem_toFinset] at hx⊢
   simpa using Multiset.mem_of_le (degrees_add _ _) hx
 #align mv_polynomial.vars_add_subset MvPolynomial.vars_add_subset
 
-theorem vars_add_of_disjoint (h : Disjoint p.vars q.vars) : (p + q).vars = p.vars ∪ q.vars := by
+theorem vars_add_of_disjoint [DecidableEq σ] (h : Disjoint p.vars q.vars) :
+    (p + q).vars = p.vars ∪ q.vars := by
   apply Finset.Subset.antisymm (vars_add_subset p q)
   intro x hx
-  simp only [vars, Multiset.disjoint_toFinset] at h hx⊢
+  simp only [vars_def, Multiset.disjoint_toFinset] at h hx⊢
   rw [degrees_add_of_disjoint h, Multiset.toFinset_union]
   exact hx
 #align mv_polynomial.vars_add_of_disjoint MvPolynomial.vars_add_of_disjoint
 
 section Mul
 
-theorem vars_mul (φ ψ : MvPolynomial σ R) : (φ * ψ).vars ⊆ φ.vars ∪ ψ.vars := by
+theorem vars_mul [DecidableEq σ] (φ ψ : MvPolynomial σ R) : (φ * ψ).vars ⊆ φ.vars ∪ ψ.vars := by
   intro i
   simp only [mem_vars, Finset.mem_union]
   rintro ⟨d, hd, hi⟩
@@ -345,6 +370,7 @@ theorem vars_one : (1 : MvPolynomial σ R).vars = ∅ :=
 #align mv_polynomial.vars_one MvPolynomial.vars_one
 
 theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars := by
+  classical
   induction' n with n ih
   · simp
   · rw [pow_succ]
@@ -355,8 +381,9 @@ theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars
 /-- The variables of the product of a family of polynomials
 are a subset of the union of the sets of variables of each polynomial.
 -/
-theorem vars_prod {ι : Type _} {s : Finset ι} (f : ι → MvPolynomial σ R) :
+theorem vars_prod {ι : Type _} [DecidableEq σ] {s : Finset ι} (f : ι → MvPolynomial σ R) :
     (∏ i in s, f i).vars ⊆ s.biUnion fun i => (f i).vars := by
+  classical
   induction s using Finset.induction_on with
   | empty => simp
   | insert hs hsub =>
@@ -388,7 +415,9 @@ section Sum
 
 variable {ι : Type _} (t : Finset ι) (φ : ι → MvPolynomial σ R)
 
-theorem vars_sum_subset : (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by
+theorem vars_sum_subset [DecidableEq σ] :
+    (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by
+  classical
   induction t using Finset.induction_on with
   | empty => simp
   | insert has hsum =>
@@ -398,8 +427,9 @@ theorem vars_sum_subset : (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i =>
     assumption
 #align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subset
 
-theorem vars_sum_of_disjoint (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
+theorem vars_sum_of_disjoint [DecidableEq σ] (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
     (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars := by
+  classical
   induction t using Finset.induction_on with
   | empty => simp
   | insert has hsum =>
@@ -423,7 +453,7 @@ variable [CommSemiring S] (f : R →+* S)
 
 variable (p)
 
-theorem vars_map : (map f p).vars ⊆ p.vars := by simp [vars, degrees_map]
+theorem vars_map : (map f p).vars ⊆ p.vars := by classical simp [vars_def, degrees_map]
 #align mv_polynomial.vars_map MvPolynomial.vars_map
 
 variable {f}
@@ -437,7 +467,8 @@ theorem vars_monomial_single (i : σ) {e : ℕ} {r : R} (he : e ≠ 0) (hr : r 
   rw [vars_monomial hr, Finsupp.support_single_ne_zero _ he]
 #align mv_polynomial.vars_monomial_single MvPolynomial.vars_monomial_single
 
-theorem vars_eq_support_biUnion_support : p.vars = p.support.biUnion Finsupp.support := by
+theorem vars_eq_support_biUnion_support [DecidableEq σ] :
+    p.vars = p.support.biUnion Finsupp.support := by
   ext i
   rw [mem_vars, Finset.mem_biUnion]
   simp
@@ -454,12 +485,18 @@ section DegreeOf
 
 /-- `degreeOf n p` gives the highest power of X_n that appears in `p` -/
 def degreeOf (n : σ) (p : MvPolynomial σ R) : ℕ :=
+  letI := Classical.decEq σ
   p.degrees.count n
 #align mv_polynomial.degree_of MvPolynomial.degreeOf
 
+theorem degreeOf_def [DecidableEq σ] (n : σ) (p : MvPolynomial σ R) :
+    p.degreeOf n = p.degrees.count n := by rw [degreeOf]; convert rfl
+#align mv_polynomial.degree_of_def MvPolynomial.degreeOf_def
+
 theorem degreeOf_eq_sup (n : σ) (f : MvPolynomial σ R) :
     degreeOf n f = f.support.sup fun m => m n := by
-  rw [degreeOf, degrees, Multiset.count_finset_sup]
+  classical
+  rw [degreeOf_def, degrees, Multiset.count_finset_sup]
   congr
   ext
   simp
@@ -472,25 +509,27 @@ theorem degreeOf_lt_iff {n : σ} {f : MvPolynomial σ R} {d : ℕ} (h : 0 < d) :
 
 @[simp]
 theorem degreeOf_zero (n : σ) : degreeOf n (0 : MvPolynomial σ R) = 0 := by
-  simp only [degreeOf, degrees_zero, Multiset.count_zero]
+  classical simp only [degreeOf_def, degrees_zero, Multiset.count_zero]
 #align mv_polynomial.degree_of_zero MvPolynomial.degreeOf_zero
 
 @[simp]
 theorem degreeOf_C (a : R) (x : σ) : degreeOf x (C a : MvPolynomial σ R) = 0 := by
-  simp [degreeOf, degrees_C]
+  classical simp [degreeOf_def, degrees_C]
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.degree_of_C MvPolynomial.degreeOf_C
 
-theorem degreeOf_X (i j : σ) [Nontrivial R] :
+theorem degreeOf_X [DecidableEq σ] (i j : σ) [Nontrivial R] :
     degreeOf i (X j : MvPolynomial σ R) = if i = j then 1 else 0 := by
+  classical
   by_cases c : i = j
-  · simp only [c, if_true, eq_self_iff_true, degreeOf, degrees_X, Multiset.count_singleton]
-  simp [c, if_false, degreeOf, degrees_X]
+  · simp only [c, if_true, eq_self_iff_true, degreeOf_def, degrees_X, Multiset.count_singleton]
+  simp [c, if_false, degreeOf_def, degrees_X]
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.degree_of_X MvPolynomial.degreeOf_X
 
 theorem degreeOf_add_le (n : σ) (f g : MvPolynomial σ R) :
     degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g) := by
+  letI := Classical.decEq σ
   repeat' rw [degreeOf]
   apply (Multiset.count_le_of_le n (degrees_add f g)).trans
   dsimp
@@ -506,6 +545,7 @@ theorem monomial_le_degreeOf (i : σ) {f : MvPolynomial σ R} {m : σ →₀ ℕ
 -- TODO we can prove equality here if R is a domain
 theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
     degreeOf i (f * g) ≤ degreeOf i f + degreeOf i g := by
+  classical
   repeat' rw [degreeOf]
   convert Multiset.count_le_of_le i (degrees_mul f g)
   rw [Multiset.count_add]
@@ -513,6 +553,7 @@ theorem degreeOf_mul_le (i : σ) (f g : MvPolynomial σ R) :
 
 theorem degreeOf_mul_X_ne {i j : σ} (f : MvPolynomial σ R) (h : i ≠ j) :
     degreeOf i (f * X j) = degreeOf i f := by
+  classical
   repeat' rw [degreeOf_eq_sup (R:=R) i]
   rw [support_mul_X]
   simp only [Finset.sup_map]
@@ -526,6 +567,7 @@ set_option linter.uppercaseLean3 false in
 -- TODO in the following we have equality iff f ≠ 0
 theorem degreeOf_mul_X_eq (j : σ) (f : MvPolynomial σ R) :
     degreeOf j (f * X j) ≤ degreeOf j f + 1 := by
+  classical
   repeat' rw [degreeOf]
   apply (Multiset.count_le_of_le j (degrees_mul f (X j))).trans
   simp only [Multiset.count_add, add_le_add_iff_left]
@@ -536,6 +578,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem degreeOf_rename_of_injective {p : MvPolynomial σ R} {f : σ → τ} (h : Function.Injective f)
     (i : σ) : degreeOf (f i) (rename f p) = degreeOf i p := by
+  classical
   simp only [degreeOf, degrees_rename_of_injective h, Multiset.count_map_eq_count' f p.degrees h]
 #align mv_polynomial.degree_of_rename_of_injective MvPolynomial.degreeOf_rename_of_injective
 
@@ -564,6 +607,7 @@ theorem le_totalDegree {p : MvPolynomial σ R} {s : σ →₀ ℕ} (h : s ∈ p.
 
 theorem totalDegree_le_degrees_card (p : MvPolynomial σ R) :
     p.totalDegree ≤ Multiset.card p.degrees := by
+  classical
   rw [totalDegree_eq]
   exact Finset.sup_le fun s hs => Multiset.card_le_of_le <| Finset.le_sup hs
 #align mv_polynomial.total_degree_le_degrees_card MvPolynomial.totalDegree_le_degrees_card
@@ -600,6 +644,7 @@ set_option linter.uppercaseLean3 false in
 theorem totalDegree_add (a b : MvPolynomial σ R) :
     (a + b).totalDegree ≤ max a.totalDegree b.totalDegree :=
   Finset.sup_le fun n hn => by
+    classical
     have := Finsupp.support_add hn
     rw [Finset.mem_union] at this
     cases' this with h h
@@ -638,6 +683,7 @@ theorem totalDegree_add_eq_right_of_totalDegree_lt {p q : MvPolynomial σ R}
 theorem totalDegree_mul (a b : MvPolynomial σ R) :
     (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
   Finset.sup_le fun n hn => by
+    classical
     have := AddMonoidAlgebra.support_mul a b hn
     simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
     rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
@@ -669,7 +715,7 @@ theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) :
 @[simp]
 theorem totalDegree_monomial (s : σ →₀ ℕ) {c : R} (hc : c ≠ 0) :
     (monomial s c : MvPolynomial σ R).totalDegree = s.sum fun _ e => e := by
-  simp [totalDegree, support_monomial, if_neg hc]
+  classical simp [totalDegree, support_monomial, if_neg hc]
 #align mv_polynomial.total_degree_monomial MvPolynomial.totalDegree_monomial
 
 @[simp]
@@ -737,6 +783,7 @@ theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ 
 theorem totalDegree_rename_le (f : σ → τ) (p : MvPolynomial σ R) :
     (rename f p).totalDegree ≤ p.totalDegree :=
   Finset.sup_le fun b => by
+    classical
     intro h
     rw [rename_eq] at h
     have h' := Finsupp.mapDomain_support h
@@ -836,14 +883,17 @@ theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ 
       · rfl⟩
 #align mv_polynomial.exists_rename_eq_of_vars_subset_range MvPolynomial.exists_rename_eq_of_vars_subset_range
 
-theorem vars_rename (f : σ → τ) (φ : MvPolynomial σ R) : (rename f φ).vars ⊆ φ.vars.image f := by
+theorem vars_rename [DecidableEq τ] (f : σ → τ) (φ : MvPolynomial σ R) :
+    (rename f φ).vars ⊆ φ.vars.image f := by
+  classical
   intro i hi
-  simp only [vars, exists_prop, Multiset.mem_toFinset, Finset.mem_image] at hi⊢
+  simp only [vars_def, exists_prop, Multiset.mem_toFinset, Finset.mem_image] at hi⊢
   simpa only [Multiset.mem_map] using degrees_rename _ _ hi
 #align mv_polynomial.vars_rename MvPolynomial.vars_rename
 
 theorem mem_vars_rename (f : σ → τ) (φ : MvPolynomial σ R) {j : τ} (h : j ∈ (rename f φ).vars) :
     ∃ i : σ, i ∈ φ.vars ∧ f i = j := by
+  classical
   simpa only [exists_prop, Finset.mem_image] using vars_rename f φ h
 #align mv_polynomial.mem_vars_rename MvPolynomial.mem_vars_rename
 

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>

@@ -153,7 +153,7 @@ theorem degrees_sum {ι : Type _} (s : Finset ι) (f : ι → MvPolynomial σ R)
 theorem degrees_mul (p q : MvPolynomial σ R) : (p * q).degrees ≤ p.degrees + q.degrees := by
   refine' Finset.sup_le fun b hb => _
   have := support_mul p q hb
-  simp only [Finset.mem_bunionᵢ, Finset.mem_singleton] at this
+  simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
   rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
   rw [Finsupp.toMultiset_add]
   exact add_le_add (Finset.le_sup h₁) (Finset.le_sup h₂)
@@ -356,11 +356,11 @@ theorem vars_pow (φ : MvPolynomial σ R) (n : ℕ) : (φ ^ n).vars ⊆ φ.vars
 are a subset of the union of the sets of variables of each polynomial.
 -/
 theorem vars_prod {ι : Type _} {s : Finset ι} (f : ι → MvPolynomial σ R) :
-    (∏ i in s, f i).vars ⊆ s.bunionᵢ fun i => (f i).vars := by
+    (∏ i in s, f i).vars ⊆ s.biUnion fun i => (f i).vars := by
   induction s using Finset.induction_on with
   | empty => simp
   | insert hs hsub =>
-    simp only [hs, Finset.bunionᵢ_insert, Finset.prod_insert, not_false_iff]
+    simp only [hs, Finset.biUnion_insert, Finset.prod_insert, not_false_iff]
     apply Finset.Subset.trans (vars_mul _ _)
     exact Finset.union_subset_union (Finset.Subset.refl _) hsub
 #align mv_polynomial.vars_prod MvPolynomial.vars_prod
@@ -388,27 +388,27 @@ section Sum
 
 variable {ι : Type _} (t : Finset ι) (φ : ι → MvPolynomial σ R)
 
-theorem vars_sum_subset : (∑ i in t, φ i).vars ⊆ Finset.bunionᵢ t fun i => (φ i).vars := by
+theorem vars_sum_subset : (∑ i in t, φ i).vars ⊆ Finset.biUnion t fun i => (φ i).vars := by
   induction t using Finset.induction_on with
   | empty => simp
   | insert has hsum =>
-    rw [Finset.bunionᵢ_insert, Finset.sum_insert has]
+    rw [Finset.biUnion_insert, Finset.sum_insert has]
     refine'
       Finset.Subset.trans (vars_add_subset _ _) (Finset.union_subset_union (Finset.Subset.refl _) _)
     assumption
 #align mv_polynomial.vars_sum_subset MvPolynomial.vars_sum_subset
 
 theorem vars_sum_of_disjoint (h : Pairwise <| (Disjoint on fun i => (φ i).vars)) :
-    (∑ i in t, φ i).vars = Finset.bunionᵢ t fun i => (φ i).vars := by
+    (∑ i in t, φ i).vars = Finset.biUnion t fun i => (φ i).vars := by
   induction t using Finset.induction_on with
   | empty => simp
   | insert has hsum =>
-    rw [Finset.bunionᵢ_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
+    rw [Finset.biUnion_insert, Finset.sum_insert has, vars_add_of_disjoint, hsum]
     unfold Pairwise onFun at h
     rw [hsum]
     simp only [Finset.disjoint_iff_ne] at h⊢
     intro v hv v2 hv2
-    rw [Finset.mem_bunionᵢ] at hv2
+    rw [Finset.mem_biUnion] at hv2
     rcases hv2 with ⟨i, his, hi⟩
     refine' h _ _ hv _ hi
     rintro rfl
@@ -437,11 +437,11 @@ theorem vars_monomial_single (i : σ) {e : ℕ} {r : R} (he : e ≠ 0) (hr : r 
   rw [vars_monomial hr, Finsupp.support_single_ne_zero _ he]
 #align mv_polynomial.vars_monomial_single MvPolynomial.vars_monomial_single
 
-theorem vars_eq_support_bunionᵢ_support : p.vars = p.support.bunionᵢ Finsupp.support := by
+theorem vars_eq_support_biUnion_support : p.vars = p.support.biUnion Finsupp.support := by
   ext i
-  rw [mem_vars, Finset.mem_bunionᵢ]
+  rw [mem_vars, Finset.mem_biUnion]
   simp
-#align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_bunionᵢ_support
+#align mv_polynomial.vars_eq_support_bUnion_support MvPolynomial.vars_eq_support_biUnion_support
 
 end Map
 
@@ -639,7 +639,7 @@ theorem totalDegree_mul (a b : MvPolynomial σ R) :
     (a * b).totalDegree ≤ a.totalDegree + b.totalDegree :=
   Finset.sup_le fun n hn => by
     have := AddMonoidAlgebra.support_mul a b hn
-    simp only [Finset.mem_bunionᵢ, Finset.mem_singleton] at this
+    simp only [Finset.mem_biUnion, Finset.mem_singleton] at this
     rcases this with ⟨a₁, h₁, a₂, h₂, rfl⟩
     rw [Finsupp.sum_add_index']
     · dsimp [totalDegree]

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

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

@@ -622,8 +622,7 @@ theorem totalDegree_add_eq_left_of_totalDegree_lt {p q : MvPolynomial σ R}
       contrapose! h
       rw [totalDegree_eq p, hb₂, totalDegree_eq]
       apply Finset.le_sup h
-    have hbb : b ∈ (p + q).support :=
-      by
+    have hbb : b ∈ (p + q).support := by
       apply support_sdiff_support_subset_support_add
       rw [Finset.mem_sdiff]
       exact ⟨hb₁, hb⟩
@@ -656,8 +655,8 @@ theorem totalDegree_smul_le [CommSemiring S] [DistribMulAction R S] (a : R) (f :
   Finset.sup_mono support_smul
 #align mv_polynomial.total_degree_smul_le MvPolynomial.totalDegree_smul_le
 
-theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree ≤ n * a.totalDegree :=
-  by
+theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) :
+    (a ^ n).totalDegree ≤ n * a.totalDegree := by
   induction' n with n ih
   · simp only [Nat.zero_eq, MulZeroClass.zero_mul, pow_zero, totalDegree_one]
   rw [pow_succ]
@@ -776,8 +775,7 @@ theorem eval₂Hom_eq_constantCoeff_of_vars (f : R →+* S) {g : σ → S} {p :
     intro
     contradiction
   repeat'
-    obtain ⟨i, hi⟩ : Finset.Nonempty (Finsupp.support d) :=
-      by
+    obtain ⟨i, hi⟩ : Finset.Nonempty (Finsupp.support d) := by
       rw [constantCoeff_eq, coeff, ← Finsupp.not_mem_support_iff] at h0
       rw [Finset.nonempty_iff_ne_empty, Ne.def, Finsupp.support_eq_empty]
       rintro rfl
@@ -828,14 +826,14 @@ theorem exists_rename_eq_of_vars_subset_range (p : MvPolynomial σ R) (f : τ 
     (hf : ↑p.vars ⊆ Set.range f) : ∃ q : MvPolynomial τ R, rename f q = p :=
   ⟨aeval (fun i : σ => Option.elim' 0 X <| partialInv f i) p,
     by
-    show (rename f).toRingHom.comp _ p = RingHom.id _ p
-    refine' hom_congr_vars _ _ _
-    · ext1
-      simp [algebraMap_eq]
-    · intro i hip _
-      rcases hf hip with ⟨i, rfl⟩
-      simp [partialInv_left hfi]
-    · rfl⟩
+      show (rename f).toRingHom.comp _ p = RingHom.id _ p
+      refine' hom_congr_vars _ _ _
+      · ext1
+        simp [algebraMap_eq]
+      · intro i hip _
+        rcases hf hip with ⟨i, rfl⟩
+        simp [partialInv_left hfi]
+      · rfl⟩
 #align mv_polynomial.exists_rename_eq_of_vars_subset_range MvPolynomial.exists_rename_eq_of_vars_subset_range
 
 theorem vars_rename (f : σ → τ) (φ : MvPolynomial σ R) : (rename f φ).vars ⊆ φ.vars.image f := by

This PR factors out a MetaM version of the rfl tactic and adds a missing whnfR and instantiateMVars in front of the goal type. This means that a few rws across mathlib4 now close the goal instead of e.g. requiring a trailing exact le_rfl.

Note: we do not use whnfR on the return type when adding the refl extension in the first place, as forallMetaTelescopeReducing already performs whnf (here, at reducible transparency).

See zulip for some discussion on the internal changes made.

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

@@ -97,7 +97,6 @@ theorem degrees_monomial (s : σ →₀ ℕ) (a : R) : degrees (monomial s a) 
     have := Finsupp.support_single_subset h
     rw [Finset.mem_singleton] at this
     rw [this]
-    exact le_refl _
 #align mv_polynomial.degrees_monomial MvPolynomial.degrees_monomial
 
 theorem degrees_monomial_eq (s : σ →₀ ℕ) (a : R) (ha : a ≠ 0) :

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -666,7 +666,6 @@ theorem totalDegree_pow (a : MvPolynomial σ R) (n : ℕ) : (a ^ n).totalDegree
     totalDegree (a * a ^ n) ≤ a.totalDegree + (a ^ n).totalDegree := totalDegree_mul _ _
     _ ≤ a.totalDegree + n * a.totalDegree := (add_le_add_left ih _)
     _ = (n + 1) * a.totalDegree := by rw [add_mul, one_mul, add_comm]
-
 #align mv_polynomial.total_degree_pow MvPolynomial.totalDegree_pow
 
 @[simp]
@@ -724,7 +723,6 @@ theorem exists_degree_lt [Fintype σ] (f : MvPolynomial σ R) (n : ℕ)
       intros
       rfl
     _ ≤ f.totalDegree := le_totalDegree hd
-
 #align mv_polynomial.exists_degree_lt MvPolynomial.exists_degree_lt
 
 theorem coeff_eq_zero_of_totalDegree_lt {f : MvPolynomial σ R} {d : σ →₀ ℕ}

Co-authored-by: Rémy Degenne <remydegenne@gmail.com>