ring_theory.mv_polynomial.homogeneous ⟷ Mathlib.RingTheory.MvPolynomial.Homogeneous

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

@@ -5,7 +5,7 @@ Authors: Johan Commelin, Eric Wieser
 -/
 import Algebra.DirectSum.Internal
 import Algebra.GradedMonoid
-import Data.MvPolynomial.Degrees
+import Algebra.MvPolynomial.Degrees
 
 #align_import ring_theory.mv_polynomial.homogeneous from "leanprover-community/mathlib"@"1b0a28e1c93409dbf6d69526863cd9984ef652ce"
 

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

@@ -5,7 +5,7 @@ Authors: Johan Commelin, Eric Wieser
 -/
 import Algebra.DirectSum.Internal
 import Algebra.GradedMonoid
-import Data.MvPolynomial.Variables
+import Data.MvPolynomial.Degrees
 
 #align_import ring_theory.mv_polynomial.homogeneous from "leanprover-community/mathlib"@"1b0a28e1c93409dbf6d69526863cd9984ef652ce"
 

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

@@ -56,7 +56,7 @@ def homogeneousSubmodule [CommSemiring R] (n : ℕ) : Submodule R (MvPolynomial
     where
   carrier := {x | x.Homogeneous n}
   smul_mem' r a ha c hc := by
-    rw [coeff_smul] at hc 
+    rw [coeff_smul] at hc
     apply ha
     intro h
     apply hc
@@ -64,7 +64,7 @@ def homogeneousSubmodule [CommSemiring R] (n : ℕ) : Submodule R (MvPolynomial
     exact smul_zero r
   zero_mem' d hd := False.elim (hd <| coeff_zero _)
   add_mem' a b ha hb c hc := by
-    rw [coeff_add] at hc 
+    rw [coeff_add] at hc
     obtain h | h : coeff c a ≠ 0 ∨ coeff c b ≠ 0 := by contrapose! hc; simp only [hc, add_zero]
     · exact ha h
     · exact hb h
@@ -103,7 +103,7 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
   by
   rw [Submodule.mul_le]
   intro φ hφ ψ hψ c hc
-  rw [coeff_mul] at hc 
+  rw [coeff_mul] at hc
   obtain ⟨⟨d, e⟩, hde, H⟩ := Finset.exists_ne_zero_of_sum_ne_zero hc
   have aux : coeff d φ ≠ 0 ∧ coeff e ψ ≠ 0 :=
     by
@@ -111,7 +111,7 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
     by_cases h : coeff d φ = 0 <;>
       simp_all only [Ne.def, not_false_iff, MulZeroClass.zero_mul, MulZeroClass.mul_zero]
   specialize hφ aux.1; specialize hψ aux.2
-  rw [Finsupp.mem_antidiagonal] at hde 
+  rw [Finsupp.mem_antidiagonal] at hde
   classical
   have hd' : d.support ⊆ d.support ∪ e.support := Finset.subset_union_left _ _
   have he' : e.support ⊆ d.support ∪ e.support := Finset.subset_union_right _ _
@@ -133,8 +133,8 @@ theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : ∑ i
     IsHomogeneous (monomial d r) n := by
   intro c hc
   classical
-  rw [coeff_monomial] at hc 
-  split_ifs at hc  with h
+  rw [coeff_monomial] at hc
+  split_ifs at hc with h
   · subst c; exact hn
   · contradiction
 #align mv_polynomial.is_homogeneous_monomial MvPolynomial.isHomogeneous_monomial
@@ -145,9 +145,9 @@ variable (σ) {R}
 #print MvPolynomial.isHomogeneous_of_totalDegree_zero /-
 theorem isHomogeneous_of_totalDegree_zero {p : MvPolynomial σ R} (hp : p.totalDegree = 0) :
     IsHomogeneous p 0 := by
-  erw [total_degree, Finset.sup_eq_bot_iff] at hp 
+  erw [total_degree, Finset.sup_eq_bot_iff] at hp
   -- we have to do this in two steps to stop simp changing bot to zero
-  simp_rw [mem_support_iff] at hp 
+  simp_rw [mem_support_iff] at hp
   exact hp
 #align mv_polynomial.is_homogeneous_of_total_degree_zero MvPolynomial.isHomogeneous_of_totalDegree_zero
 -/
@@ -195,7 +195,7 @@ variable [CommSemiring R] {φ ψ : MvPolynomial σ R} {m n : ℕ}
 theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : ∑ i in d.support, d i ≠ n) :
     coeff d φ = 0 := by
   have aux := mt (@hφ d) hd
-  classical rwa [Classical.not_not] at aux 
+  classical rwa [Classical.not_not] at aux
 #align mv_polynomial.is_homogeneous.coeff_eq_zero MvPolynomial.IsHomogeneous.coeff_eq_zero
 -/
 
@@ -248,7 +248,7 @@ theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ =
   apply le_antisymm
   · apply Finset.sup_le
     intro d hd
-    rw [mem_support_iff] at hd 
+    rw [mem_support_iff] at hd
     rw [Finsupp.sum, hφ hd]
   · obtain ⟨d, hd⟩ : ∃ d, coeff d φ ≠ 0 := exists_coeff_ne_zero h
     simp only [← hφ hd, Finsupp.sum]
@@ -333,7 +333,7 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :
     classical simp only [coeff_homogeneous_component, sum_eq_zero_iff, Finsupp.zero_apply, if_true,
       coeff_C, eq_self_iff_true, forall_true_iff]
   · rw [coeff_homogeneous_component, if_neg, coeff_C, if_neg (Ne.symm hd)]
-    simp only [Finsupp.ext_iff, Finsupp.zero_apply] at hd 
+    simp only [Finsupp.ext_iff, Finsupp.zero_apply] at hd
     simp [hd]
 #align mv_polynomial.homogeneous_component_zero MvPolynomial.homogeneousComponent_zero
 -/
@@ -351,7 +351,7 @@ theorem homogeneousComponent_eq_zero'
     (h : ∀ d : σ →₀ ℕ, d ∈ φ.support → ∑ i in d.support, d i ≠ n) : homogeneousComponent n φ = 0 :=
   by
   rw [homogeneous_component_apply, sum_eq_zero]
-  intro d hd; rw [mem_filter] at hd 
+  intro d hd; rw [mem_filter] at hd
   exfalso; exact h _ hd.1 hd.2
 #align mv_polynomial.homogeneous_component_eq_zero' MvPolynomial.homogeneousComponent_eq_zero'
 -/
@@ -360,7 +360,7 @@ theorem homogeneousComponent_eq_zero'
 theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousComponent n φ = 0 :=
   by
   apply homogeneous_component_eq_zero'
-  rw [total_degree, Finset.sup_lt_iff] at h 
+  rw [total_degree, Finset.sup_lt_iff] at h
   · intro d hd; exact ne_of_lt (h d hd)
   · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.homogeneous_component_eq_zero MvPolynomial.homogeneousComponent_eq_zero
@@ -380,7 +380,7 @@ theorem sum_homogeneousComponent : ∑ i in range (φ.totalDegree + 1), homogene
 theorem homogeneousComponent_homogeneous_polynomial (m n : ℕ) (p : MvPolynomial σ R)
     (h : p ∈ homogeneousSubmodule σ R n) : homogeneousComponent m p = if m = n then p else 0 :=
   by
-  simp only [mem_homogeneous_submodule] at h 
+  simp only [mem_homogeneous_submodule] at h
   ext x
   rw [coeff_homogeneous_component]
   by_cases zero_coeff : coeff x p = 0

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

@@ -113,6 +113,12 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
   specialize hφ aux.1; specialize hψ aux.2
   rw [Finsupp.mem_antidiagonal] at hde 
   classical
+  have hd' : d.support ⊆ d.support ∪ e.support := Finset.subset_union_left _ _
+  have he' : e.support ⊆ d.support ∪ e.support := Finset.subset_union_right _ _
+  rw [← hde, ← hφ, ← hψ, Finset.sum_subset Finsupp.support_add, Finset.sum_subset hd',
+    Finset.sum_subset he', ← Finset.sum_add_distrib]
+  · congr
+  all_goals intro i hi; apply finsupp.not_mem_support_iff.mp
 #align mv_polynomial.homogeneous_submodule_mul MvPolynomial.homogeneousSubmodule_mul
 -/
 
@@ -127,6 +133,10 @@ theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : ∑ i
     IsHomogeneous (monomial d r) n := by
   intro c hc
   classical
+  rw [coeff_monomial] at hc 
+  split_ifs at hc  with h
+  · subst c; exact hn
+  · contradiction
 #align mv_polynomial.is_homogeneous_monomial MvPolynomial.isHomogeneous_monomial
 -/
 
@@ -185,7 +195,7 @@ variable [CommSemiring R] {φ ψ : MvPolynomial σ R} {m n : ℕ}
 theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : ∑ i in d.support, d i ≠ n) :
     coeff d φ = 0 := by
   have aux := mt (@hφ d) hd
-  classical
+  classical rwa [Classical.not_not] at aux 
 #align mv_polynomial.is_homogeneous.coeff_eq_zero MvPolynomial.IsHomogeneous.coeff_eq_zero
 -/
 
@@ -220,6 +230,14 @@ theorem mul (hφ : IsHomogeneous φ m) (hψ : IsHomogeneous ψ n) : IsHomogeneou
 theorem prod {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ι → ℕ)
     (h : ∀ i ∈ s, IsHomogeneous (φ i) (n i)) : IsHomogeneous (∏ i in s, φ i) (∑ i in s, n i) := by
   classical
+  revert h
+  apply Finset.induction_on s
+  · intro; simp only [is_homogeneous_one, Finset.sum_empty, Finset.prod_empty]
+  · intro i s his IH h
+    simp only [his, Finset.prod_insert, Finset.sum_insert, not_false_iff]
+    apply (h i (Finset.mem_insert_self _ _)).mul (IH _)
+    intro j hjs
+    exact h j (Finset.mem_insert_of_mem hjs)
 #align mv_polynomial.is_homogeneous.prod MvPolynomial.IsHomogeneous.prod
 -/
 
@@ -311,7 +329,9 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :
   by
   ext1 d
   rcases em (d = 0) with (rfl | hd)
-  · classical
+  ·
+    classical simp only [coeff_homogeneous_component, sum_eq_zero_iff, Finsupp.zero_apply, if_true,
+      coeff_C, eq_self_iff_true, forall_true_iff]
   · rw [coeff_homogeneous_component, if_neg, coeff_C, if_neg (Ne.symm hd)]
     simp only [Finsupp.ext_iff, Finsupp.zero_apply] at hd 
     simp [hd]

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

@@ -113,12 +113,6 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
   specialize hφ aux.1; specialize hψ aux.2
   rw [Finsupp.mem_antidiagonal] at hde 
   classical
-  have hd' : d.support ⊆ d.support ∪ e.support := Finset.subset_union_left _ _
-  have he' : e.support ⊆ d.support ∪ e.support := Finset.subset_union_right _ _
-  rw [← hde, ← hφ, ← hψ, Finset.sum_subset Finsupp.support_add, Finset.sum_subset hd',
-    Finset.sum_subset he', ← Finset.sum_add_distrib]
-  · congr
-  all_goals intro i hi; apply finsupp.not_mem_support_iff.mp
 #align mv_polynomial.homogeneous_submodule_mul MvPolynomial.homogeneousSubmodule_mul
 -/
 
@@ -133,10 +127,6 @@ theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : ∑ i
     IsHomogeneous (monomial d r) n := by
   intro c hc
   classical
-  rw [coeff_monomial] at hc 
-  split_ifs at hc  with h
-  · subst c; exact hn
-  · contradiction
 #align mv_polynomial.is_homogeneous_monomial MvPolynomial.isHomogeneous_monomial
 -/
 
@@ -195,7 +185,7 @@ variable [CommSemiring R] {φ ψ : MvPolynomial σ R} {m n : ℕ}
 theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : ∑ i in d.support, d i ≠ n) :
     coeff d φ = 0 := by
   have aux := mt (@hφ d) hd
-  classical rwa [Classical.not_not] at aux 
+  classical
 #align mv_polynomial.is_homogeneous.coeff_eq_zero MvPolynomial.IsHomogeneous.coeff_eq_zero
 -/
 
@@ -230,14 +220,6 @@ theorem mul (hφ : IsHomogeneous φ m) (hψ : IsHomogeneous ψ n) : IsHomogeneou
 theorem prod {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ι → ℕ)
     (h : ∀ i ∈ s, IsHomogeneous (φ i) (n i)) : IsHomogeneous (∏ i in s, φ i) (∑ i in s, n i) := by
   classical
-  revert h
-  apply Finset.induction_on s
-  · intro; simp only [is_homogeneous_one, Finset.sum_empty, Finset.prod_empty]
-  · intro i s his IH h
-    simp only [his, Finset.prod_insert, Finset.sum_insert, not_false_iff]
-    apply (h i (Finset.mem_insert_self _ _)).mul (IH _)
-    intro j hjs
-    exact h j (Finset.mem_insert_of_mem hjs)
 #align mv_polynomial.is_homogeneous.prod MvPolynomial.IsHomogeneous.prod
 -/
 
@@ -329,9 +311,7 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :
   by
   ext1 d
   rcases em (d = 0) with (rfl | hd)
-  ·
-    classical simp only [coeff_homogeneous_component, sum_eq_zero_iff, Finsupp.zero_apply, if_true,
-      coeff_C, eq_self_iff_true, forall_true_iff]
+  · classical
   · rw [coeff_homogeneous_component, if_neg, coeff_C, if_neg (Ne.symm hd)]
     simp only [Finsupp.ext_iff, Finsupp.zero_apply] at hd 
     simp [hd]

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Eric Wieser
 -/
-import Mathbin.Algebra.DirectSum.Internal
-import Mathbin.Algebra.GradedMonoid
-import Mathbin.Data.MvPolynomial.Variables
+import Algebra.DirectSum.Internal
+import Algebra.GradedMonoid
+import Data.MvPolynomial.Variables
 
 #align_import ring_theory.mv_polynomial.homogeneous from "leanprover-community/mathlib"@"1b0a28e1c93409dbf6d69526863cd9984ef652ce"
 

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

@@ -264,7 +264,7 @@ and `direct_sum.algebra`. -/
 instance HomogeneousSubmodule.gcommSemiring : SetLike.GradedMonoid (homogeneousSubmodule σ R)
     where
   one_mem := isHomogeneous_one σ R
-  mul_mem i j xi xj := IsHomogeneous.mul
+  hMul_mem i j xi xj := IsHomogeneous.mul
 #align mv_polynomial.is_homogeneous.homogeneous_submodule.gcomm_semiring MvPolynomial.IsHomogeneous.HomogeneousSubmodule.gcommSemiring
 -/
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Eric Wieser
-
-! This file was ported from Lean 3 source module ring_theory.mv_polynomial.homogeneous
-! leanprover-community/mathlib commit 1b0a28e1c93409dbf6d69526863cd9984ef652ce
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.DirectSum.Internal
 import Mathbin.Algebra.GradedMonoid
 import Mathbin.Data.MvPolynomial.Variables
 
+#align_import ring_theory.mv_polynomial.homogeneous from "leanprover-community/mathlib"@"1b0a28e1c93409dbf6d69526863cd9984ef652ce"
+
 /-!
 # Homogeneous polynomials
 

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

@@ -131,6 +131,7 @@ variable [CommSemiring R]
 
 variable {σ R}
 
+#print MvPolynomial.isHomogeneous_monomial /-
 theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : ∑ i in d.support, d i = n) :
     IsHomogeneous (monomial d r) n := by
   intro c hc
@@ -140,9 +141,11 @@ theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : ∑ i
   · subst c; exact hn
   · contradiction
 #align mv_polynomial.is_homogeneous_monomial MvPolynomial.isHomogeneous_monomial
+-/
 
 variable (σ) {R}
 
+#print MvPolynomial.isHomogeneous_of_totalDegree_zero /-
 theorem isHomogeneous_of_totalDegree_zero {p : MvPolynomial σ R} (hp : p.totalDegree = 0) :
     IsHomogeneous p 0 := by
   erw [total_degree, Finset.sup_eq_bot_iff] at hp 
@@ -150,31 +153,40 @@ theorem isHomogeneous_of_totalDegree_zero {p : MvPolynomial σ R} (hp : p.totalD
   simp_rw [mem_support_iff] at hp 
   exact hp
 #align mv_polynomial.is_homogeneous_of_total_degree_zero MvPolynomial.isHomogeneous_of_totalDegree_zero
+-/
 
+#print MvPolynomial.isHomogeneous_C /-
 theorem isHomogeneous_C (r : R) : IsHomogeneous (C r : MvPolynomial σ R) 0 :=
   by
   apply is_homogeneous_monomial
   simp only [Finsupp.zero_apply, Finset.sum_const_zero]
 #align mv_polynomial.is_homogeneous_C MvPolynomial.isHomogeneous_C
+-/
 
 variable (σ R)
 
+#print MvPolynomial.isHomogeneous_zero /-
 theorem isHomogeneous_zero (n : ℕ) : IsHomogeneous (0 : MvPolynomial σ R) n :=
   (homogeneousSubmodule σ R n).zero_mem
 #align mv_polynomial.is_homogeneous_zero MvPolynomial.isHomogeneous_zero
+-/
 
+#print MvPolynomial.isHomogeneous_one /-
 theorem isHomogeneous_one : IsHomogeneous (1 : MvPolynomial σ R) 0 :=
   isHomogeneous_C _ _
 #align mv_polynomial.is_homogeneous_one MvPolynomial.isHomogeneous_one
+-/
 
 variable {σ} (R)
 
+#print MvPolynomial.isHomogeneous_X /-
 theorem isHomogeneous_X (i : σ) : IsHomogeneous (X i : MvPolynomial σ R) 1 :=
   by
   apply is_homogeneous_monomial
   simp only [Finsupp.support_single_ne_zero _ one_ne_zero, Finset.sum_singleton]
   exact Finsupp.single_eq_same
 #align mv_polynomial.is_homogeneous_X MvPolynomial.isHomogeneous_X
+-/
 
 end
 
@@ -182,31 +194,42 @@ namespace IsHomogeneous
 
 variable [CommSemiring R] {φ ψ : MvPolynomial σ R} {m n : ℕ}
 
+#print MvPolynomial.IsHomogeneous.coeff_eq_zero /-
 theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : ∑ i in d.support, d i ≠ n) :
     coeff d φ = 0 := by
   have aux := mt (@hφ d) hd
   classical rwa [Classical.not_not] at aux 
 #align mv_polynomial.is_homogeneous.coeff_eq_zero MvPolynomial.IsHomogeneous.coeff_eq_zero
+-/
 
+#print MvPolynomial.IsHomogeneous.inj_right /-
 theorem inj_right (hm : IsHomogeneous φ m) (hn : IsHomogeneous φ n) (hφ : φ ≠ 0) : m = n :=
   by
   obtain ⟨d, hd⟩ : ∃ d, coeff d φ ≠ 0 := exists_coeff_ne_zero hφ
   rw [← hm hd, ← hn hd]
 #align mv_polynomial.is_homogeneous.inj_right MvPolynomial.IsHomogeneous.inj_right
+-/
 
+#print MvPolynomial.IsHomogeneous.add /-
 theorem add (hφ : IsHomogeneous φ n) (hψ : IsHomogeneous ψ n) : IsHomogeneous (φ + ψ) n :=
   (homogeneousSubmodule σ R n).add_mem hφ hψ
 #align mv_polynomial.is_homogeneous.add MvPolynomial.IsHomogeneous.add
+-/
 
+#print MvPolynomial.IsHomogeneous.sum /-
 theorem sum {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ℕ)
     (h : ∀ i ∈ s, IsHomogeneous (φ i) n) : IsHomogeneous (∑ i in s, φ i) n :=
   (homogeneousSubmodule σ R n).sum_mem h
 #align mv_polynomial.is_homogeneous.sum MvPolynomial.IsHomogeneous.sum
+-/
 
+#print MvPolynomial.IsHomogeneous.mul /-
 theorem mul (hφ : IsHomogeneous φ m) (hψ : IsHomogeneous ψ n) : IsHomogeneous (φ * ψ) (m + n) :=
   homogeneousSubmodule_mul m n <| Submodule.mul_mem_mul hφ hψ
 #align mv_polynomial.is_homogeneous.mul MvPolynomial.IsHomogeneous.mul
+-/
 
+#print MvPolynomial.IsHomogeneous.prod /-
 theorem prod {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ι → ℕ)
     (h : ∀ i ∈ s, IsHomogeneous (φ i) (n i)) : IsHomogeneous (∏ i in s, φ i) (∑ i in s, n i) := by
   classical
@@ -219,7 +242,9 @@ theorem prod {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n :
     intro j hjs
     exact h j (Finset.mem_insert_of_mem hjs)
 #align mv_polynomial.is_homogeneous.prod MvPolynomial.IsHomogeneous.prod
+-/
 
+#print MvPolynomial.IsHomogeneous.totalDegree /-
 theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ = n :=
   by
   rw [total_degree]
@@ -233,6 +258,7 @@ theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ =
     replace hd := finsupp.mem_support_iff.mpr hd
     exact Finset.le_sup hd
 #align mv_polynomial.is_homogeneous.total_degree MvPolynomial.IsHomogeneous.totalDegree
+-/
 
 #print MvPolynomial.IsHomogeneous.HomogeneousSubmodule.gcommSemiring /-
 /--
@@ -276,24 +302,31 @@ open Finset
 
 variable [CommSemiring R] (n : ℕ) (φ ψ : MvPolynomial σ R)
 
+#print MvPolynomial.coeff_homogeneousComponent /-
 theorem coeff_homogeneousComponent (d : σ →₀ ℕ) :
     coeff d (homogeneousComponent n φ) = if ∑ i in d.support, d i = n then coeff d φ else 0 := by
   convert Finsupp.filter_apply (fun d : σ →₀ ℕ => ∑ i in d.support, d i = n) φ d
 #align mv_polynomial.coeff_homogeneous_component MvPolynomial.coeff_homogeneousComponent
+-/
 
+#print MvPolynomial.homogeneousComponent_apply /-
 theorem homogeneousComponent_apply :
     homogeneousComponent n φ =
       ∑ d in φ.support.filterₓ fun d => ∑ i in d.support, d i = n, monomial d (coeff d φ) :=
   by convert Finsupp.filter_eq_sum (fun d : σ →₀ ℕ => ∑ i in d.support, d i = n) φ
 #align mv_polynomial.homogeneous_component_apply MvPolynomial.homogeneousComponent_apply
+-/
 
+#print MvPolynomial.homogeneousComponent_isHomogeneous /-
 theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).Homogeneous n :=
   by
   intro d hd
   contrapose! hd
   rw [coeff_homogeneous_component, if_neg hd]
 #align mv_polynomial.homogeneous_component_is_homogeneous MvPolynomial.homogeneousComponent_isHomogeneous
+-/
 
+#print MvPolynomial.homogeneousComponent_zero /-
 @[simp]
 theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :=
   by
@@ -306,13 +339,17 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :
     simp only [Finsupp.ext_iff, Finsupp.zero_apply] at hd 
     simp [hd]
 #align mv_polynomial.homogeneous_component_zero MvPolynomial.homogeneousComponent_zero
+-/
 
+#print MvPolynomial.homogeneousComponent_C_mul /-
 @[simp]
 theorem homogeneousComponent_C_mul (n : ℕ) (r : R) :
     homogeneousComponent n (C r * φ) = C r * homogeneousComponent n φ := by
   simp only [C_mul', LinearMap.map_smul]
 #align mv_polynomial.homogeneous_component_C_mul MvPolynomial.homogeneousComponent_C_mul
+-/
 
+#print MvPolynomial.homogeneousComponent_eq_zero' /-
 theorem homogeneousComponent_eq_zero'
     (h : ∀ d : σ →₀ ℕ, d ∈ φ.support → ∑ i in d.support, d i ≠ n) : homogeneousComponent n φ = 0 :=
   by
@@ -320,7 +357,9 @@ theorem homogeneousComponent_eq_zero'
   intro d hd; rw [mem_filter] at hd 
   exfalso; exact h _ hd.1 hd.2
 #align mv_polynomial.homogeneous_component_eq_zero' MvPolynomial.homogeneousComponent_eq_zero'
+-/
 
+#print MvPolynomial.homogeneousComponent_eq_zero /-
 theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousComponent n φ = 0 :=
   by
   apply homogeneous_component_eq_zero'
@@ -328,7 +367,9 @@ theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousCompo
   · intro d hd; exact ne_of_lt (h d hd)
   · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.homogeneous_component_eq_zero MvPolynomial.homogeneousComponent_eq_zero
+-/
 
+#print MvPolynomial.sum_homogeneousComponent /-
 theorem sum_homogeneousComponent : ∑ i in range (φ.totalDegree + 1), homogeneousComponent i φ = φ :=
   by
   ext1 d
@@ -336,7 +377,9 @@ theorem sum_homogeneousComponent : ∑ i in range (φ.totalDegree + 1), homogene
     simpa [coeff_sum, coeff_homogeneous_component]
   exact fun h => (coeff_eq_zero_of_total_degree_lt h).symm
 #align mv_polynomial.sum_homogeneous_component MvPolynomial.sum_homogeneousComponent
+-/
 
+#print MvPolynomial.homogeneousComponent_homogeneous_polynomial /-
 theorem homogeneousComponent_homogeneous_polynomial (m n : ℕ) (p : MvPolynomial σ R)
     (h : p ∈ homogeneousSubmodule σ R n) : homogeneousComponent m p = if m = n then p else 0 :=
   by
@@ -352,6 +395,7 @@ theorem homogeneousComponent_homogeneous_polynomial (m n : ℕ) (p : MvPolynomia
     · rfl
     · simp only [coeff_zero]
 #align mv_polynomial.homogeneous_component_homogeneous_polynomial MvPolynomial.homogeneousComponent_homogeneous_polynomial
+-/
 
 end HomogeneousComponent
 

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

@@ -47,7 +47,7 @@ TODO
 /-- A multivariate polynomial `φ` is homogeneous of degree `n`
 if all monomials occuring in `φ` have degree `n`. -/
 def IsHomogeneous [CommSemiring R] (φ : MvPolynomial σ R) (n : ℕ) :=
-  ∀ ⦃d⦄, coeff d φ ≠ 0 → (∑ i in d.support, d i) = n
+  ∀ ⦃d⦄, coeff d φ ≠ 0 → ∑ i in d.support, d i = n
 #align mv_polynomial.is_homogeneous MvPolynomial.IsHomogeneous
 -/
 
@@ -89,7 +89,7 @@ variable (σ R)
 #print MvPolynomial.homogeneousSubmodule_eq_finsupp_supported /-
 /-- While equal, the former has a convenient definitional reduction. -/
 theorem homogeneousSubmodule_eq_finsupp_supported [CommSemiring R] (n : ℕ) :
-    homogeneousSubmodule σ R n = Finsupp.supported _ R {d | (∑ i in d.support, d i) = n} :=
+    homogeneousSubmodule σ R n = Finsupp.supported _ R {d | ∑ i in d.support, d i = n} :=
   by
   ext
   rw [Finsupp.mem_supported, Set.subset_def]
@@ -131,7 +131,7 @@ variable [CommSemiring R]
 
 variable {σ R}
 
-theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : (∑ i in d.support, d i) = n) :
+theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : ∑ i in d.support, d i = n) :
     IsHomogeneous (monomial d r) n := by
   intro c hc
   classical
@@ -182,7 +182,7 @@ namespace IsHomogeneous
 
 variable [CommSemiring R] {φ ψ : MvPolynomial σ R} {m n : ℕ}
 
-theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : (∑ i in d.support, d i) ≠ n) :
+theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : ∑ i in d.support, d i ≠ n) :
     coeff d φ = 0 := by
   have aux := mt (@hφ d) hd
   classical rwa [Classical.not_not] at aux 
@@ -266,7 +266,7 @@ open Finset
 See `sum_homogeneous_component` for the statement that `φ` is equal to the sum
 of all its homogeneous components. -/
 def homogeneousComponent [CommSemiring R] (n : ℕ) : MvPolynomial σ R →ₗ[R] MvPolynomial σ R :=
-  (Submodule.subtype _).comp <| Finsupp.restrictDom _ _ {d | (∑ i in d.support, d i) = n}
+  (Submodule.subtype _).comp <| Finsupp.restrictDom _ _ {d | ∑ i in d.support, d i = n}
 #align mv_polynomial.homogeneous_component MvPolynomial.homogeneousComponent
 -/
 
@@ -277,14 +277,14 @@ open Finset
 variable [CommSemiring R] (n : ℕ) (φ ψ : MvPolynomial σ R)
 
 theorem coeff_homogeneousComponent (d : σ →₀ ℕ) :
-    coeff d (homogeneousComponent n φ) = if (∑ i in d.support, d i) = n then coeff d φ else 0 := by
-  convert Finsupp.filter_apply (fun d : σ →₀ ℕ => (∑ i in d.support, d i) = n) φ d
+    coeff d (homogeneousComponent n φ) = if ∑ i in d.support, d i = n then coeff d φ else 0 := by
+  convert Finsupp.filter_apply (fun d : σ →₀ ℕ => ∑ i in d.support, d i = n) φ d
 #align mv_polynomial.coeff_homogeneous_component MvPolynomial.coeff_homogeneousComponent
 
 theorem homogeneousComponent_apply :
     homogeneousComponent n φ =
-      ∑ d in φ.support.filterₓ fun d => (∑ i in d.support, d i) = n, monomial d (coeff d φ) :=
-  by convert Finsupp.filter_eq_sum (fun d : σ →₀ ℕ => (∑ i in d.support, d i) = n) φ
+      ∑ d in φ.support.filterₓ fun d => ∑ i in d.support, d i = n, monomial d (coeff d φ) :=
+  by convert Finsupp.filter_eq_sum (fun d : σ →₀ ℕ => ∑ i in d.support, d i = n) φ
 #align mv_polynomial.homogeneous_component_apply MvPolynomial.homogeneousComponent_apply
 
 theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).Homogeneous n :=
@@ -314,8 +314,7 @@ theorem homogeneousComponent_C_mul (n : ℕ) (r : R) :
 #align mv_polynomial.homogeneous_component_C_mul MvPolynomial.homogeneousComponent_C_mul
 
 theorem homogeneousComponent_eq_zero'
-    (h : ∀ d : σ →₀ ℕ, d ∈ φ.support → (∑ i in d.support, d i) ≠ n) :
-    homogeneousComponent n φ = 0 :=
+    (h : ∀ d : σ →₀ ℕ, d ∈ φ.support → ∑ i in d.support, d i ≠ n) : homogeneousComponent n φ = 0 :=
   by
   rw [homogeneous_component_apply, sum_eq_zero]
   intro d hd; rw [mem_filter] at hd 
@@ -330,8 +329,7 @@ theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousCompo
   · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.homogeneous_component_eq_zero MvPolynomial.homogeneousComponent_eq_zero
 
-theorem sum_homogeneousComponent :
-    (∑ i in range (φ.totalDegree + 1), homogeneousComponent i φ) = φ :=
+theorem sum_homogeneousComponent : ∑ i in range (φ.totalDegree + 1), homogeneousComponent i φ = φ :=
   by
   ext1 d
   suffices φ.total_degree < d.support.sum d → 0 = coeff d φ by

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

@@ -57,7 +57,7 @@ variable (σ R)
 /-- The submodule of homogeneous `mv_polynomial`s of degree `n`. -/
 def homogeneousSubmodule [CommSemiring R] (n : ℕ) : Submodule R (MvPolynomial σ R)
     where
-  carrier := { x | x.Homogeneous n }
+  carrier := {x | x.Homogeneous n}
   smul_mem' r a ha c hc := by
     rw [coeff_smul] at hc 
     apply ha
@@ -89,7 +89,7 @@ variable (σ R)
 #print MvPolynomial.homogeneousSubmodule_eq_finsupp_supported /-
 /-- While equal, the former has a convenient definitional reduction. -/
 theorem homogeneousSubmodule_eq_finsupp_supported [CommSemiring R] (n : ℕ) :
-    homogeneousSubmodule σ R n = Finsupp.supported _ R { d | (∑ i in d.support, d i) = n } :=
+    homogeneousSubmodule σ R n = Finsupp.supported _ R {d | (∑ i in d.support, d i) = n} :=
   by
   ext
   rw [Finsupp.mem_supported, Set.subset_def]
@@ -116,12 +116,12 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
   specialize hφ aux.1; specialize hψ aux.2
   rw [Finsupp.mem_antidiagonal] at hde 
   classical
-    have hd' : d.support ⊆ d.support ∪ e.support := Finset.subset_union_left _ _
-    have he' : e.support ⊆ d.support ∪ e.support := Finset.subset_union_right _ _
-    rw [← hde, ← hφ, ← hψ, Finset.sum_subset Finsupp.support_add, Finset.sum_subset hd',
-      Finset.sum_subset he', ← Finset.sum_add_distrib]
-    · congr
-    all_goals intro i hi; apply finsupp.not_mem_support_iff.mp
+  have hd' : d.support ⊆ d.support ∪ e.support := Finset.subset_union_left _ _
+  have he' : e.support ⊆ d.support ∪ e.support := Finset.subset_union_right _ _
+  rw [← hde, ← hφ, ← hψ, Finset.sum_subset Finsupp.support_add, Finset.sum_subset hd',
+    Finset.sum_subset he', ← Finset.sum_add_distrib]
+  · congr
+  all_goals intro i hi; apply finsupp.not_mem_support_iff.mp
 #align mv_polynomial.homogeneous_submodule_mul MvPolynomial.homogeneousSubmodule_mul
 -/
 
@@ -135,10 +135,10 @@ theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : (∑
     IsHomogeneous (monomial d r) n := by
   intro c hc
   classical
-    rw [coeff_monomial] at hc 
-    split_ifs  at hc  with h
-    · subst c; exact hn
-    · contradiction
+  rw [coeff_monomial] at hc 
+  split_ifs at hc  with h
+  · subst c; exact hn
+  · contradiction
 #align mv_polynomial.is_homogeneous_monomial MvPolynomial.isHomogeneous_monomial
 
 variable (σ) {R}
@@ -210,14 +210,14 @@ theorem mul (hφ : IsHomogeneous φ m) (hψ : IsHomogeneous ψ n) : IsHomogeneou
 theorem prod {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ι → ℕ)
     (h : ∀ i ∈ s, IsHomogeneous (φ i) (n i)) : IsHomogeneous (∏ i in s, φ i) (∑ i in s, n i) := by
   classical
-    revert h
-    apply Finset.induction_on s
-    · intro; simp only [is_homogeneous_one, Finset.sum_empty, Finset.prod_empty]
-    · intro i s his IH h
-      simp only [his, Finset.prod_insert, Finset.sum_insert, not_false_iff]
-      apply (h i (Finset.mem_insert_self _ _)).mul (IH _)
-      intro j hjs
-      exact h j (Finset.mem_insert_of_mem hjs)
+  revert h
+  apply Finset.induction_on s
+  · intro; simp only [is_homogeneous_one, Finset.sum_empty, Finset.prod_empty]
+  · intro i s his IH h
+    simp only [his, Finset.prod_insert, Finset.sum_insert, not_false_iff]
+    apply (h i (Finset.mem_insert_self _ _)).mul (IH _)
+    intro j hjs
+    exact h j (Finset.mem_insert_of_mem hjs)
 #align mv_polynomial.is_homogeneous.prod MvPolynomial.IsHomogeneous.prod
 
 theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ = n :=
@@ -266,7 +266,7 @@ open Finset
 See `sum_homogeneous_component` for the statement that `φ` is equal to the sum
 of all its homogeneous components. -/
 def homogeneousComponent [CommSemiring R] (n : ℕ) : MvPolynomial σ R →ₗ[R] MvPolynomial σ R :=
-  (Submodule.subtype _).comp <| Finsupp.restrictDom _ _ { d | (∑ i in d.support, d i) = n }
+  (Submodule.subtype _).comp <| Finsupp.restrictDom _ _ {d | (∑ i in d.support, d i) = n}
 #align mv_polynomial.homogeneous_component MvPolynomial.homogeneousComponent
 -/
 
@@ -301,7 +301,7 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :
   rcases em (d = 0) with (rfl | hd)
   ·
     classical simp only [coeff_homogeneous_component, sum_eq_zero_iff, Finsupp.zero_apply, if_true,
-        coeff_C, eq_self_iff_true, forall_true_iff]
+      coeff_C, eq_self_iff_true, forall_true_iff]
   · rw [coeff_homogeneous_component, if_neg, coeff_C, if_neg (Ne.symm hd)]
     simp only [Finsupp.ext_iff, Finsupp.zero_apply] at hd 
     simp [hd]

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

@@ -59,7 +59,7 @@ def homogeneousSubmodule [CommSemiring R] (n : ℕ) : Submodule R (MvPolynomial
     where
   carrier := { x | x.Homogeneous n }
   smul_mem' r a ha c hc := by
-    rw [coeff_smul] at hc
+    rw [coeff_smul] at hc 
     apply ha
     intro h
     apply hc
@@ -67,7 +67,7 @@ def homogeneousSubmodule [CommSemiring R] (n : ℕ) : Submodule R (MvPolynomial
     exact smul_zero r
   zero_mem' d hd := False.elim (hd <| coeff_zero _)
   add_mem' a b ha hb c hc := by
-    rw [coeff_add] at hc
+    rw [coeff_add] at hc 
     obtain h | h : coeff c a ≠ 0 ∨ coeff c b ≠ 0 := by contrapose! hc; simp only [hc, add_zero]
     · exact ha h
     · exact hb h
@@ -106,7 +106,7 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
   by
   rw [Submodule.mul_le]
   intro φ hφ ψ hψ c hc
-  rw [coeff_mul] at hc
+  rw [coeff_mul] at hc 
   obtain ⟨⟨d, e⟩, hde, H⟩ := Finset.exists_ne_zero_of_sum_ne_zero hc
   have aux : coeff d φ ≠ 0 ∧ coeff e ψ ≠ 0 :=
     by
@@ -114,7 +114,7 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
     by_cases h : coeff d φ = 0 <;>
       simp_all only [Ne.def, not_false_iff, MulZeroClass.zero_mul, MulZeroClass.mul_zero]
   specialize hφ aux.1; specialize hψ aux.2
-  rw [Finsupp.mem_antidiagonal] at hde
+  rw [Finsupp.mem_antidiagonal] at hde 
   classical
     have hd' : d.support ⊆ d.support ∪ e.support := Finset.subset_union_left _ _
     have he' : e.support ⊆ d.support ∪ e.support := Finset.subset_union_right _ _
@@ -135,8 +135,8 @@ theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : (∑
     IsHomogeneous (monomial d r) n := by
   intro c hc
   classical
-    rw [coeff_monomial] at hc
-    split_ifs  at hc with h
+    rw [coeff_monomial] at hc 
+    split_ifs  at hc  with h
     · subst c; exact hn
     · contradiction
 #align mv_polynomial.is_homogeneous_monomial MvPolynomial.isHomogeneous_monomial
@@ -145,9 +145,9 @@ variable (σ) {R}
 
 theorem isHomogeneous_of_totalDegree_zero {p : MvPolynomial σ R} (hp : p.totalDegree = 0) :
     IsHomogeneous p 0 := by
-  erw [total_degree, Finset.sup_eq_bot_iff] at hp
+  erw [total_degree, Finset.sup_eq_bot_iff] at hp 
   -- we have to do this in two steps to stop simp changing bot to zero
-  simp_rw [mem_support_iff] at hp
+  simp_rw [mem_support_iff] at hp 
   exact hp
 #align mv_polynomial.is_homogeneous_of_total_degree_zero MvPolynomial.isHomogeneous_of_totalDegree_zero
 
@@ -185,7 +185,7 @@ variable [CommSemiring R] {φ ψ : MvPolynomial σ R} {m n : ℕ}
 theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : (∑ i in d.support, d i) ≠ n) :
     coeff d φ = 0 := by
   have aux := mt (@hφ d) hd
-  classical rwa [Classical.not_not] at aux
+  classical rwa [Classical.not_not] at aux 
 #align mv_polynomial.is_homogeneous.coeff_eq_zero MvPolynomial.IsHomogeneous.coeff_eq_zero
 
 theorem inj_right (hm : IsHomogeneous φ m) (hn : IsHomogeneous φ n) (hφ : φ ≠ 0) : m = n :=
@@ -212,7 +212,7 @@ theorem prod {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n :
   classical
     revert h
     apply Finset.induction_on s
-    · intro ; simp only [is_homogeneous_one, Finset.sum_empty, Finset.prod_empty]
+    · intro; simp only [is_homogeneous_one, Finset.sum_empty, Finset.prod_empty]
     · intro i s his IH h
       simp only [his, Finset.prod_insert, Finset.sum_insert, not_false_iff]
       apply (h i (Finset.mem_insert_self _ _)).mul (IH _)
@@ -226,7 +226,7 @@ theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ =
   apply le_antisymm
   · apply Finset.sup_le
     intro d hd
-    rw [mem_support_iff] at hd
+    rw [mem_support_iff] at hd 
     rw [Finsupp.sum, hφ hd]
   · obtain ⟨d, hd⟩ : ∃ d, coeff d φ ≠ 0 := exists_coeff_ne_zero h
     simp only [← hφ hd, Finsupp.sum]
@@ -303,7 +303,7 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :
     classical simp only [coeff_homogeneous_component, sum_eq_zero_iff, Finsupp.zero_apply, if_true,
         coeff_C, eq_self_iff_true, forall_true_iff]
   · rw [coeff_homogeneous_component, if_neg, coeff_C, if_neg (Ne.symm hd)]
-    simp only [Finsupp.ext_iff, Finsupp.zero_apply] at hd
+    simp only [Finsupp.ext_iff, Finsupp.zero_apply] at hd 
     simp [hd]
 #align mv_polynomial.homogeneous_component_zero MvPolynomial.homogeneousComponent_zero
 
@@ -318,14 +318,14 @@ theorem homogeneousComponent_eq_zero'
     homogeneousComponent n φ = 0 :=
   by
   rw [homogeneous_component_apply, sum_eq_zero]
-  intro d hd; rw [mem_filter] at hd
+  intro d hd; rw [mem_filter] at hd 
   exfalso; exact h _ hd.1 hd.2
 #align mv_polynomial.homogeneous_component_eq_zero' MvPolynomial.homogeneousComponent_eq_zero'
 
 theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousComponent n φ = 0 :=
   by
   apply homogeneous_component_eq_zero'
-  rw [total_degree, Finset.sup_lt_iff] at h
+  rw [total_degree, Finset.sup_lt_iff] at h 
   · intro d hd; exact ne_of_lt (h d hd)
   · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.homogeneous_component_eq_zero MvPolynomial.homogeneousComponent_eq_zero
@@ -342,7 +342,7 @@ theorem sum_homogeneousComponent :
 theorem homogeneousComponent_homogeneous_polynomial (m n : ℕ) (p : MvPolynomial σ R)
     (h : p ∈ homogeneousSubmodule σ R n) : homogeneousComponent m p = if m = n then p else 0 :=
   by
-  simp only [mem_homogeneous_submodule] at h
+  simp only [mem_homogeneous_submodule] at h 
   ext x
   rw [coeff_homogeneous_component]
   by_cases zero_coeff : coeff x p = 0

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

@@ -32,7 +32,7 @@ if all monomials occuring in `φ` have degree `n`.
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
 namespace MvPolynomial
 
@@ -100,6 +100,7 @@ theorem homogeneousSubmodule_eq_finsupp_supported [CommSemiring R] (n : ℕ) :
 
 variable {σ R}
 
+#print MvPolynomial.homogeneousSubmodule_mul /-
 theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
     homogeneousSubmodule σ R m * homogeneousSubmodule σ R n ≤ homogeneousSubmodule σ R (m + n) :=
   by
@@ -122,6 +123,7 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
     · congr
     all_goals intro i hi; apply finsupp.not_mem_support_iff.mp
 #align mv_polynomial.homogeneous_submodule_mul MvPolynomial.homogeneousSubmodule_mul
+-/
 
 section
 
@@ -243,7 +245,7 @@ instance HomogeneousSubmodule.gcommSemiring : SetLike.GradedMonoid (homogeneousS
 #align mv_polynomial.is_homogeneous.homogeneous_submodule.gcomm_semiring MvPolynomial.IsHomogeneous.HomogeneousSubmodule.gcommSemiring
 -/
 
-open DirectSum
+open scoped DirectSum
 
 noncomputable example : CommSemiring (⨁ i, homogeneousSubmodule σ R i) :=
   inferInstance

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

@@ -100,9 +100,6 @@ theorem homogeneousSubmodule_eq_finsupp_supported [CommSemiring R] (n : ℕ) :
 
 variable {σ R}
 
-/- warning: mv_polynomial.homogeneous_submodule_mul -> MvPolynomial.homogeneousSubmodule_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_submodule_mul MvPolynomial.homogeneousSubmodule_mulₓ'. -/
 theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
     homogeneousSubmodule σ R m * homogeneousSubmodule σ R n ≤ homogeneousSubmodule σ R (m + n) :=
   by
@@ -132,12 +129,6 @@ variable [CommSemiring R]
 
 variable {σ R}
 
-/- warning: mv_polynomial.is_homogeneous_monomial -> MvPolynomial.isHomogeneous_monomial is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous_monomial MvPolynomial.isHomogeneous_monomialₓ'. -/
 theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : (∑ i in d.support, d i) = n) :
     IsHomogeneous (monomial d r) n := by
   intro c hc
@@ -150,12 +141,6 @@ theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : (∑
 
 variable (σ) {R}
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous_of_total_degree_zero MvPolynomial.isHomogeneous_of_totalDegree_zeroₓ'. -/
 theorem isHomogeneous_of_totalDegree_zero {p : MvPolynomial σ R} (hp : p.totalDegree = 0) :
     IsHomogeneous p 0 := by
   erw [total_degree, Finset.sup_eq_bot_iff] at hp
@@ -164,12 +149,6 @@ theorem isHomogeneous_of_totalDegree_zero {p : MvPolynomial σ R} (hp : p.totalD
   exact hp
 #align mv_polynomial.is_homogeneous_of_total_degree_zero MvPolynomial.isHomogeneous_of_totalDegree_zero
 
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 theorem isHomogeneous_C (r : R) : IsHomogeneous (C r : MvPolynomial σ R) 0 :=
   by
   apply is_homogeneous_monomial
@@ -178,34 +157,16 @@ theorem isHomogeneous_C (r : R) : IsHomogeneous (C r : MvPolynomial σ R) 0 :=
 
 variable (σ R)
 
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 theorem isHomogeneous_zero (n : ℕ) : IsHomogeneous (0 : MvPolynomial σ R) n :=
   (homogeneousSubmodule σ R n).zero_mem
 #align mv_polynomial.is_homogeneous_zero MvPolynomial.isHomogeneous_zero
 
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 theorem isHomogeneous_one : IsHomogeneous (1 : MvPolynomial σ R) 0 :=
   isHomogeneous_C _ _
 #align mv_polynomial.is_homogeneous_one MvPolynomial.isHomogeneous_one
 
 variable {σ} (R)
 
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 theorem isHomogeneous_X (i : σ) : IsHomogeneous (X i : MvPolynomial σ R) 1 :=
   by
   apply is_homogeneous_monomial
@@ -219,67 +180,31 @@ namespace IsHomogeneous
 
 variable [CommSemiring R] {φ ψ : MvPolynomial σ R} {m n : ℕ}
 
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 theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : (∑ i in d.support, d i) ≠ n) :
     coeff d φ = 0 := by
   have aux := mt (@hφ d) hd
   classical rwa [Classical.not_not] at aux
 #align mv_polynomial.is_homogeneous.coeff_eq_zero MvPolynomial.IsHomogeneous.coeff_eq_zero
 
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 theorem inj_right (hm : IsHomogeneous φ m) (hn : IsHomogeneous φ n) (hφ : φ ≠ 0) : m = n :=
   by
   obtain ⟨d, hd⟩ : ∃ d, coeff d φ ≠ 0 := exists_coeff_ne_zero hφ
   rw [← hm hd, ← hn hd]
 #align mv_polynomial.is_homogeneous.inj_right MvPolynomial.IsHomogeneous.inj_right
 
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 theorem add (hφ : IsHomogeneous φ n) (hψ : IsHomogeneous ψ n) : IsHomogeneous (φ + ψ) n :=
   (homogeneousSubmodule σ R n).add_mem hφ hψ
 #align mv_polynomial.is_homogeneous.add MvPolynomial.IsHomogeneous.add
 
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 theorem sum {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ℕ)
     (h : ∀ i ∈ s, IsHomogeneous (φ i) n) : IsHomogeneous (∑ i in s, φ i) n :=
   (homogeneousSubmodule σ R n).sum_mem h
 #align mv_polynomial.is_homogeneous.sum MvPolynomial.IsHomogeneous.sum
 
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 theorem mul (hφ : IsHomogeneous φ m) (hψ : IsHomogeneous ψ n) : IsHomogeneous (φ * ψ) (m + n) :=
   homogeneousSubmodule_mul m n <| Submodule.mul_mem_mul hφ hψ
 #align mv_polynomial.is_homogeneous.mul MvPolynomial.IsHomogeneous.mul
 
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 theorem prod {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ι → ℕ)
     (h : ∀ i ∈ s, IsHomogeneous (φ i) (n i)) : IsHomogeneous (∏ i in s, φ i) (∑ i in s, n i) := by
   classical
@@ -293,12 +218,6 @@ theorem prod {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n :
       exact h j (Finset.mem_insert_of_mem hjs)
 #align mv_polynomial.is_homogeneous.prod MvPolynomial.IsHomogeneous.prod
 
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 theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ = n :=
   by
   rw [total_degree]
@@ -355,29 +274,17 @@ open Finset
 
 variable [CommSemiring R] (n : ℕ) (φ ψ : MvPolynomial σ R)
 
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 theorem coeff_homogeneousComponent (d : σ →₀ ℕ) :
     coeff d (homogeneousComponent n φ) = if (∑ i in d.support, d i) = n then coeff d φ else 0 := by
   convert Finsupp.filter_apply (fun d : σ →₀ ℕ => (∑ i in d.support, d i) = n) φ d
 #align mv_polynomial.coeff_homogeneous_component MvPolynomial.coeff_homogeneousComponent
 
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 theorem homogeneousComponent_apply :
     homogeneousComponent n φ =
       ∑ d in φ.support.filterₓ fun d => (∑ i in d.support, d i) = n, monomial d (coeff d φ) :=
   by convert Finsupp.filter_eq_sum (fun d : σ →₀ ℕ => (∑ i in d.support, d i) = n) φ
 #align mv_polynomial.homogeneous_component_apply MvPolynomial.homogeneousComponent_apply
 
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 theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).Homogeneous n :=
   by
   intro d hd
@@ -385,9 +292,6 @@ theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).Homogen
   rw [coeff_homogeneous_component, if_neg hd]
 #align mv_polynomial.homogeneous_component_is_homogeneous MvPolynomial.homogeneousComponent_isHomogeneous
 
-/- warning: mv_polynomial.homogeneous_component_zero -> MvPolynomial.homogeneousComponent_zero is a dubious translation:
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 @[simp]
 theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :=
   by
@@ -401,18 +305,12 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :
     simp [hd]
 #align mv_polynomial.homogeneous_component_zero MvPolynomial.homogeneousComponent_zero
 
-/- warning: mv_polynomial.homogeneous_component_C_mul -> MvPolynomial.homogeneousComponent_C_mul is a dubious translation:
-<too large>
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 @[simp]
 theorem homogeneousComponent_C_mul (n : ℕ) (r : R) :
     homogeneousComponent n (C r * φ) = C r * homogeneousComponent n φ := by
   simp only [C_mul', LinearMap.map_smul]
 #align mv_polynomial.homogeneous_component_C_mul MvPolynomial.homogeneousComponent_C_mul
 
-/- warning: mv_polynomial.homogeneous_component_eq_zero' -> MvPolynomial.homogeneousComponent_eq_zero' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_eq_zero' MvPolynomial.homogeneousComponent_eq_zero'ₓ'. -/
 theorem homogeneousComponent_eq_zero'
     (h : ∀ d : σ →₀ ℕ, d ∈ φ.support → (∑ i in d.support, d i) ≠ n) :
     homogeneousComponent n φ = 0 :=
@@ -422,12 +320,6 @@ theorem homogeneousComponent_eq_zero'
   exfalso; exact h _ hd.1 hd.2
 #align mv_polynomial.homogeneous_component_eq_zero' MvPolynomial.homogeneousComponent_eq_zero'
 
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 theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousComponent n φ = 0 :=
   by
   apply homogeneous_component_eq_zero'
@@ -436,12 +328,6 @@ theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousCompo
   · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.homogeneous_component_eq_zero MvPolynomial.homogeneousComponent_eq_zero
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_homogeneous_component MvPolynomial.sum_homogeneousComponentₓ'. -/
 theorem sum_homogeneousComponent :
     (∑ i in range (φ.totalDegree + 1), homogeneousComponent i φ) = φ :=
   by
@@ -451,9 +337,6 @@ theorem sum_homogeneousComponent :
   exact fun h => (coeff_eq_zero_of_total_degree_lt h).symm
 #align mv_polynomial.sum_homogeneous_component MvPolynomial.sum_homogeneousComponent
 
-/- warning: mv_polynomial.homogeneous_component_homogeneous_polynomial -> MvPolynomial.homogeneousComponent_homogeneous_polynomial is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_homogeneous_polynomial MvPolynomial.homogeneousComponent_homogeneous_polynomialₓ'. -/
 theorem homogeneousComponent_homogeneous_polynomial (m n : ℕ) (p : MvPolynomial σ R)
     (h : p ∈ homogeneousSubmodule σ R n) : homogeneousComponent m p = if m = n then p else 0 :=
   by

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

@@ -68,10 +68,7 @@ def homogeneousSubmodule [CommSemiring R] (n : ℕ) : Submodule R (MvPolynomial
   zero_mem' d hd := False.elim (hd <| coeff_zero _)
   add_mem' a b ha hb c hc := by
     rw [coeff_add] at hc
-    obtain h | h : coeff c a ≠ 0 ∨ coeff c b ≠ 0 :=
-      by
-      contrapose! hc
-      simp only [hc, add_zero]
+    obtain h | h : coeff c a ≠ 0 ∨ coeff c b ≠ 0 := by contrapose! hc; simp only [hc, add_zero]
     · exact ha h
     · exact hb h
 #align mv_polynomial.homogeneous_submodule MvPolynomial.homogeneousSubmodule
@@ -118,8 +115,7 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
     contrapose! H
     by_cases h : coeff d φ = 0 <;>
       simp_all only [Ne.def, not_false_iff, MulZeroClass.zero_mul, MulZeroClass.mul_zero]
-  specialize hφ aux.1
-  specialize hψ aux.2
+  specialize hφ aux.1; specialize hψ aux.2
   rw [Finsupp.mem_antidiagonal] at hde
   classical
     have hd' : d.support ⊆ d.support ∪ e.support := Finset.subset_union_left _ _
@@ -148,8 +144,7 @@ theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : (∑
   classical
     rw [coeff_monomial] at hc
     split_ifs  at hc with h
-    · subst c
-      exact hn
+    · subst c; exact hn
     · contradiction
 #align mv_polynomial.is_homogeneous_monomial MvPolynomial.isHomogeneous_monomial
 
@@ -290,8 +285,7 @@ theorem prod {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n :
   classical
     revert h
     apply Finset.induction_on s
-    · intro
-      simp only [is_homogeneous_one, Finset.sum_empty, Finset.prod_empty]
+    · intro ; simp only [is_homogeneous_one, Finset.sum_empty, Finset.prod_empty]
     · intro i s his IH h
       simp only [his, Finset.prod_insert, Finset.sum_insert, not_false_iff]
       apply (h i (Finset.mem_insert_self _ _)).mul (IH _)
@@ -438,8 +432,7 @@ theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousCompo
   by
   apply homogeneous_component_eq_zero'
   rw [total_degree, Finset.sup_lt_iff] at h
-  · intro d hd
-    exact ne_of_lt (h d hd)
+  · intro d hd; exact ne_of_lt (h d hd)
   · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.homogeneous_component_eq_zero MvPolynomial.homogeneousComponent_eq_zero
 

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

@@ -104,10 +104,7 @@ theorem homogeneousSubmodule_eq_finsupp_supported [CommSemiring R] (n : ℕ) :
 variable {σ R}
 
 /- warning: mv_polynomial.homogeneous_submodule_mul -> MvPolynomial.homogeneousSubmodule_mul is a dubious translation:
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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)))) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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)))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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)))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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)))) (Submodule.completeLattice.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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)))))))) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Submodule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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)))) (Submodule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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)))) (Submodule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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)))) (instHMul.{max u1 u2} (Submodule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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)))) (Submodule.mul.{u2, max u1 u2} R _inst_1 (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.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (MvPolynomial.homogeneousSubmodule.{u1, u2} σ R _inst_1 m) (MvPolynomial.homogeneousSubmodule.{u1, u2} σ R _inst_1 n)) (MvPolynomial.homogeneousSubmodule.{u1, u2} σ R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_submodule_mul MvPolynomial.homogeneousSubmodule_mulₓ'. -/
 theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
     homogeneousSubmodule σ R m * homogeneousSubmodule σ R n ≤ homogeneousSubmodule σ R (m + n) :=
@@ -365,10 +362,7 @@ open Finset
 variable [CommSemiring R] (n : ℕ) (φ ψ : MvPolynomial σ R)
 
 /- warning: mv_polynomial.coeff_homogeneous_component -> MvPolynomial.coeff_homogeneousComponent is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coeff_homogeneous_component MvPolynomial.coeff_homogeneousComponentₓ'. -/
 theorem coeff_homogeneousComponent (d : σ →₀ ℕ) :
     coeff d (homogeneousComponent n φ) = if (∑ i in d.support, d i) = n then coeff d φ else 0 := by
@@ -376,10 +370,7 @@ theorem coeff_homogeneousComponent (d : σ →₀ ℕ) :
 #align mv_polynomial.coeff_homogeneous_component MvPolynomial.coeff_homogeneousComponent
 
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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_apply MvPolynomial.homogeneousComponent_applyₓ'. -/
 theorem homogeneousComponent_apply :
     homogeneousComponent n φ =
@@ -401,10 +392,7 @@ theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).Homogen
 #align mv_polynomial.homogeneous_component_is_homogeneous MvPolynomial.homogeneousComponent_isHomogeneous
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_zero MvPolynomial.homogeneousComponent_zeroₓ'. -/
 @[simp]
 theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :=
@@ -420,10 +408,7 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :
 #align mv_polynomial.homogeneous_component_zero MvPolynomial.homogeneousComponent_zero
 
 /- warning: mv_polynomial.homogeneous_component_C_mul -> MvPolynomial.homogeneousComponent_C_mul is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_C_mul MvPolynomial.homogeneousComponent_C_mulₓ'. -/
 @[simp]
 theorem homogeneousComponent_C_mul (n : ℕ) (r : R) :
@@ -432,10 +417,7 @@ theorem homogeneousComponent_C_mul (n : ℕ) (r : R) :
 #align mv_polynomial.homogeneous_component_C_mul MvPolynomial.homogeneousComponent_C_mul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_eq_zero' MvPolynomial.homogeneousComponent_eq_zero'ₓ'. -/
 theorem homogeneousComponent_eq_zero'
     (h : ∀ d : σ →₀ ℕ, d ∈ φ.support → (∑ i in d.support, d i) ≠ n) :
@@ -477,10 +459,7 @@ theorem sum_homogeneousComponent :
 #align mv_polynomial.sum_homogeneous_component MvPolynomial.sum_homogeneousComponent
 
 /- warning: mv_polynomial.homogeneous_component_homogeneous_polynomial -> MvPolynomial.homogeneousComponent_homogeneous_polynomial is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_homogeneous_polynomial MvPolynomial.homogeneousComponent_homogeneous_polynomialₓ'. -/
 theorem homogeneousComponent_homogeneous_polynomial (m n : ℕ) (p : MvPolynomial σ R)
     (h : p ∈ homogeneousSubmodule σ R n) : homogeneousComponent m p = if m = n then p else 0 :=

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

@@ -143,7 +143,7 @@ variable {σ R}
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (d : Finsupp.{u1, 0} σ Nat Nat.hasZero) (r : R) (n : Nat), (Eq.{1} Nat (Finset.sum.{0, u1} Nat σ Nat.addCommMonoid (Finsupp.support.{u1, 0} σ Nat Nat.hasZero d) (fun (i : σ) => coeFn.{succ u1, succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u1, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u1, 0} σ Nat Nat.hasZero) d i)) n) -> (MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPolynomial.monomial.{u2, u1} R σ _inst_1 d) r) n)
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (r : R) (n : Nat), (Eq.{1} Nat (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 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.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i)) n) -> (MvPolynomial.IsHomogeneous.{u2, u1} σ R _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) 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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.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 (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.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 d) r) n)
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (r : R) (n : Nat), (Eq.{1} Nat (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 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.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i)) n) -> (MvPolynomial.IsHomogeneous.{u2, u1} σ R _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) 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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.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 (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.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 d) r) n)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous_monomial MvPolynomial.isHomogeneous_monomialₓ'. -/
 theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : (∑ i in d.support, d i) = n) :
     IsHomogeneous (monomial d r) n := by
@@ -368,7 +368,7 @@ variable [CommSemiring R] (n : ℕ) (φ ψ : MvPolynomial σ R)
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (n : Nat) (φ : MvPolynomial.{u1, u2} σ R _inst_1) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero), Eq.{succ u2} R (MvPolynomial.coeff.{u2, u1} R σ _inst_1 d (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 n) φ)) (ite.{succ u2} R (Eq.{1} Nat (Finset.sum.{0, u1} Nat σ Nat.addCommMonoid (Finsupp.support.{u1, 0} σ Nat Nat.hasZero d) (fun (i : σ) => coeFn.{succ u1, succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u1, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u1, 0} σ Nat Nat.hasZero) d i)) n) (Nat.decidableEq (Finset.sum.{0, u1} Nat σ Nat.addCommMonoid (Finsupp.support.{u1, 0} σ Nat Nat.hasZero d) (fun (i : σ) => coeFn.{succ u1, succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u1, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u1, 0} σ Nat Nat.hasZero) d i)) n) (MvPolynomial.coeff.{u2, u1} R σ _inst_1 d φ) (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat) (φ : MvPolynomial.{u2, u1} σ R _inst_1) (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Eq.{succ u1} R (MvPolynomial.coeff.{u1, u2} R σ _inst_1 d (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 n) φ)) (ite.{succ u1} R (Eq.{1} Nat (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 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.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i)) n) (instDecidableEqNat (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 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.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i)) n) (MvPolynomial.coeff.{u1, u2} R σ _inst_1 d φ) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat) (φ : MvPolynomial.{u2, u1} σ R _inst_1) (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Eq.{succ u1} R (MvPolynomial.coeff.{u1, u2} R σ _inst_1 d (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 n) φ)) (ite.{succ u1} R (Eq.{1} Nat (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 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.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i)) n) (instDecidableEqNat (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 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.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i)) n) (MvPolynomial.coeff.{u1, u2} R σ _inst_1 d φ) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coeff_homogeneous_component MvPolynomial.coeff_homogeneousComponentₓ'. -/
 theorem coeff_homogeneousComponent (d : σ →₀ ℕ) :
     coeff d (homogeneousComponent n φ) = if (∑ i in d.support, d i) = n then coeff d φ else 0 := by
@@ -379,7 +379,7 @@ theorem coeff_homogeneousComponent (d : σ →₀ ℕ) :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (n : Nat) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 n) φ) (Finset.sum.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Finsupp.{u1, 0} σ Nat Nat.hasZero) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Finset.filter.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (d : Finsupp.{u1, 0} σ Nat Nat.hasZero) => Eq.{1} Nat (Finset.sum.{0, u1} Nat σ Nat.addCommMonoid (Finsupp.support.{u1, 0} σ Nat Nat.hasZero d) (fun (i : σ) => coeFn.{succ u1, succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u1, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u1, 0} σ Nat Nat.hasZero) d i)) n) (fun (a : Finsupp.{u1, 0} σ Nat Nat.hasZero) => Nat.decidableEq (Finset.sum.{0, u1} Nat σ Nat.addCommMonoid (Finsupp.support.{u1, 0} σ Nat Nat.hasZero a) (fun (i : σ) => coeFn.{succ u1, succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u1, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u1, 0} σ Nat Nat.hasZero) a i)) n) (MvPolynomial.support.{u2, u1} R σ _inst_1 φ)) (fun (d : Finsupp.{u1, 0} σ Nat Nat.hasZero) => coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} 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(Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) 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(CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPolynomial.monomial.{u2, u1} R σ _inst_1 d) (MvPolynomial.coeff.{u2, u1} R σ _inst_1 d φ)))
 but is expected to have type
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(MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Finset.filter.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Eq.{1} Nat (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 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.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i)) n) (fun (a : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => instDecidableEqNat (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) a) (fun (i : σ) => FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 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.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) a i)) n) (MvPolynomial.support.{u1, u2} R σ _inst_1 φ)) (fun (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) 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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.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 (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.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 d) (MvPolynomial.coeff.{u1, u2} R σ _inst_1 d φ)))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat) (φ : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 n) φ) (Finset.sum.{max u2 u1, u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (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))))) (Finset.filter.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => Eq.{1} Nat (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 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.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i)) n) (fun (a : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => instDecidableEqNat (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) a) (fun (i : σ) => FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 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.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) a i)) n) (MvPolynomial.support.{u1, u2} R σ _inst_1 φ)) (fun (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) 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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.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 (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.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 d) (MvPolynomial.coeff.{u1, u2} R σ _inst_1 d φ)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_apply MvPolynomial.homogeneousComponent_applyₓ'. -/
 theorem homogeneousComponent_apply :
     homogeneousComponent n φ =
@@ -391,7 +391,7 @@ theorem homogeneousComponent_apply :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (n : Nat) (φ : MvPolynomial.{u1, u2} σ R _inst_1), MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 n) φ) n
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat) (φ : MvPolynomial.{u2, u1} σ R _inst_1), MvPolynomial.IsHomogeneous.{u2, u1} σ R _inst_1 (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 n) φ) n
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat) (φ : MvPolynomial.{u2, u1} σ R _inst_1), MvPolynomial.IsHomogeneous.{u2, u1} σ R _inst_1 (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 n) φ) n
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_is_homogeneous MvPolynomial.homogeneousComponent_isHomogeneousₓ'. -/
 theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).Homogeneous n :=
   by
@@ -404,7 +404,7 @@ theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).Homogen
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) φ) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) (MvPolynomial.coeff.{u2, u1} R σ _inst_1 (OfNat.ofNat.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (OfNat.mk.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) 0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero)))) φ))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) φ) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (MvPolynomial.C.{u1, u2} R σ _inst_1) (MvPolynomial.coeff.{u1, u2} R σ _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) φ))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) φ) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (MvPolynomial.C.{u1, u2} R σ _inst_1) (MvPolynomial.coeff.{u1, u2} R σ _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) φ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_zero MvPolynomial.homogeneousComponent_zeroₓ'. -/
 @[simp]
 theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :=
@@ -423,7 +423,7 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{u1, u2} σ R _inst_1) (n : Nat) (r : R), Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 n) (HMul.hMul.{max u1 u2, 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 u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 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(CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r) φ)) (HMul.hMul.{max u1 u2, 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 u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} 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_inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (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) 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_inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 n) φ))
 but is expected to have type
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+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{u1, u2} σ R _inst_1) (n : Nat) (r : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) (HMul.hMul.{max u2 u1, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (Semiring.toNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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_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) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u2, u2, max u2 u1, 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))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 n) φ))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_C_mul MvPolynomial.homogeneousComponent_C_mulₓ'. -/
 @[simp]
 theorem homogeneousComponent_C_mul (n : ℕ) (r : R) :
@@ -435,7 +435,7 @@ theorem homogeneousComponent_C_mul (n : ℕ) (r : R) :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (n : Nat) (φ : MvPolynomial.{u1, u2} σ R _inst_1), (forall (d : Finsupp.{u1, 0} σ Nat Nat.hasZero), (Membership.Mem.{u1, u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finset.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero)) (Finset.hasMem.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero)) d (MvPolynomial.support.{u2, u1} R σ _inst_1 φ)) -> (Ne.{1} Nat (Finset.sum.{0, u1} Nat σ Nat.addCommMonoid (Finsupp.support.{u1, 0} σ Nat Nat.hasZero d) (fun (i : σ) => coeFn.{succ u1, succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u1, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u1, 0} σ Nat Nat.hasZero) d i)) n)) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 n) φ) (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (OfNat.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (Zero.zero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulZeroClass.toHasZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat) (φ : MvPolynomial.{u2, u1} σ R _inst_1), (forall (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), (Membership.mem.{u2, u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finset.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finset.instMembershipFinset.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) d (MvPolynomial.support.{u1, u2} R σ _inst_1 φ)) -> (Ne.{1} Nat (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 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.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i)) n)) -> (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 n) φ) (OfNat.ofNat.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) 0 (Zero.toOfNat0.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (CommMonoidWithZero.toZero.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (CommSemiring.toCommMonoidWithZero.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat) (φ : MvPolynomial.{u2, u1} σ R _inst_1), (forall (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), (Membership.mem.{u2, u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finset.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finset.instMembershipFinset.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) d (MvPolynomial.support.{u1, u2} R σ _inst_1 φ)) -> (Ne.{1} Nat (Finset.sum.{0, u2} Nat σ Nat.addCommMonoid (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 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.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i)) n)) -> (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 n) φ) (OfNat.ofNat.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) 0 (Zero.toOfNat0.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (CommMonoidWithZero.toZero.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (CommSemiring.toCommMonoidWithZero.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_eq_zero' MvPolynomial.homogeneousComponent_eq_zero'ₓ'. -/
 theorem homogeneousComponent_eq_zero'
     (h : ∀ d : σ →₀ ℕ, d ∈ φ.support → (∑ i in d.support, d i) ≠ n) :
@@ -450,7 +450,7 @@ theorem homogeneousComponent_eq_zero'
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (n : Nat) (φ : MvPolynomial.{u1, u2} σ R _inst_1), (LT.lt.{0} Nat Nat.hasLt (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 φ) n) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 n) φ) (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (OfNat.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (Zero.zero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulZeroClass.toHasZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))))))
 but is expected to have type
-  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (n : Nat) (φ : MvPolynomial.{u1, u2} σ R _inst_1), (LT.lt.{0} Nat instLTNat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 φ) n) -> (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u2, u2, max u2 u1, 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))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 n) φ) (OfNat.ofNat.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) 0 (Zero.toOfNat0.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) (CommMonoidWithZero.toZero.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) (CommSemiring.toCommMonoidWithZero.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))
+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (n : Nat) (φ : MvPolynomial.{u1, u2} σ R _inst_1), (LT.lt.{0} Nat instLTNat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 φ) n) -> (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u2, u2, max u2 u1, 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))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 n) φ) (OfNat.ofNat.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) 0 (Zero.toOfNat0.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) (CommMonoidWithZero.toZero.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) (CommSemiring.toCommMonoidWithZero.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) φ) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_eq_zero MvPolynomial.homogeneousComponent_eq_zeroₓ'. -/
 theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousComponent n φ = 0 :=
   by
@@ -465,7 +465,7 @@ theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousCompo
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{succ (max u1 u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (Finset.sum.{max u1 u2, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 φ) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 i) φ)) φ
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (Finset.sum.{max u2 u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (Semiring.toNonAssocSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (CommSemiring.toSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 φ) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 i) φ)) φ
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (Finset.sum.{max u2 u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (Semiring.toNonAssocSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (CommSemiring.toSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 φ) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 i) φ)) φ
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_homogeneous_component MvPolynomial.sum_homogeneousComponentₓ'. -/
 theorem sum_homogeneousComponent :
     (∑ i in range (φ.totalDegree + 1), homogeneousComponent i φ) = φ :=
@@ -480,7 +480,7 @@ theorem sum_homogeneousComponent :
 lean 3 declaration is
   forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (m : Nat) (n : Nat) (p : MvPolynomial.{u1, u2} σ R _inst_1), (Membership.Mem.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Submodule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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)))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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)))) (MvPolynomial.{u1, u2} σ R _inst_1) (Submodule.setLike.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))))) p (MvPolynomial.homogeneousSubmodule.{u1, u2} σ R _inst_1 n)) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 m) p) (ite.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (Eq.{1} Nat m n) (Nat.decidableEq m n) p (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (OfNat.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (Zero.zero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulZeroClass.toHasZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))))))))
 but is expected to have type
-  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (m : Nat) (n : Nat) (p : MvPolynomial.{u2, u1} σ R _inst_1), (Membership.mem.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Submodule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (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))))) (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)))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (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))))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (Submodule.setLike.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (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))))) (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))))) p (MvPolynomial.homogeneousSubmodule.{u2, u1} σ R _inst_1 n)) -> (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 m) p) (ite.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R _inst_1) (Eq.{1} Nat m n) (instDecidableEqNat m n) p (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 0 (Zero.toOfNat0.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommMonoidWithZero.toZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toCommMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))))
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (m : Nat) (n : Nat) (p : MvPolynomial.{u2, u1} σ R _inst_1), (Membership.mem.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Submodule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (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))))) (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)))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (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))))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (Submodule.setLike.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (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))))) (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))))) p (MvPolynomial.homogeneousSubmodule.{u2, u1} σ R _inst_1 n)) -> (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 m) p) (ite.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R _inst_1) (Eq.{1} Nat m n) (instDecidableEqNat m n) p (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 0 (Zero.toOfNat0.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommMonoidWithZero.toZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toCommMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_homogeneous_polynomial MvPolynomial.homogeneousComponent_homogeneous_polynomialₓ'. -/
 theorem homogeneousComponent_homogeneous_polynomial (m n : ℕ) (p : MvPolynomial σ R)
     (h : p ∈ homogeneousSubmodule σ R n) : homogeneousComponent m p = if m = n then p else 0 :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/1b0a28e1c93409dbf6d69526863cd9984ef652ce

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Eric Wieser
 
 ! This file was ported from Lean 3 source module ring_theory.mv_polynomial.homogeneous
-! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
+! leanprover-community/mathlib commit 1b0a28e1c93409dbf6d69526863cd9984ef652ce
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Data.MvPolynomial.Variables
 /-!
 # Homogeneous polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A multivariate polynomial `φ` is homogeneous of degree `n`
 if all monomials occuring in `φ` have degree `n`.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed

@@ -35,6 +35,7 @@ namespace MvPolynomial
 
 variable {σ : Type _} {τ : Type _} {R : Type _} {S : Type _}
 
+#print MvPolynomial.IsHomogeneous /-
 /-
 TODO
 * create definition for `∑ i in d.support, d i`
@@ -45,9 +46,11 @@ if all monomials occuring in `φ` have degree `n`. -/
 def IsHomogeneous [CommSemiring R] (φ : MvPolynomial σ R) (n : ℕ) :=
   ∀ ⦃d⦄, coeff d φ ≠ 0 → (∑ i in d.support, d i) = n
 #align mv_polynomial.is_homogeneous MvPolynomial.IsHomogeneous
+-/
 
 variable (σ R)
 
+#print MvPolynomial.homogeneousSubmodule /-
 /-- The submodule of homogeneous `mv_polynomial`s of degree `n`. -/
 def homogeneousSubmodule [CommSemiring R] (n : ℕ) : Submodule R (MvPolynomial σ R)
     where
@@ -69,17 +72,21 @@ def homogeneousSubmodule [CommSemiring R] (n : ℕ) : Submodule R (MvPolynomial
     · exact ha h
     · exact hb h
 #align mv_polynomial.homogeneous_submodule MvPolynomial.homogeneousSubmodule
+-/
 
 variable {σ R}
 
+#print MvPolynomial.mem_homogeneousSubmodule /-
 @[simp]
 theorem mem_homogeneousSubmodule [CommSemiring R] (n : ℕ) (p : MvPolynomial σ R) :
     p ∈ homogeneousSubmodule σ R n ↔ p.Homogeneous n :=
   Iff.rfl
 #align mv_polynomial.mem_homogeneous_submodule MvPolynomial.mem_homogeneousSubmodule
+-/
 
 variable (σ R)
 
+#print MvPolynomial.homogeneousSubmodule_eq_finsupp_supported /-
 /-- While equal, the former has a convenient definitional reduction. -/
 theorem homogeneousSubmodule_eq_finsupp_supported [CommSemiring R] (n : ℕ) :
     homogeneousSubmodule σ R n = Finsupp.supported _ R { d | (∑ i in d.support, d i) = n } :=
@@ -89,9 +96,16 @@ theorem homogeneousSubmodule_eq_finsupp_supported [CommSemiring R] (n : ℕ) :
   simp only [Finsupp.mem_support_iff, Finset.mem_coe]
   rfl
 #align mv_polynomial.homogeneous_submodule_eq_finsupp_supported MvPolynomial.homogeneousSubmodule_eq_finsupp_supported
+-/
 
 variable {σ R}
 
+/- warning: mv_polynomial.homogeneous_submodule_mul -> MvPolynomial.homogeneousSubmodule_mul is a dubious translation:
+lean 3 declaration is
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(Submodule.mul.{u2, max u1 u2} R _inst_1 (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.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (MvPolynomial.homogeneousSubmodule.{u1, u2} σ R _inst_1 m) (MvPolynomial.homogeneousSubmodule.{u1, u2} σ R _inst_1 n)) (MvPolynomial.homogeneousSubmodule.{u1, u2} σ R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_submodule_mul MvPolynomial.homogeneousSubmodule_mulₓ'. -/
 theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
     homogeneousSubmodule σ R m * homogeneousSubmodule σ R n ≤ homogeneousSubmodule σ R (m + n) :=
   by
@@ -122,6 +136,12 @@ variable [CommSemiring R]
 
 variable {σ R}
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous_monomial MvPolynomial.isHomogeneous_monomialₓ'. -/
 theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : (∑ i in d.support, d i) = n) :
     IsHomogeneous (monomial d r) n := by
   intro c hc
@@ -135,6 +155,12 @@ theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : (∑
 
 variable (σ) {R}
 
+/- warning: mv_polynomial.is_homogeneous_of_total_degree_zero -> MvPolynomial.isHomogeneous_of_totalDegree_zero is a dubious translation:
+lean 3 declaration is
+  forall (σ : Type.{u1}) {R : Type.{u2}} [_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) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
+but is expected to have type
+  forall (σ : Type.{u2}) {R : Type.{u1}} [_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) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (MvPolynomial.IsHomogeneous.{u2, u1} σ R _inst_1 p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous_of_total_degree_zero MvPolynomial.isHomogeneous_of_totalDegree_zeroₓ'. -/
 theorem isHomogeneous_of_totalDegree_zero {p : MvPolynomial σ R} (hp : p.totalDegree = 0) :
     IsHomogeneous p 0 := by
   erw [total_degree, Finset.sup_eq_bot_iff] at hp
@@ -143,30 +169,54 @@ theorem isHomogeneous_of_totalDegree_zero {p : MvPolynomial σ R} (hp : p.totalD
   exact hp
 #align mv_polynomial.is_homogeneous_of_total_degree_zero MvPolynomial.isHomogeneous_of_totalDegree_zero
 
-theorem isHomogeneous_c (r : R) : IsHomogeneous (C r : MvPolynomial σ R) 0 :=
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous_C MvPolynomial.isHomogeneous_Cₓ'. -/
+theorem isHomogeneous_C (r : R) : IsHomogeneous (C r : MvPolynomial σ R) 0 :=
   by
   apply is_homogeneous_monomial
   simp only [Finsupp.zero_apply, Finset.sum_const_zero]
-#align mv_polynomial.is_homogeneous_C MvPolynomial.isHomogeneous_c
+#align mv_polynomial.is_homogeneous_C MvPolynomial.isHomogeneous_C
 
 variable (σ R)
 
+/- warning: mv_polynomial.is_homogeneous_zero -> MvPolynomial.isHomogeneous_zero is a dubious translation:
+lean 3 declaration is
+  forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommSemiring.{u2} R] (n : Nat), MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (OfNat.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (Zero.zero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulZeroClass.toHasZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))))) n
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous_zero MvPolynomial.isHomogeneous_zeroₓ'. -/
 theorem isHomogeneous_zero (n : ℕ) : IsHomogeneous (0 : MvPolynomial σ R) n :=
   (homogeneousSubmodule σ R n).zero_mem
 #align mv_polynomial.is_homogeneous_zero MvPolynomial.isHomogeneous_zero
 
+/- warning: mv_polynomial.is_homogeneous_one -> MvPolynomial.isHomogeneous_one is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall (σ : Type.{u2}) (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R], MvPolynomial.IsHomogeneous.{u2, u1} σ R _inst_1 (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 1 (One.toOfNat1.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toOne.{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 (instOfNatNat 0))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous_one MvPolynomial.isHomogeneous_oneₓ'. -/
 theorem isHomogeneous_one : IsHomogeneous (1 : MvPolynomial σ R) 0 :=
-  isHomogeneous_c _ _
+  isHomogeneous_C _ _
 #align mv_polynomial.is_homogeneous_one MvPolynomial.isHomogeneous_one
 
 variable {σ} (R)
 
-theorem isHomogeneous_x (i : σ) : IsHomogeneous (X i : MvPolynomial σ R) 1 :=
+/- warning: mv_polynomial.is_homogeneous_X -> MvPolynomial.isHomogeneous_X is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} (R : Type.{u2}) [_inst_1 : CommSemiring.{u2} R] (i : σ), MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 (MvPolynomial.X.{u2, u1} R σ _inst_1 i) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))
+but is expected to have type
+  forall {σ : Type.{u2}} (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (i : σ), MvPolynomial.IsHomogeneous.{u2, u1} σ R _inst_1 (MvPolynomial.X.{u1, u2} R σ _inst_1 i) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous_X MvPolynomial.isHomogeneous_Xₓ'. -/
+theorem isHomogeneous_X (i : σ) : IsHomogeneous (X i : MvPolynomial σ R) 1 :=
   by
   apply is_homogeneous_monomial
   simp only [Finsupp.support_single_ne_zero _ one_ne_zero, Finset.sum_singleton]
   exact Finsupp.single_eq_same
-#align mv_polynomial.is_homogeneous_X MvPolynomial.isHomogeneous_x
+#align mv_polynomial.is_homogeneous_X MvPolynomial.isHomogeneous_X
 
 end
 
@@ -174,31 +224,67 @@ namespace IsHomogeneous
 
 variable [CommSemiring R] {φ ψ : MvPolynomial σ R} {m n : ℕ}
 
+/- warning: mv_polynomial.is_homogeneous.coeff_eq_zero -> MvPolynomial.IsHomogeneous.coeff_eq_zero 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.is_homogeneous.coeff_eq_zero MvPolynomial.IsHomogeneous.coeff_eq_zeroₓ'. -/
 theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : (∑ i in d.support, d i) ≠ n) :
     coeff d φ = 0 := by
   have aux := mt (@hφ d) hd
   classical rwa [Classical.not_not] at aux
 #align mv_polynomial.is_homogeneous.coeff_eq_zero MvPolynomial.IsHomogeneous.coeff_eq_zero
 
+/- warning: mv_polynomial.is_homogeneous.inj_right -> MvPolynomial.IsHomogeneous.inj_right is a dubious translation:
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+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {φ : MvPolynomial.{u1, u2} σ R _inst_1} {m : Nat} {n : Nat}, (MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 φ m) -> (MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 φ n) -> (Ne.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) φ (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (OfNat.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (Zero.zero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulZeroClass.toHasZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))))))) -> (Eq.{1} Nat m n)
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous.inj_right MvPolynomial.IsHomogeneous.inj_rightₓ'. -/
 theorem inj_right (hm : IsHomogeneous φ m) (hn : IsHomogeneous φ n) (hφ : φ ≠ 0) : m = n :=
   by
   obtain ⟨d, hd⟩ : ∃ d, coeff d φ ≠ 0 := exists_coeff_ne_zero hφ
   rw [← hm hd, ← hn hd]
 #align mv_polynomial.is_homogeneous.inj_right MvPolynomial.IsHomogeneous.inj_right
 
+/- warning: mv_polynomial.is_homogeneous.add -> MvPolynomial.IsHomogeneous.add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous.add MvPolynomial.IsHomogeneous.addₓ'. -/
 theorem add (hφ : IsHomogeneous φ n) (hψ : IsHomogeneous ψ n) : IsHomogeneous (φ + ψ) n :=
   (homogeneousSubmodule σ R n).add_mem hφ hψ
 #align mv_polynomial.is_homogeneous.add MvPolynomial.IsHomogeneous.add
 
+/- warning: mv_polynomial.is_homogeneous.sum -> MvPolynomial.IsHomogeneous.sum 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.is_homogeneous.sum MvPolynomial.IsHomogeneous.sumₓ'. -/
 theorem sum {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ℕ)
     (h : ∀ i ∈ s, IsHomogeneous (φ i) n) : IsHomogeneous (∑ i in s, φ i) n :=
   (homogeneousSubmodule σ R n).sum_mem h
 #align mv_polynomial.is_homogeneous.sum MvPolynomial.IsHomogeneous.sum
 
+/- warning: mv_polynomial.is_homogeneous.mul -> MvPolynomial.IsHomogeneous.mul is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {φ : MvPolynomial.{u1, u2} σ R _inst_1} {ψ : MvPolynomial.{u1, u2} σ R _inst_1} {m : Nat} {n : Nat}, (MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 φ m) -> (MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 ψ n) -> (MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 (HMul.hMul.{max u1 u2, 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 u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) φ ψ) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous.mul MvPolynomial.IsHomogeneous.mulₓ'. -/
 theorem mul (hφ : IsHomogeneous φ m) (hψ : IsHomogeneous ψ n) : IsHomogeneous (φ * ψ) (m + n) :=
   homogeneousSubmodule_mul m n <| Submodule.mul_mem_mul hφ hψ
 #align mv_polynomial.is_homogeneous.mul MvPolynomial.IsHomogeneous.mul
 
+/- warning: mv_polynomial.is_homogeneous.prod -> MvPolynomial.IsHomogeneous.prod is a dubious translation:
+lean 3 declaration is
+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {ι : Type.{u3}} (s : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u1, u2} σ R _inst_1)) (n : ι -> Nat), (forall (i : ι), (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) -> (MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 (φ i) (n i))) -> (MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 (Finset.prod.{max u1 u2, u3} (MvPolynomial.{u1, u2} σ R _inst_1) ι (CommSemiring.toCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) s (fun (i : ι) => φ i)) (Finset.sum.{0, u3} Nat ι Nat.addCommMonoid s (fun (i : ι) => n i)))
+but is expected to have type
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u3}} (s : Finset.{u3} ι) (φ : ι -> (MvPolynomial.{u2, u1} σ R _inst_1)) (n : ι -> Nat), (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (MvPolynomial.IsHomogeneous.{u2, u1} σ R _inst_1 (φ i) (n i))) -> (MvPolynomial.IsHomogeneous.{u2, u1} σ R _inst_1 (Finset.prod.{max u1 u2, 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) => φ i)) (Finset.sum.{0, u3} Nat ι Nat.addCommMonoid s (fun (i : ι) => n i)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous.prod MvPolynomial.IsHomogeneous.prodₓ'. -/
 theorem prod {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ι → ℕ)
     (h : ∀ i ∈ s, IsHomogeneous (φ i) (n i)) : IsHomogeneous (∏ i in s, φ i) (∑ i in s, n i) := by
   classical
@@ -213,6 +299,12 @@ theorem prod {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n :
       exact h j (Finset.mem_insert_of_mem hjs)
 #align mv_polynomial.is_homogeneous.prod MvPolynomial.IsHomogeneous.prod
 
+/- warning: mv_polynomial.is_homogeneous.total_degree -> MvPolynomial.IsHomogeneous.totalDegree is a dubious translation:
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+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {φ : MvPolynomial.{u1, u2} σ R _inst_1} {n : Nat}, (MvPolynomial.IsHomogeneous.{u1, u2} σ R _inst_1 φ n) -> (Ne.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) φ (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (OfNat.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 0 (Zero.zero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MulZeroClass.toHasZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))))))) -> (Eq.{1} Nat (MvPolynomial.totalDegree.{u2, u1} R σ _inst_1 φ) n)
+but is expected to have type
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {φ : MvPolynomial.{u2, u1} σ R _inst_1} {n : Nat}, (MvPolynomial.IsHomogeneous.{u2, u1} σ R _inst_1 φ n) -> (Ne.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R _inst_1) φ (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 0 (Zero.toOfNat0.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommMonoidWithZero.toZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toCommMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) -> (Eq.{1} Nat (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 φ) n)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_homogeneous.total_degree MvPolynomial.IsHomogeneous.totalDegreeₓ'. -/
 theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ = n :=
   by
   rw [total_degree]
@@ -227,14 +319,16 @@ theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ =
     exact Finset.le_sup hd
 #align mv_polynomial.is_homogeneous.total_degree MvPolynomial.IsHomogeneous.totalDegree
 
+#print MvPolynomial.IsHomogeneous.HomogeneousSubmodule.gcommSemiring /-
 /--
 The homogeneous submodules form a graded ring. This instance is used by `direct_sum.comm_semiring`
 and `direct_sum.algebra`. -/
-instance HomogeneousSubmodule.gcomm_semiring : SetLike.GradedMonoid (homogeneousSubmodule σ R)
+instance HomogeneousSubmodule.gcommSemiring : SetLike.GradedMonoid (homogeneousSubmodule σ R)
     where
   one_mem := isHomogeneous_one σ R
   mul_mem i j xi xj := IsHomogeneous.mul
-#align mv_polynomial.is_homogeneous.homogeneous_submodule.gcomm_semiring MvPolynomial.IsHomogeneous.HomogeneousSubmodule.gcomm_semiring
+#align mv_polynomial.is_homogeneous.homogeneous_submodule.gcomm_semiring MvPolynomial.IsHomogeneous.HomogeneousSubmodule.gcommSemiring
+-/
 
 open DirectSum
 
@@ -252,12 +346,14 @@ noncomputable section
 
 open Finset
 
+#print MvPolynomial.homogeneousComponent /-
 /-- `homogeneous_component n φ` is the part of `φ` that is homogeneous of degree `n`.
 See `sum_homogeneous_component` for the statement that `φ` is equal to the sum
 of all its homogeneous components. -/
 def homogeneousComponent [CommSemiring R] (n : ℕ) : MvPolynomial σ R →ₗ[R] MvPolynomial σ R :=
   (Submodule.subtype _).comp <| Finsupp.restrictDom _ _ { d | (∑ i in d.support, d i) = n }
 #align mv_polynomial.homogeneous_component MvPolynomial.homogeneousComponent
+-/
 
 section HomogeneousComponent
 
@@ -265,17 +361,35 @@ open Finset
 
 variable [CommSemiring R] (n : ℕ) (φ ψ : MvPolynomial σ R)
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.coeff_homogeneous_component MvPolynomial.coeff_homogeneousComponentₓ'. -/
 theorem coeff_homogeneousComponent (d : σ →₀ ℕ) :
     coeff d (homogeneousComponent n φ) = if (∑ i in d.support, d i) = n then coeff d φ else 0 := by
   convert Finsupp.filter_apply (fun d : σ →₀ ℕ => (∑ i in d.support, d i) = n) φ d
 #align mv_polynomial.coeff_homogeneous_component MvPolynomial.coeff_homogeneousComponent
 
+/- warning: mv_polynomial.homogeneous_component_apply -> MvPolynomial.homogeneousComponent_apply is a dubious translation:
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R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 d) (MvPolynomial.coeff.{u1, u2} R σ _inst_1 d φ)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_apply MvPolynomial.homogeneousComponent_applyₓ'. -/
 theorem homogeneousComponent_apply :
     homogeneousComponent n φ =
       ∑ d in φ.support.filterₓ fun d => (∑ i in d.support, d i) = n, monomial d (coeff d φ) :=
   by convert Finsupp.filter_eq_sum (fun d : σ →₀ ℕ => (∑ i in d.support, d i) = n) φ
 #align mv_polynomial.homogeneous_component_apply MvPolynomial.homogeneousComponent_apply
 
+/- warning: mv_polynomial.homogeneous_component_is_homogeneous -> MvPolynomial.homogeneousComponent_isHomogeneous is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_is_homogeneous MvPolynomial.homogeneousComponent_isHomogeneousₓ'. -/
 theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).Homogeneous n :=
   by
   intro d hd
@@ -283,6 +397,12 @@ theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).Homogen
   rw [coeff_homogeneous_component, if_neg hd]
 #align mv_polynomial.homogeneous_component_is_homogeneous MvPolynomial.homogeneousComponent_isHomogeneous
 
+/- warning: mv_polynomial.homogeneous_component_zero -> MvPolynomial.homogeneousComponent_zero is a dubious translation:
+lean 3 declaration is
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0 (Zero.zero.{u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (Finsupp.zero.{u1, 0} σ Nat Nat.hasZero)))) φ))
+but is expected to have type
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(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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) φ) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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(MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (MvPolynomial.C.{u1, u2} R σ _inst_1) (MvPolynomial.coeff.{u1, u2} R σ _inst_1 (OfNat.ofNat.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) 0 (Zero.toOfNat0.{u2} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finsupp.zero.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) φ))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_zero MvPolynomial.homogeneousComponent_zeroₓ'. -/
 @[simp]
 theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :=
   by
@@ -296,12 +416,24 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :
     simp [hd]
 #align mv_polynomial.homogeneous_component_zero MvPolynomial.homogeneousComponent_zero
 
+/- warning: mv_polynomial.homogeneous_component_C_mul -> MvPolynomial.homogeneousComponent_C_mul is a dubious translation:
+lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 n) (HMul.hMul.{max u1 u2, 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 u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r) φ)) (HMul.hMul.{max u1 u2, 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 u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} 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_inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 n) φ))
+but is expected to have type
+  forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (φ : MvPolynomial.{u1, u2} σ R _inst_1) (n : Nat) (r : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u1, u2} σ R _inst_1) (HMul.hMul.{max u2 u1, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u1, u2} σ R _inst_1) r) (Semiring.toNonAssocSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_C_mul MvPolynomial.homogeneousComponent_C_mulₓ'. -/
 @[simp]
-theorem homogeneousComponent_c_mul (n : ℕ) (r : R) :
+theorem homogeneousComponent_C_mul (n : ℕ) (r : R) :
     homogeneousComponent n (C r * φ) = C r * homogeneousComponent n φ := by
   simp only [C_mul', LinearMap.map_smul]
-#align mv_polynomial.homogeneous_component_C_mul MvPolynomial.homogeneousComponent_c_mul
-
+#align mv_polynomial.homogeneous_component_C_mul MvPolynomial.homogeneousComponent_C_mul
+
+/- warning: mv_polynomial.homogeneous_component_eq_zero' -> MvPolynomial.homogeneousComponent_eq_zero' 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.homogeneous_component_eq_zero' MvPolynomial.homogeneousComponent_eq_zero'ₓ'. -/
 theorem homogeneousComponent_eq_zero'
     (h : ∀ d : σ →₀ ℕ, d ∈ φ.support → (∑ i in d.support, d i) ≠ n) :
     homogeneousComponent n φ = 0 :=
@@ -311,6 +443,12 @@ theorem homogeneousComponent_eq_zero'
   exfalso; exact h _ hd.1 hd.2
 #align mv_polynomial.homogeneous_component_eq_zero' MvPolynomial.homogeneousComponent_eq_zero'
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_eq_zero MvPolynomial.homogeneousComponent_eq_zeroₓ'. -/
 theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousComponent n φ = 0 :=
   by
   apply homogeneous_component_eq_zero'
@@ -320,6 +458,12 @@ theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousCompo
   · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.homogeneous_component_eq_zero MvPolynomial.homogeneousComponent_eq_zero
 
+/- warning: mv_polynomial.sum_homogeneous_component -> MvPolynomial.sum_homogeneousComponent is a dubious translation:
+lean 3 declaration is
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(CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} R R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (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))) (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.homogeneousComponent.{u1, u2} σ R _inst_1 i) φ)) φ
+but is expected to have type
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (φ : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (Finset.sum.{max u2 u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (Semiring.toNonAssocSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (CommSemiring.toSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) φ) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (MvPolynomial.totalDegree.{u1, u2} R σ _inst_1 φ) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ 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))))) (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))))) (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))) (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)))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (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))))) (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))))) (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))) (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.homogeneousComponent.{u2, u1} σ R _inst_1 i) φ)) φ
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_homogeneous_component MvPolynomial.sum_homogeneousComponentₓ'. -/
 theorem sum_homogeneousComponent :
     (∑ i in range (φ.totalDegree + 1), homogeneousComponent i φ) = φ :=
   by
@@ -329,6 +473,12 @@ theorem sum_homogeneousComponent :
   exact fun h => (coeff_eq_zero_of_total_degree_lt h).symm
 #align mv_polynomial.sum_homogeneous_component MvPolynomial.sum_homogeneousComponent
 
+/- warning: mv_polynomial.homogeneous_component_homogeneous_polynomial -> MvPolynomial.homogeneousComponent_homogeneous_polynomial is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (m : Nat) (n : Nat) (p : MvPolynomial.{u2, u1} σ R _inst_1), (Membership.mem.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Submodule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (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))))) (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)))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.homogeneous_component_homogeneous_polynomial MvPolynomial.homogeneousComponent_homogeneous_polynomialₓ'. -/
 theorem homogeneousComponent_homogeneous_polynomial (m n : ℕ) (p : MvPolynomial σ R)
     (h : p ∈ homogeneousSubmodule σ R n) : homogeneousComponent m p = if m = n then p else 0 :=
   by

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Eric Wieser
 
 ! This file was ported from Lean 3 source module ring_theory.mv_polynomial.homogeneous
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -250,8 +250,6 @@ section
 
 noncomputable section
 
-open Classical
-
 open Finset
 
 /-- `homogeneous_component n φ` is the part of `φ` that is homogeneous of degree `n`.
@@ -291,8 +289,8 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :
   ext1 d
   rcases em (d = 0) with (rfl | hd)
   ·
-    simp only [coeff_homogeneous_component, sum_eq_zero_iff, Finsupp.zero_apply, if_true, coeff_C,
-      eq_self_iff_true, forall_true_iff]
+    classical simp only [coeff_homogeneous_component, sum_eq_zero_iff, Finsupp.zero_apply, if_true,
+        coeff_C, eq_self_iff_true, forall_true_iff]
   · rw [coeff_homogeneous_component, if_neg, coeff_C, if_neg (Ne.symm hd)]
     simp only [Finsupp.ext_iff, Finsupp.zero_apply] at hd
     simp [hd]

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

@@ -143,7 +143,7 @@ theorem isHomogeneous_of_totalDegree_zero {p : MvPolynomial σ R} (hp : p.totalD
   exact hp
 #align mv_polynomial.is_homogeneous_of_total_degree_zero MvPolynomial.isHomogeneous_of_totalDegree_zero
 
-theorem isHomogeneous_c (r : R) : IsHomogeneous (c r : MvPolynomial σ R) 0 :=
+theorem isHomogeneous_c (r : R) : IsHomogeneous (C r : MvPolynomial σ R) 0 :=
   by
   apply is_homogeneous_monomial
   simp only [Finsupp.zero_apply, Finset.sum_const_zero]
@@ -161,7 +161,7 @@ theorem isHomogeneous_one : IsHomogeneous (1 : MvPolynomial σ R) 0 :=
 
 variable {σ} (R)
 
-theorem isHomogeneous_x (i : σ) : IsHomogeneous (x i : MvPolynomial σ R) 1 :=
+theorem isHomogeneous_x (i : σ) : IsHomogeneous (X i : MvPolynomial σ R) 1 :=
   by
   apply is_homogeneous_monomial
   simp only [Finsupp.support_single_ne_zero _ one_ne_zero, Finset.sum_singleton]
@@ -286,7 +286,7 @@ theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).Homogen
 #align mv_polynomial.homogeneous_component_is_homogeneous MvPolynomial.homogeneousComponent_isHomogeneous
 
 @[simp]
-theorem homogeneousComponent_zero : homogeneousComponent 0 φ = c (coeff 0 φ) :=
+theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :=
   by
   ext1 d
   rcases em (d = 0) with (rfl | hd)
@@ -300,7 +300,7 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = c (coeff 0 φ) :
 
 @[simp]
 theorem homogeneousComponent_c_mul (n : ℕ) (r : R) :
-    homogeneousComponent n (c r * φ) = c r * homogeneousComponent n φ := by
+    homogeneousComponent n (C r * φ) = C r * homogeneousComponent n φ := by
   simp only [C_mul', LinearMap.map_smul]
 #align mv_polynomial.homogeneous_component_C_mul MvPolynomial.homogeneousComponent_c_mul
 

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

@@ -102,7 +102,8 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
   have aux : coeff d φ ≠ 0 ∧ coeff e ψ ≠ 0 :=
     by
     contrapose! H
-    by_cases h : coeff d φ = 0 <;> simp_all only [Ne.def, not_false_iff, zero_mul, mul_zero]
+    by_cases h : coeff d φ = 0 <;>
+      simp_all only [Ne.def, not_false_iff, MulZeroClass.zero_mul, MulZeroClass.mul_zero]
   specialize hφ aux.1
   specialize hψ aux.2
   rw [Finsupp.mem_antidiagonal] at hde

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

@@ -332,7 +332,7 @@ private
 lemma exists_eval_ne_zero_of_coeff_finSuccEquiv_ne_zero_aux
     {N : ℕ} {F : MvPolynomial (Fin (Nat.succ N)) R} {n : ℕ} (hF : IsHomogeneous F n)
     (hFn : ((finSuccEquiv R N) F).coeff n ≠ 0) :
-    ∃ r, (eval r) F ≠ 0 := by
+    ∃ r, eval r F ≠ 0 := by
   have hF₀ : F ≠ 0 := by contrapose! hFn; simp [hFn]
   have hdeg : natDegree (finSuccEquiv R N F) < n + 1 := by
     linarith [natDegree_finSuccEquiv F, degreeOf_le_totalDegree F 0, hF.totalDegree hF₀]

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>

@@ -60,7 +60,7 @@ theorem weightedTotalDegree_one (φ : MvPolynomial σ R) :
     weightedTotalDegree (1 : σ → ℕ) φ = φ.totalDegree := by
   simp only [totalDegree, weightedTotalDegree, weightedDegree, LinearMap.toAddMonoidHom_coe,
     Finsupp.total, Pi.one_apply, Finsupp.coe_lsum, LinearMap.coe_smulRight, LinearMap.id_coe,
-    id.def, Algebra.id.smul_eq_mul, mul_one]
+    id, Algebra.id.smul_eq_mul, mul_one]
 
 variable (σ R)
 

We rewrite the definition of homogeneous polynomial as a special case of weighted homogeneous polynomial.

Question: should all uses of ∑ i in d.support, d i be replaced by degree d?

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

Co-authored-by: María Inés de Frutos-Fernández <88536493+mariainesdff@users.noreply.github.com>

@@ -8,6 +8,7 @@ import Mathlib.Algebra.GradedMonoid
 import Mathlib.Algebra.MvPolynomial.CommRing
 import Mathlib.Algebra.MvPolynomial.Equiv
 import Mathlib.Algebra.MvPolynomial.Variables
+import Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous
 import Mathlib.Algebra.Polynomial.RingDivision
 
 #align_import ring_theory.mv_polynomial.homogeneous from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
@@ -37,19 +38,34 @@ variable {σ : Type*} {τ : Type*} {R : Type*} {S : Type*}
 
 /-
 TODO
-* create definition for `∑ i in d.support, d i`
 * show that `MvPolynomial σ R ≃ₐ[R] ⨁ i, homogeneousSubmodule σ R i`
 -/
+
+/-- The degree of a monomial. -/
+def degree (d : σ →₀ ℕ) := ∑ i in d.support, d i
+
+theorem weightedDegree_one (d : σ →₀ ℕ) :
+    weightedDegree 1 d = degree d := by
+  simp [weightedDegree, degree, Finsupp.total, Finsupp.sum]
+
 /-- A multivariate polynomial `φ` is homogeneous of degree `n`
 if all monomials occurring in `φ` have degree `n`. -/
 def IsHomogeneous [CommSemiring R] (φ : MvPolynomial σ R) (n : ℕ) :=
-  ∀ ⦃d⦄, coeff d φ ≠ 0 → ∑ i in d.support, d i = n
+  IsWeightedHomogeneous 1 φ n
 #align mv_polynomial.is_homogeneous MvPolynomial.IsHomogeneous
 
+variable [CommSemiring R]
+
+theorem weightedTotalDegree_one (φ : MvPolynomial σ R) :
+    weightedTotalDegree (1 : σ → ℕ) φ = φ.totalDegree := by
+  simp only [totalDegree, weightedTotalDegree, weightedDegree, LinearMap.toAddMonoidHom_coe,
+    Finsupp.total, Pi.one_apply, Finsupp.coe_lsum, LinearMap.coe_smulRight, LinearMap.id_coe,
+    id.def, Algebra.id.smul_eq_mul, mul_one]
+
 variable (σ R)
 
 /-- The submodule of homogeneous `MvPolynomial`s of degree `n`. -/
-def homogeneousSubmodule [CommSemiring R] (n : ℕ) : Submodule R (MvPolynomial σ R) where
+def homogeneousSubmodule (n : ℕ) : Submodule R (MvPolynomial σ R) where
   carrier := { x | x.IsHomogeneous n }
   smul_mem' r a ha c hc := by
     rw [coeff_smul] at hc
@@ -68,6 +84,10 @@ def homogeneousSubmodule [CommSemiring R] (n : ℕ) : Submodule R (MvPolynomial
     · exact hb h
 #align mv_polynomial.homogeneous_submodule MvPolynomial.homogeneousSubmodule
 
+@[simp]
+lemma weightedHomogeneousSubmodule_one (n : ℕ) :
+    weightedHomogeneousSubmodule R 1 n = homogeneousSubmodule σ R n := rfl
+
 variable {σ R}
 
 @[simp]
@@ -79,66 +99,41 @@ variable (σ R)
 
 /-- While equal, the former has a convenient definitional reduction. -/
 theorem homogeneousSubmodule_eq_finsupp_supported [CommSemiring R] (n : ℕ) :
-    homogeneousSubmodule σ R n = Finsupp.supported _ R { d | ∑ i in d.support, d i = n } := by
-  ext
-  rw [Finsupp.mem_supported, Set.subset_def]
-  simp only [Finsupp.mem_support_iff, Finset.mem_coe]
-  rfl
+    homogeneousSubmodule σ R n = Finsupp.supported _ R { d | degree d = n } := by
+  simp_rw [← weightedDegree_one]
+  exact weightedHomogeneousSubmodule_eq_finsupp_supported R 1 n
 #align mv_polynomial.homogeneous_submodule_eq_finsupp_supported MvPolynomial.homogeneousSubmodule_eq_finsupp_supported
 
 variable {σ R}
 
 theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
-    homogeneousSubmodule σ R m * homogeneousSubmodule σ R n ≤ homogeneousSubmodule σ R (m + n) := by
-  rw [Submodule.mul_le]
-  intro φ hφ ψ hψ c hc
-  classical
-  rw [coeff_mul] at hc
-  obtain ⟨⟨d, e⟩, hde, H⟩ := Finset.exists_ne_zero_of_sum_ne_zero hc
-  have aux : coeff d φ ≠ 0 ∧ coeff e ψ ≠ 0 := by
-    contrapose! H
-    by_cases h : coeff d φ = 0 <;>
-      simp_all only [Ne, not_false_iff, zero_mul, mul_zero]
-  specialize hφ aux.1
-  specialize hψ aux.2
-  rw [Finset.mem_antidiagonal] at hde
-  classical
-  have hd' : d.support ⊆ d.support ∪ e.support := Finset.subset_union_left _ _
-  have he' : e.support ⊆ d.support ∪ e.support := Finset.subset_union_right _ _
-  rw [← hde, ← hφ, ← hψ, Finset.sum_subset Finsupp.support_add, Finset.sum_subset hd',
-    Finset.sum_subset he', ← Finset.sum_add_distrib]
-  · congr
-  all_goals intro _ _; apply Finsupp.not_mem_support_iff.mp
+    homogeneousSubmodule σ R m * homogeneousSubmodule σ R n ≤ homogeneousSubmodule σ R (m + n) :=
+  weightedHomogeneousSubmodule_mul 1 m n
 #align mv_polynomial.homogeneous_submodule_mul MvPolynomial.homogeneousSubmodule_mul
 
 section
 
 variable [CommSemiring R]
 
-theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : ∑ i in d.support, d i = n) :
+theorem isHomogeneous_monomial {d : σ →₀ ℕ} (r : R) {n : ℕ} (hn : degree d = n) :
     IsHomogeneous (monomial d r) n := by
-  intro c hc
-  classical
-  rw [coeff_monomial] at hc
-  split_ifs at hc with h
-  · subst c
-    exact hn
-  · contradiction
+  simp_rw [← weightedDegree_one] at hn
+  exact isWeightedHomogeneous_monomial 1 d r hn
 #align mv_polynomial.is_homogeneous_monomial MvPolynomial.isHomogeneous_monomial
 
 variable (σ)
 
-theorem isHomogeneous_of_totalDegree_zero {p : MvPolynomial σ R} (hp : p.totalDegree = 0) :
-    IsHomogeneous p 0 := by
-  erw [totalDegree, Finset.sup_eq_bot_iff] at hp
-  -- we have to do this in two steps to stop simp changing bot to zero
-  simp_rw [mem_support_iff] at hp
-  exact hp
+theorem totalDegree_zero_iff_isHomogeneous {p : MvPolynomial σ R} :
+    p.totalDegree = 0 ↔ IsHomogeneous p 0 := by
+  rw [← weightedTotalDegree_one,
+    ← isWeightedHomogeneous_zero_iff_weightedTotalDegree_eq_zero, IsHomogeneous]
+
+alias ⟨isHomogeneous_of_totalDegree_zero, _⟩ := totalDegree_zero_iff_isHomogeneous
 #align mv_polynomial.is_homogeneous_of_total_degree_zero MvPolynomial.isHomogeneous_of_totalDegree_zero
 
 theorem isHomogeneous_C (r : R) : IsHomogeneous (C r : MvPolynomial σ R) 0 := by
   apply isHomogeneous_monomial
-  simp only [Finsupp.zero_apply, Finset.sum_const_zero]
+  simp only [degree, Finsupp.zero_apply, Finset.sum_const_zero]
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.is_homogeneous_C MvPolynomial.isHomogeneous_C
 
@@ -156,7 +151,7 @@ variable {σ}
 
 theorem isHomogeneous_X (i : σ) : IsHomogeneous (X i : MvPolynomial σ R) 1 := by
   apply isHomogeneous_monomial
-  rw [Finsupp.support_single_ne_zero _ one_ne_zero, Finset.sum_singleton]
+  rw [degree, Finsupp.support_single_ne_zero _ one_ne_zero, Finset.sum_singleton]
   exact Finsupp.single_eq_same
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.is_homogeneous_X MvPolynomial.isHomogeneous_X
@@ -167,11 +162,10 @@ namespace IsHomogeneous
 
 variable [CommSemiring R] [CommSemiring S] {φ ψ : MvPolynomial σ R} {m n : ℕ}
 
-theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : ∑ i in d.support, d i ≠ n) :
+theorem coeff_eq_zero (hφ : IsHomogeneous φ n) {d : σ →₀ ℕ} (hd : degree d ≠ n) :
     coeff d φ = 0 := by
-  have aux := mt (@hφ d) hd
-  classical
-  rwa [Classical.not_not] at aux
+  simp_rw [← weightedDegree_one] at hd
+  exact IsWeightedHomogeneous.coeff_eq_zero hφ d hd
 #align mv_polynomial.is_homogeneous.coeff_eq_zero MvPolynomial.IsHomogeneous.coeff_eq_zero
 
 theorem inj_right (hm : IsHomogeneous φ m) (hn : IsHomogeneous φ n) (hφ : φ ≠ 0) : m = n := by
@@ -239,7 +233,8 @@ lemma eval₂ (hφ : φ.IsHomogeneous m) (f : R →+* MvPolynomial τ S) (g : σ
   apply IsHomogeneous.mul (hf _) _
   convert IsHomogeneous.prod _ _ (fun k ↦ n * i k) _
   · rw [Finsupp.mem_support_iff] at hi
-    rw [← Finset.mul_sum, hφ hi]
+    rw [← Finset.mul_sum, ← hφ hi, weightedDegree_apply]
+    simp_rw [smul_eq_mul, Finsupp.sum, Pi.one_apply, mul_one]
   · rintro k -
     apply (hg k).pow
 
@@ -271,13 +266,16 @@ lemma totalDegree_le (hφ : IsHomogeneous φ n) : φ.totalDegree ≤ n := by
   apply Finset.sup_le
   intro d hd
   rw [mem_support_iff] at hd
-  rw [Finsupp.sum, hφ hd]
+  rw [Finsupp.sum, ← hφ hd, weightedDegree_apply]
+  simp only [Pi.one_apply, smul_eq_mul, mul_one]
+  exact Nat.le.refl
 
 theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ = n := by
   apply le_antisymm hφ.totalDegree_le
   obtain ⟨d, hd⟩ : ∃ d, coeff d φ ≠ 0 := exists_coeff_ne_zero h
   simp only [← hφ hd, MvPolynomial.totalDegree, Finsupp.sum]
   replace hd := Finsupp.mem_support_iff.mpr hd
+  simp only [weightedDegree_apply,Pi.one_apply, smul_eq_mul, mul_one, ge_iff_le]
   -- Porting note: Original proof did not define `f`
   exact Finset.le_sup (f := fun s ↦ ∑ x in s.support, s x) hd
 #align mv_polynomial.is_homogeneous.total_degree MvPolynomial.IsHomogeneous.totalDegree
@@ -285,14 +283,18 @@ theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ =
 theorem rename_isHomogeneous {f : σ → τ} (h : φ.IsHomogeneous n):
     (rename f φ).IsHomogeneous n := by
   rw [← φ.support_sum_monomial_coeff, map_sum]; simp_rw [rename_monomial]
-  exact IsHomogeneous.sum _ _ _ fun d hd ↦ isHomogeneous_monomial _ _ _
-    ((Finsupp.sum_mapDomain_index_addMonoidHom fun _ ↦ .id ℕ).trans <| h <| mem_support_iff.mp hd)
+  apply IsHomogeneous.sum _ _ _ fun d hd ↦ isHomogeneous_monomial _ _
+  intro d hd
+  apply (Finsupp.sum_mapDomain_index_addMonoidHom fun _ ↦ .id ℕ).trans
+  convert h (mem_support_iff.mp hd)
+  simp only [weightedDegree_apply, AddMonoidHom.id_apply, Pi.one_apply, smul_eq_mul, mul_one]
 
 theorem rename_isHomogeneous_iff {f : σ → τ} (hf : f.Injective) :
     (rename f φ).IsHomogeneous n ↔ φ.IsHomogeneous n := by
   refine ⟨fun h d hd ↦ ?_, rename_isHomogeneous⟩
   convert ← @h (d.mapDomain f) _
-  · exact Finsupp.sum_mapDomain_index_inj (h := fun _ ↦ id) hf
+  · simp only [weightedDegree_apply, Pi.one_apply, smul_eq_mul, mul_one]
+    exact Finsupp.sum_mapDomain_index_inj (h := fun _ ↦ id) hf
   · rwa [coeff_rename_mapDomain f hf]
 
 lemma finSuccEquiv_coeff_isHomogeneous {N : ℕ} {φ : MvPolynomial (Fin (N+1)) R} {n : ℕ}
@@ -300,9 +302,12 @@ lemma finSuccEquiv_coeff_isHomogeneous {N : ℕ} {φ : MvPolynomial (Fin (N+1))
     ((finSuccEquiv _ _ φ).coeff i).IsHomogeneous j := by
   intro d hd
   rw [finSuccEquiv_coeff_coeff] at hd
-  have aux : 0 ∉ Finset.map (Fin.succEmb N).toEmbedding d.support := by simp [Fin.succ_ne_zero]
-  simpa [Finset.sum_subset_zero_on_sdiff (g := d.cons i)
-    (d.cons_support (y := i)) (by simp) (fun _ _ ↦ rfl), Finset.sum_insert aux, ← h] using hφ hd
+  have h' : (weightedDegree 1) (Finsupp.cons i d) = i + j := by
+    simpa [Finset.sum_subset_zero_on_sdiff (g := d.cons i)
+     (d.cons_support (y := i)) (by simp) (fun _ _ ↦ rfl), ← h] using hφ hd
+  simp only [weightedDegree_apply, Pi.one_apply, smul_eq_mul, mul_one, Finsupp.sum_cons,
+    add_right_inj] at h' ⊢
+  exact h'
 
 -- TODO: develop API for `optionEquivLeft` and get rid of the `[Fintype σ]` assumption
 lemma coeff_isHomogeneous_of_optionEquivLeft_symm
@@ -336,7 +341,7 @@ lemma exists_eval_ne_zero_of_coeff_finSuccEquiv_ne_zero_aux
     intro i hi
     rw [Finset.mem_range] at hi
     apply (hF.finSuccEquiv_coeff_isHomogeneous i (n-i) (by omega)).coeff_eq_zero
-    simp only [Finsupp.support_zero, Finsupp.coe_zero, Pi.zero_apply, Finset.sum_const_zero]
+    simp only [degree, Finsupp.support_zero, Finsupp.coe_zero, Pi.zero_apply, Finset.sum_const_zero]
     omega
   simp_rw [eval_eq_eval_mv_eval', eval_one_map, Polynomial.eval_eq_sum_range' hdeg,
     eval_zero, one_pow, mul_one, map_sum, Finset.sum_range_succ, Finset.sum_eq_zero aux, zero_add]
@@ -350,6 +355,7 @@ lemma exists_eval_ne_zero_of_coeff_finSuccEquiv_ne_zero_aux
     rw [Finsupp.coe_zero, Pi.zero_apply]
     by_cases hi : i ∈ d.support
     · have := hF.finSuccEquiv_coeff_isHomogeneous n 0 (add_zero _) hd
+      simp only [weightedDegree_apply, Pi.one_apply, smul_eq_mul, mul_one, Finsupp.sum] at this
       rw [Finset.sum_eq_zero_iff_of_nonneg (fun _ _ ↦ zero_le')] at this
       exact this i hi
     · simpa using hi
@@ -468,7 +474,7 @@ open Finset
 See `sum_homogeneousComponent` for the statement that `φ` is equal to the sum
 of all its homogeneous components. -/
 def homogeneousComponent [CommSemiring R] (n : ℕ) : MvPolynomial σ R →ₗ[R] MvPolynomial σ R :=
-  (Submodule.subtype _).comp <| Finsupp.restrictDom _ _ { d | ∑ i in d.support, d i = n }
+  weightedHomogeneousComponent 1 n
 #align mv_polynomial.homogeneous_component MvPolynomial.homogeneousComponent
 
 section HomogeneousComponent
@@ -478,54 +484,45 @@ open Finset
 variable [CommSemiring R] (n : ℕ) (φ ψ : MvPolynomial σ R)
 
 theorem coeff_homogeneousComponent (d : σ →₀ ℕ) :
-    coeff d (homogeneousComponent n φ) = if (∑ i in d.support, d i) = n then coeff d φ else 0 :=
-  Finsupp.filter_apply (fun d : σ →₀ ℕ => ∑ i in d.support, d i = n) φ d
+    coeff d (homogeneousComponent n φ) = if (degree d) = n then coeff d φ else 0 := by
+  simp_rw [← weightedDegree_one]
+  convert coeff_weightedHomogeneousComponent n φ d
 #align mv_polynomial.coeff_homogeneous_component MvPolynomial.coeff_homogeneousComponent
 
 theorem homogeneousComponent_apply :
     homogeneousComponent n φ =
-      ∑ d in φ.support.filter fun d => ∑ i in d.support, d i = n, monomial d (coeff d φ) :=
-  Finsupp.filter_eq_sum (fun d : σ →₀ ℕ => ∑ i in d.support, d i = n) φ
+      ∑ d in φ.support.filter fun d => degree d = n, monomial d (coeff d φ) := by
+  simp_rw [← weightedDegree_one]
+  convert weightedHomogeneousComponent_apply n φ
 #align mv_polynomial.homogeneous_component_apply MvPolynomial.homogeneousComponent_apply
 
-theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).IsHomogeneous n := by
-  intro d hd
-  contrapose! hd
-  rw [coeff_homogeneousComponent, if_neg hd]
+theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).IsHomogeneous n :=
+  weightedHomogeneousComponent_isWeightedHomogeneous n φ
 #align mv_polynomial.homogeneous_component_is_homogeneous MvPolynomial.homogeneousComponent_isHomogeneous
 
 @[simp]
-theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) := by
-  ext1 d
-  rcases em (d = 0) with (rfl | hd)
-  classical
-  · simp only [coeff_homogeneousComponent, sum_eq_zero_iff, Finsupp.zero_apply, if_true, coeff_C,
-      eq_self_iff_true, forall_true_iff]
-  · rw [coeff_homogeneousComponent, if_neg, coeff_C, if_neg (Ne.symm hd)]
-    simp only [DFunLike.ext_iff, Finsupp.zero_apply] at hd
-    simp [hd]
+theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :=
+  weightedHomogeneousComponent_zero φ (fun _ => Nat.succ_ne_zero Nat.zero)
 #align mv_polynomial.homogeneous_component_zero MvPolynomial.homogeneousComponent_zero
 
 @[simp]
 theorem homogeneousComponent_C_mul (n : ℕ) (r : R) :
-    homogeneousComponent n (C r * φ) = C r * homogeneousComponent n φ := by
-  simp only [C_mul', LinearMap.map_smul]
+    homogeneousComponent n (C r * φ) = C r * homogeneousComponent n φ :=
+  weightedHomogeneousComponent_C_mul φ n r
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.homogeneous_component_C_mul MvPolynomial.homogeneousComponent_C_mul
 
 theorem homogeneousComponent_eq_zero'
-    (h : ∀ d : σ →₀ ℕ, d ∈ φ.support → ∑ i in d.support, d i ≠ n) :
+    (h : ∀ d : σ →₀ ℕ, d ∈ φ.support → degree d ≠ n) :
     homogeneousComponent n φ = 0 := by
-  rw [homogeneousComponent_apply, sum_eq_zero]
-  intro d hd; rw [mem_filter] at hd
-  exfalso; exact h _ hd.1 hd.2
+  simp_rw [← weightedDegree_one] at h
+  exact weightedHomogeneousComponent_eq_zero' n φ h
 #align mv_polynomial.homogeneous_component_eq_zero' MvPolynomial.homogeneousComponent_eq_zero'
 
 theorem homogeneousComponent_eq_zero (h : φ.totalDegree < n) : homogeneousComponent n φ = 0 := by
   apply homogeneousComponent_eq_zero'
   rw [totalDegree, Finset.sup_lt_iff] at h
-  · intro d hd
-    exact ne_of_lt (h d hd)
+  · intro d hd; exact ne_of_lt (h d hd)
   · exact lt_of_le_of_lt (Nat.zero_le _) h
 #align mv_polynomial.homogeneous_component_eq_zero MvPolynomial.homogeneousComponent_eq_zero
 
@@ -539,17 +536,7 @@ theorem sum_homogeneousComponent :
 
 theorem homogeneousComponent_homogeneous_polynomial (m n : ℕ) (p : MvPolynomial σ R)
     (h : p ∈ homogeneousSubmodule σ R n) : homogeneousComponent m p = if m = n then p else 0 := by
-  simp only [mem_homogeneousSubmodule] at h
-  ext x
-  rw [coeff_homogeneousComponent]
-  by_cases zero_coeff : coeff x p = 0
-  · split_ifs
-    all_goals simp only [zero_coeff, coeff_zero]
-  · rw [h zero_coeff]
-    simp only [show n = m ↔ m = n from eq_comm]
-    split_ifs with h1
-    · rfl
-    · simp only [coeff_zero]
+  convert weightedHomogeneousComponent_weighted_homogeneous_polynomial m n p h
 #align mv_polynomial.homogeneous_component_homogeneous_polynomial MvPolynomial.homogeneousComponent_homogeneous_polynomial
 
 end HomogeneousComponent

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

@@ -5,10 +5,10 @@ Authors: Johan Commelin, Eric Wieser
 -/
 import Mathlib.Algebra.DirectSum.Internal
 import Mathlib.Algebra.GradedMonoid
-import Mathlib.Data.MvPolynomial.CommRing
-import Mathlib.Data.MvPolynomial.Equiv
-import Mathlib.Data.MvPolynomial.Variables
-import Mathlib.Data.Polynomial.RingDivision
+import Mathlib.Algebra.MvPolynomial.CommRing
+import Mathlib.Algebra.MvPolynomial.Equiv
+import Mathlib.Algebra.MvPolynomial.Variables
+import Mathlib.Algebra.Polynomial.RingDivision
 
 #align_import ring_theory.mv_polynomial.homogeneous from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 

@@ -98,7 +98,7 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
   have aux : coeff d φ ≠ 0 ∧ coeff e ψ ≠ 0 := by
     contrapose! H
     by_cases h : coeff d φ = 0 <;>
-      simp_all only [Ne.def, not_false_iff, zero_mul, mul_zero]
+      simp_all only [Ne, not_false_iff, zero_mul, mul_zero]
   specialize hφ aux.1
   specialize hψ aux.2
   rw [Finset.mem_antidiagonal] at hde

This makes it consistent with MvPolynomial.isHomogeneous_X_pow and MvPolynomial.isHomogeneous_C_mul_X_pow below. Alternatively all three could go into the MvPolynomial.IsHomogeneous namespace.

@@ -210,10 +210,13 @@ lemma C_mul (hφ : φ.IsHomogeneous m) (r : R) :
     (C r * φ).IsHomogeneous m := by
   simpa only [zero_add] using (isHomogeneous_C _ _).mul hφ
 
-lemma _root_.MvPolynomial.C_mul_X (r : R) (i : σ) :
+lemma _root_.MvPolynomial.isHomogeneous_C_mul_X (r : R) (i : σ) :
     (C r * X i).IsHomogeneous 1 :=
   (isHomogeneous_X _ _).C_mul _
 
+@[deprecated] -- 2024-03-21
+alias _root_.MvPolynomial.C_mul_X := _root_.MvPolynomial.isHomogeneous_C_mul_X
+
 lemma pow (hφ : φ.IsHomogeneous m) (n : ℕ) : (φ ^ n).IsHomogeneous (m * n) := by
   rw [show φ ^ n = ∏ _i in Finset.range n, φ by simp]
   rw [show m * n = ∑ _i in Finset.range n, m by simp [mul_comm]]

These will be caught by the linter in a future lean version.

@@ -108,7 +108,7 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
   rw [← hde, ← hφ, ← hψ, Finset.sum_subset Finsupp.support_add, Finset.sum_subset hd',
     Finset.sum_subset he', ← Finset.sum_add_distrib]
   · congr
-  all_goals intro i hi; apply Finsupp.not_mem_support_iff.mp
+  all_goals intro _ _; apply Finsupp.not_mem_support_iff.mp
 #align mv_polynomial.homogeneous_submodule_mul MvPolynomial.homogeneousSubmodule_mul
 
 section

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -315,7 +315,7 @@ lemma coeff_isHomogeneous_of_optionEquivLeft_symm
   suffices IsHomogeneous (F (p.coeff i)) j by
     rwa [← (IsHomogeneous.rename_isHomogeneous_iff e.injective)]
   convert hφ.finSuccEquiv_coeff_isHomogeneous i j h using 1
-  dsimp only [renameEquiv_apply]
+  dsimp only [φ, F', F, renameEquiv_apply]
   rw [finSuccEquiv_rename_finSuccEquiv, AlgEquiv.apply_symm_apply]
   simp
 

@@ -261,18 +261,22 @@ theorem sub (hφ : IsHomogeneous φ n) (hψ : IsHomogeneous ψ n) : IsHomogeneou
 
 end CommRing
 
+/-- The homogeneous degree bounds the total degree.
+
+See also `MvPolynomial.IsHomogeneous.totalDegree` when `φ` is non-zero. -/
+lemma totalDegree_le (hφ : IsHomogeneous φ n) : φ.totalDegree ≤ n := by
+  apply Finset.sup_le
+  intro d hd
+  rw [mem_support_iff] at hd
+  rw [Finsupp.sum, hφ hd]
+
 theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ = n := by
-  rw [MvPolynomial.totalDegree]
-  apply le_antisymm
-  · apply Finset.sup_le
-    intro d hd
-    rw [mem_support_iff] at hd
-    rw [Finsupp.sum, hφ hd]
-  · obtain ⟨d, hd⟩ : ∃ d, coeff d φ ≠ 0 := exists_coeff_ne_zero h
-    simp only [← hφ hd, Finsupp.sum]
-    replace hd := Finsupp.mem_support_iff.mpr hd
-    -- Porting note: Original proof did not define `f`
-    exact Finset.le_sup (f := fun s ↦ ∑ x in s.support, (⇑s) x) hd
+  apply le_antisymm hφ.totalDegree_le
+  obtain ⟨d, hd⟩ : ∃ d, coeff d φ ≠ 0 := exists_coeff_ne_zero h
+  simp only [← hφ hd, MvPolynomial.totalDegree, Finsupp.sum]
+  replace hd := Finsupp.mem_support_iff.mpr hd
+  -- Porting note: Original proof did not define `f`
+  exact Finset.le_sup (f := fun s ↦ ∑ x in s.support, s x) hd
 #align mv_polynomial.is_homogeneous.total_degree MvPolynomial.IsHomogeneous.totalDegree
 
 theorem rename_isHomogeneous {f : σ → τ} (h : φ.IsHomogeneous n):

@@ -165,7 +165,7 @@ end
 
 namespace IsHomogeneous
 
-variable [CommSemiring R] {φ ψ : MvPolynomial σ R} {m n : ℕ}
+variable [CommSemiring R] [CommSemiring S] {φ ψ : MvPolynomial σ R} {m n : ℕ}
 
 theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : ∑ i in d.support, d i ≠ n) :
     coeff d φ = 0 := by
@@ -206,6 +206,48 @@ theorem prod {ι : Type*} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : 
     exact h j (Finset.mem_insert_of_mem hjs)
 #align mv_polynomial.is_homogeneous.prod MvPolynomial.IsHomogeneous.prod
 
+lemma C_mul (hφ : φ.IsHomogeneous m) (r : R) :
+    (C r * φ).IsHomogeneous m := by
+  simpa only [zero_add] using (isHomogeneous_C _ _).mul hφ
+
+lemma _root_.MvPolynomial.C_mul_X (r : R) (i : σ) :
+    (C r * X i).IsHomogeneous 1 :=
+  (isHomogeneous_X _ _).C_mul _
+
+lemma pow (hφ : φ.IsHomogeneous m) (n : ℕ) : (φ ^ n).IsHomogeneous (m * n) := by
+  rw [show φ ^ n = ∏ _i in Finset.range n, φ by simp]
+  rw [show m * n = ∑ _i in Finset.range n, m by simp [mul_comm]]
+  apply IsHomogeneous.prod _ _ _ (fun _ _ ↦ hφ)
+
+lemma _root_.MvPolynomial.isHomogeneous_X_pow (i : σ) (n : ℕ) :
+    (X (R := R) i ^ n).IsHomogeneous n := by
+  simpa only [one_mul] using (isHomogeneous_X _ _).pow n
+
+lemma _root_.MvPolynomial.isHomogeneous_C_mul_X_pow (r : R) (i : σ) (n : ℕ) :
+    (C r * X i ^ n).IsHomogeneous n :=
+  (isHomogeneous_X_pow _ _).C_mul _
+
+lemma eval₂ (hφ : φ.IsHomogeneous m) (f : R →+* MvPolynomial τ S) (g : σ → MvPolynomial τ S)
+    (hf : ∀ r, (f r).IsHomogeneous 0) (hg : ∀ i, (g i).IsHomogeneous n) :
+    (eval₂ f g φ).IsHomogeneous (n * m) := by
+  apply IsHomogeneous.sum
+  intro i hi
+  rw [← zero_add (n * m)]
+  apply IsHomogeneous.mul (hf _) _
+  convert IsHomogeneous.prod _ _ (fun k ↦ n * i k) _
+  · rw [Finsupp.mem_support_iff] at hi
+    rw [← Finset.mul_sum, hφ hi]
+  · rintro k -
+    apply (hg k).pow
+
+lemma map (hφ : φ.IsHomogeneous n) (f : R →+* S) : (map f φ).IsHomogeneous n := by
+  simpa only [one_mul] using hφ.eval₂ _ _ (fun r ↦ isHomogeneous_C _ (f r)) (isHomogeneous_X _)
+
+lemma aeval [Algebra R S] (hφ : φ.IsHomogeneous m)
+    (g : σ → MvPolynomial τ S) (hg : ∀ i, (g i).IsHomogeneous n) :
+    (aeval g φ).IsHomogeneous (n * m) :=
+  hφ.eval₂ _ _ (fun _ ↦ isHomogeneous_C _ _) hg
+
 section CommRing
 
 -- In this section we shadow the semiring `R` with a ring `R`.

@@ -255,6 +255,24 @@ lemma finSuccEquiv_coeff_isHomogeneous {N : ℕ} {φ : MvPolynomial (Fin (N+1))
   simpa [Finset.sum_subset_zero_on_sdiff (g := d.cons i)
     (d.cons_support (y := i)) (by simp) (fun _ _ ↦ rfl), Finset.sum_insert aux, ← h] using hφ hd
 
+-- TODO: develop API for `optionEquivLeft` and get rid of the `[Fintype σ]` assumption
+lemma coeff_isHomogeneous_of_optionEquivLeft_symm
+    [hσ : Finite σ] {p : Polynomial (MvPolynomial σ R)}
+    (hp : ((optionEquivLeft R σ).symm p).IsHomogeneous n) (i j : ℕ) (h : i + j = n) :
+    (p.coeff i).IsHomogeneous j := by
+  obtain ⟨k, ⟨e⟩⟩ := Finite.exists_equiv_fin σ
+  let e' := e.optionCongr.trans (_root_.finSuccEquiv _).symm
+  let F := renameEquiv R e
+  let F' := renameEquiv R e'
+  let φ := F' ((optionEquivLeft R σ).symm p)
+  have hφ : φ.IsHomogeneous n := hp.rename_isHomogeneous
+  suffices IsHomogeneous (F (p.coeff i)) j by
+    rwa [← (IsHomogeneous.rename_isHomogeneous_iff e.injective)]
+  convert hφ.finSuccEquiv_coeff_isHomogeneous i j h using 1
+  dsimp only [renameEquiv_apply]
+  rw [finSuccEquiv_rename_finSuccEquiv, AlgEquiv.apply_symm_apply]
+  simp
+
 open Polynomial in
 private
 lemma exists_eval_ne_zero_of_coeff_finSuccEquiv_ne_zero_aux

@@ -5,7 +5,10 @@ Authors: Johan Commelin, Eric Wieser
 -/
 import Mathlib.Algebra.DirectSum.Internal
 import Mathlib.Algebra.GradedMonoid
+import Mathlib.Data.MvPolynomial.CommRing
+import Mathlib.Data.MvPolynomial.Equiv
 import Mathlib.Data.MvPolynomial.Variables
+import Mathlib.Data.Polynomial.RingDivision
 
 #align_import ring_theory.mv_polynomial.homogeneous from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 
@@ -203,6 +206,19 @@ theorem prod {ι : Type*} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : 
     exact h j (Finset.mem_insert_of_mem hjs)
 #align mv_polynomial.is_homogeneous.prod MvPolynomial.IsHomogeneous.prod
 
+section CommRing
+
+-- In this section we shadow the semiring `R` with a ring `R`.
+variable {R σ : Type*} [CommRing R] {φ ψ : MvPolynomial σ R} {n : ℕ}
+
+theorem neg (hφ : IsHomogeneous φ n) : IsHomogeneous (-φ) n :=
+  (homogeneousSubmodule σ R n).neg_mem hφ
+
+theorem sub (hφ : IsHomogeneous φ n) (hψ : IsHomogeneous ψ n) : IsHomogeneous (φ - ψ) n :=
+  (homogeneousSubmodule σ R n).sub_mem hφ hψ
+
+end CommRing
+
 theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ = n := by
   rw [MvPolynomial.totalDegree]
   apply le_antisymm
@@ -230,6 +246,136 @@ theorem rename_isHomogeneous_iff {f : σ → τ} (hf : f.Injective) :
   · exact Finsupp.sum_mapDomain_index_inj (h := fun _ ↦ id) hf
   · rwa [coeff_rename_mapDomain f hf]
 
+lemma finSuccEquiv_coeff_isHomogeneous {N : ℕ} {φ : MvPolynomial (Fin (N+1)) R} {n : ℕ}
+    (hφ : φ.IsHomogeneous n) (i j : ℕ) (h : i + j = n) :
+    ((finSuccEquiv _ _ φ).coeff i).IsHomogeneous j := by
+  intro d hd
+  rw [finSuccEquiv_coeff_coeff] at hd
+  have aux : 0 ∉ Finset.map (Fin.succEmb N).toEmbedding d.support := by simp [Fin.succ_ne_zero]
+  simpa [Finset.sum_subset_zero_on_sdiff (g := d.cons i)
+    (d.cons_support (y := i)) (by simp) (fun _ _ ↦ rfl), Finset.sum_insert aux, ← h] using hφ hd
+
+open Polynomial in
+private
+lemma exists_eval_ne_zero_of_coeff_finSuccEquiv_ne_zero_aux
+    {N : ℕ} {F : MvPolynomial (Fin (Nat.succ N)) R} {n : ℕ} (hF : IsHomogeneous F n)
+    (hFn : ((finSuccEquiv R N) F).coeff n ≠ 0) :
+    ∃ r, (eval r) F ≠ 0 := by
+  have hF₀ : F ≠ 0 := by contrapose! hFn; simp [hFn]
+  have hdeg : natDegree (finSuccEquiv R N F) < n + 1 := by
+    linarith [natDegree_finSuccEquiv F, degreeOf_le_totalDegree F 0, hF.totalDegree hF₀]
+  use Fin.cons 1 0
+  have aux : ∀ i ∈ Finset.range n, constantCoeff ((finSuccEquiv R N F).coeff i) = 0 := by
+    intro i hi
+    rw [Finset.mem_range] at hi
+    apply (hF.finSuccEquiv_coeff_isHomogeneous i (n-i) (by omega)).coeff_eq_zero
+    simp only [Finsupp.support_zero, Finsupp.coe_zero, Pi.zero_apply, Finset.sum_const_zero]
+    omega
+  simp_rw [eval_eq_eval_mv_eval', eval_one_map, Polynomial.eval_eq_sum_range' hdeg,
+    eval_zero, one_pow, mul_one, map_sum, Finset.sum_range_succ, Finset.sum_eq_zero aux, zero_add]
+  contrapose! hFn
+  ext d
+  rw [coeff_zero]
+  obtain rfl | hd := eq_or_ne d 0
+  · apply hFn
+  · contrapose! hd
+    ext i
+    rw [Finsupp.coe_zero, Pi.zero_apply]
+    by_cases hi : i ∈ d.support
+    · have := hF.finSuccEquiv_coeff_isHomogeneous n 0 (add_zero _) hd
+      rw [Finset.sum_eq_zero_iff_of_nonneg (fun _ _ ↦ zero_le')] at this
+      exact this i hi
+    · simpa using hi
+
+section IsDomain
+
+-- In this section we shadow the semiring `R` with a domain `R`.
+variable {R σ : Type*} [CommRing R] [IsDomain R] {F G : MvPolynomial σ R} {n : ℕ}
+
+open Cardinal Polynomial
+
+private
+lemma exists_eval_ne_zero_of_totalDegree_le_card_aux {N : ℕ} {F : MvPolynomial (Fin N) R} {n : ℕ}
+    (hF : F.IsHomogeneous n) (hF₀ : F ≠ 0) (hnR : n ≤ #R) :
+    ∃ r, eval r F ≠ 0 := by
+  induction N generalizing n with
+  | zero =>
+    use 0
+    contrapose! hF₀
+    ext d
+    simpa only [Subsingleton.elim d 0, eval_zero, coeff_zero] using hF₀
+  | succ N IH =>
+    have hdeg : natDegree (finSuccEquiv R N F) < n + 1 := by
+      linarith [natDegree_finSuccEquiv F, degreeOf_le_totalDegree F 0, hF.totalDegree hF₀]
+    obtain ⟨i, hi⟩ : ∃ i : ℕ, (finSuccEquiv R N F).coeff i ≠ 0 := by
+      contrapose! hF₀
+      exact (finSuccEquiv _ _).injective <| Polynomial.ext <| by simpa using hF₀
+    have hin : i ≤ n := by
+      contrapose! hi
+      exact coeff_eq_zero_of_natDegree_lt <| (Nat.le_of_lt_succ hdeg).trans_lt hi
+    obtain hFn | hFn := ne_or_eq ((finSuccEquiv R N F).coeff n) 0
+    · exact hF.exists_eval_ne_zero_of_coeff_finSuccEquiv_ne_zero_aux hFn
+    have hin : i < n := hin.lt_or_eq.elim id <| by aesop
+    obtain ⟨j, hj⟩ : ∃ j, i + (j + 1) = n := (Nat.exists_eq_add_of_lt hin).imp <| by intros; omega
+    obtain ⟨r, hr⟩ : ∃ r, (eval r) (Polynomial.coeff ((finSuccEquiv R N) F) i) ≠ 0 :=
+      IH (hF.finSuccEquiv_coeff_isHomogeneous _ _ hj) hi (.trans (by norm_cast; omega) hnR)
+    set φ : R[X] := Polynomial.map (eval r) (finSuccEquiv _ _ F) with hφ
+    have hφ₀ : φ ≠ 0 := fun hφ₀ ↦ hr <| by
+      rw [← coeff_eval_eq_eval_coeff, ← hφ, hφ₀, Polynomial.coeff_zero]
+    have hφR : φ.natDegree < #R := by
+      refine lt_of_lt_of_le ?_ hnR
+      norm_cast
+      refine lt_of_le_of_lt (natDegree_map_le _ _) ?_
+      suffices (finSuccEquiv _ _ F).natDegree ≠ n by omega
+      rintro rfl
+      refine leadingCoeff_ne_zero.mpr ?_ hFn
+      simpa using (finSuccEquiv R N).injective.ne hF₀
+    obtain ⟨r₀, hr₀⟩ : ∃ r₀, Polynomial.eval r₀ φ ≠ 0 :=
+      φ.exists_eval_ne_zero_of_natDegree_lt_card hφ₀ hφR
+    use Fin.cons r₀ r
+    rwa [eval_eq_eval_mv_eval']
+
+/-- See `MvPolynomial.IsHomogeneous.eq_zero_of_forall_eval_eq_zero`
+for a version that assumes `Infinite R`. -/
+lemma eq_zero_of_forall_eval_eq_zero_of_le_card
+    (hF : F.IsHomogeneous n) (h : ∀ r : σ → R, eval r F = 0) (hnR : n ≤ #R) :
+    F = 0 := by
+  contrapose! h
+  -- reduce to the case where σ is finite
+  obtain ⟨k, f, hf, F, rfl⟩ := exists_fin_rename F
+  have hF₀ : F ≠ 0 := by rintro rfl; simp at h
+  have hF : F.IsHomogeneous n := by rwa [rename_isHomogeneous_iff hf] at hF
+  obtain ⟨r, hr⟩ := exists_eval_ne_zero_of_totalDegree_le_card_aux hF hF₀ hnR
+  obtain ⟨r, rfl⟩ := (Function.factorsThrough_iff _).mp <| (hf.factorsThrough r)
+  use r
+  rwa [eval_rename]
+
+/-- See `MvPolynomial.IsHomogeneous.funext`
+for a version that assumes `Infinite R`. -/
+lemma funext_of_le_card (hF : F.IsHomogeneous n) (hG : G.IsHomogeneous n)
+    (h : ∀ r : σ → R, eval r F = eval r G) (hnR : n ≤ #R) :
+    F = G := by
+  rw [← sub_eq_zero]
+  apply eq_zero_of_forall_eval_eq_zero_of_le_card (hF.sub hG) _ hnR
+  simpa [sub_eq_zero] using h
+
+/-- See `MvPolynomial.IsHomogeneous.eq_zero_of_forall_eval_eq_zero_of_le_card`
+for a version that assumes `n ≤ #R`. -/
+lemma eq_zero_of_forall_eval_eq_zero [Infinite R] {F : MvPolynomial σ R} {n : ℕ}
+    (hF : F.IsHomogeneous n) (h : ∀ r : σ → R, eval r F = 0) : F = 0 := by
+  apply eq_zero_of_forall_eval_eq_zero_of_le_card hF h
+  exact (Cardinal.nat_lt_aleph0 _).le.trans <| Cardinal.infinite_iff.mp ‹Infinite R›
+
+/-- See `MvPolynomial.IsHomogeneous.funext_of_le_card`
+for a version that assumes `n ≤ #R`. -/
+lemma funext [Infinite R] {F G : MvPolynomial σ R} {n : ℕ}
+    (hF : F.IsHomogeneous n) (hG : G.IsHomogeneous n)
+    (h : ∀ r : σ → R, eval r F = eval r G) : F = G := by
+  apply funext_of_le_card hF hG h
+  exact (Cardinal.nat_lt_aleph0 _).le.trans <| Cardinal.infinite_iff.mp ‹Infinite R›
+
+end IsDomain
+
 /-- The homogeneous submodules form a graded ring. This instance is used by `DirectSum.commSemiring`
 and `DirectSum.algebra`. -/
 instance HomogeneousSubmodule.gcommSemiring : SetLike.GradedMonoid (homogeneousSubmodule σ R) where

• 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>

@@ -217,18 +217,18 @@ theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ =
     exact Finset.le_sup (f := fun s ↦ ∑ x in s.support, (⇑s) x) hd
 #align mv_polynomial.is_homogeneous.total_degree MvPolynomial.IsHomogeneous.totalDegree
 
-theorem rename_isHomogeneous {f : σ → τ} (hf : f.Injective) :
+theorem rename_isHomogeneous {f : σ → τ} (h : φ.IsHomogeneous n):
+    (rename f φ).IsHomogeneous n := by
+  rw [← φ.support_sum_monomial_coeff, map_sum]; simp_rw [rename_monomial]
+  exact IsHomogeneous.sum _ _ _ fun d hd ↦ isHomogeneous_monomial _ _ _
+    ((Finsupp.sum_mapDomain_index_addMonoidHom fun _ ↦ .id ℕ).trans <| h <| mem_support_iff.mp hd)
+
+theorem rename_isHomogeneous_iff {f : σ → τ} (hf : f.Injective) :
     (rename f φ).IsHomogeneous n ↔ φ.IsHomogeneous n := by
-  obtain ⟨f, rfl⟩ : ∃ f' : σ ↪ τ, f = f' := ⟨⟨f, hf⟩, rfl⟩
-  have aux : ∀ d : σ →₀ ℕ,
-    ∑ i in (d.embDomain f).support, (d.embDomain f) i = ∑ i in d.support, d i := fun d ↦ by
-    simp only [Finsupp.support_embDomain, Finset.sum_map, Finsupp.embDomain_apply]
-  constructor
-  · intro h d hd
-    rw [← (@h (d.embDomain f) (by rwa [coeff_rename_embDomain])), aux]
-  · intro h d hd
-    obtain ⟨d', rfl, hd'⟩ := coeff_rename_ne_zero _ _ _ hd
-    rw [← Finsupp.embDomain_eq_mapDomain, ← h hd', aux]
+  refine ⟨fun h d hd ↦ ?_, rename_isHomogeneous⟩
+  convert ← @h (d.mapDomain f) _
+  · exact Finsupp.sum_mapDomain_index_inj (h := fun _ ↦ id) hf
+  · rwa [coeff_rename_mapDomain f hf]
 
 /-- The homogeneous submodules form a graded ring. This instance is used by `DirectSum.commSemiring`
 and `DirectSum.algebra`. -/

@@ -217,6 +217,19 @@ theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ =
     exact Finset.le_sup (f := fun s ↦ ∑ x in s.support, (⇑s) x) hd
 #align mv_polynomial.is_homogeneous.total_degree MvPolynomial.IsHomogeneous.totalDegree
 
+theorem rename_isHomogeneous {f : σ → τ} (hf : f.Injective) :
+    (rename f φ).IsHomogeneous n ↔ φ.IsHomogeneous n := by
+  obtain ⟨f, rfl⟩ : ∃ f' : σ ↪ τ, f = f' := ⟨⟨f, hf⟩, rfl⟩
+  have aux : ∀ d : σ →₀ ℕ,
+    ∑ i in (d.embDomain f).support, (d.embDomain f) i = ∑ i in d.support, d i := fun d ↦ by
+    simp only [Finsupp.support_embDomain, Finset.sum_map, Finsupp.embDomain_apply]
+  constructor
+  · intro h d hd
+    rw [← (@h (d.embDomain f) (by rwa [coeff_rename_embDomain])), aux]
+  · intro h d hd
+    obtain ⟨d', rfl, hd'⟩ := coeff_rename_ne_zero _ _ _ hd
+    rw [← Finsupp.embDomain_eq_mapDomain, ← h hd', aux]
+
 /-- The homogeneous submodules form a graded ring. This instance is used by `DirectSum.commSemiring`
 and `DirectSum.algebra`. -/
 instance HomogeneousSubmodule.gcommSemiring : SetLike.GradedMonoid (homogeneousSubmodule σ R) where

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

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

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

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

@@ -276,7 +276,7 @@ theorem homogeneousComponent_zero : homogeneousComponent 0 φ = C (coeff 0 φ) :
   · simp only [coeff_homogeneousComponent, sum_eq_zero_iff, Finsupp.zero_apply, if_true, coeff_C,
       eq_self_iff_true, forall_true_iff]
   · rw [coeff_homogeneousComponent, if_neg, coeff_C, if_neg (Ne.symm hd)]
-    simp only [FunLike.ext_iff, Finsupp.zero_apply] at hd
+    simp only [DFunLike.ext_iff, Finsupp.zero_apply] at hd
     simp [hd]
 #align mv_polynomial.homogeneous_component_zero MvPolynomial.homogeneousComponent_zero
 

This incorporates changes from

• #7845
• #7847
• #7853
• #7872 (was never actually made to work, but the diffs in nightly-testing are unexciting: we need to fully qualify a few names)

They can all be closed when this is merged.

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

@@ -204,7 +204,7 @@ theorem prod {ι : Type*} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : 
 #align mv_polynomial.is_homogeneous.prod MvPolynomial.IsHomogeneous.prod
 
 theorem totalDegree (hφ : IsHomogeneous φ n) (h : φ ≠ 0) : totalDegree φ = n := by
-  rw [totalDegree]
+  rw [MvPolynomial.totalDegree]
   apply le_antisymm
   · apply Finset.sup_le
     intro d hd

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>

@@ -98,7 +98,7 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
       simp_all only [Ne.def, not_false_iff, zero_mul, mul_zero]
   specialize hφ aux.1
   specialize hψ aux.2
-  rw [Finsupp.mem_antidiagonal] at hde
+  rw [Finset.mem_antidiagonal] at hde
   classical
   have hd' : d.support ⊆ d.support ∪ e.support := Finset.subset_union_left _ _
   have he' : e.support ⊆ d.support ∪ e.support := Finset.subset_union_right _ _

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).

@@ -95,7 +95,7 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
   have aux : coeff d φ ≠ 0 ∧ coeff e ψ ≠ 0 := by
     contrapose! H
     by_cases h : coeff d φ = 0 <;>
-      simp_all only [Ne.def, not_false_iff, MulZeroClass.zero_mul, MulZeroClass.mul_zero]
+      simp_all only [Ne.def, not_false_iff, zero_mul, mul_zero]
   specialize hφ aux.1
   specialize hψ aux.2
   rw [Finsupp.mem_antidiagonal] at hde

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

This has nice performance benefits.

@@ -30,7 +30,7 @@ open BigOperators
 
 namespace MvPolynomial
 
-variable {σ : Type _} {τ : Type _} {R : Type _} {S : Type _}
+variable {σ : Type*} {τ : Type*} {R : Type*} {S : Type*}
 
 /-
 TODO
@@ -180,7 +180,7 @@ theorem add (hφ : IsHomogeneous φ n) (hψ : IsHomogeneous ψ n) : IsHomogeneou
   (homogeneousSubmodule σ R n).add_mem hφ hψ
 #align mv_polynomial.is_homogeneous.add MvPolynomial.IsHomogeneous.add
 
-theorem sum {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ℕ)
+theorem sum {ι : Type*} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ℕ)
     (h : ∀ i ∈ s, IsHomogeneous (φ i) n) : IsHomogeneous (∑ i in s, φ i) n :=
   (homogeneousSubmodule σ R n).sum_mem h
 #align mv_polynomial.is_homogeneous.sum MvPolynomial.IsHomogeneous.sum
@@ -189,7 +189,7 @@ theorem mul (hφ : IsHomogeneous φ m) (hψ : IsHomogeneous ψ n) : IsHomogeneou
   homogeneousSubmodule_mul m n <| Submodule.mul_mem_mul hφ hψ
 #align mv_polynomial.is_homogeneous.mul MvPolynomial.IsHomogeneous.mul
 
-theorem prod {ι : Type _} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ι → ℕ)
+theorem prod {ι : Type*} (s : Finset ι) (φ : ι → MvPolynomial σ R) (n : ι → ℕ)
     (h : ∀ i ∈ s, IsHomogeneous (φ i) (n i)) : IsHomogeneous (∏ i in s, φ i) (∑ i in s, n i) := by
   classical
   revert h

In Lean 3, the computability of Finsupp.toMultiset was poisoned by the AddMonoid (α →₀ ℕ) instance, even though this was not used in computation. This is no longer the case in Lean 4, so we can make this computable by adding a DecidableEq α argument.

We loosely follow the pattern used with DFinsupp, where we split the declaration in two, as only one direction needs DecidableEq α. As a result, Finsupp.toMultiset is now only an AddMonoidHom, though Multiset.toFinset remains an equiv.

We're missing some of the formatting infrastructure for this to be pretty, but this now works:

#eval ((Finsupp.mk Finset.univ ![1, 2, 3] sorry).antidiagonal).image
  fun x : _ × _ => (x.1.toFun, x.2.toFun)

@@ -89,6 +89,7 @@ theorem homogeneousSubmodule_mul [CommSemiring R] (m n : ℕ) :
     homogeneousSubmodule σ R m * homogeneousSubmodule σ R n ≤ homogeneousSubmodule σ R (m + n) := by
   rw [Submodule.mul_le]
   intro φ hφ ψ hψ c hc
+  classical
   rw [coeff_mul] at hc
   obtain ⟨⟨d, e⟩, hde, H⟩ := Finset.exists_ne_zero_of_sum_ne_zero hc
   have aux : coeff d φ ≠ 0 ∧ coeff e ψ ≠ 0 := by

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Eric Wieser
-
-! This file was ported from Lean 3 source module ring_theory.mv_polynomial.homogeneous
-! 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.DirectSum.Internal
 import Mathlib.Algebra.GradedMonoid
 import Mathlib.Data.MvPolynomial.Variables
 
+#align_import ring_theory.mv_polynomial.homogeneous from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
+
 /-!
 # Homogeneous polynomials
 

• Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
• roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤]) replaced by $1 $2 $3

@@ -43,7 +43,7 @@ TODO
 /-- A multivariate polynomial `φ` is homogeneous of degree `n`
 if all monomials occurring in `φ` have degree `n`. -/
 def IsHomogeneous [CommSemiring R] (φ : MvPolynomial σ R) (n : ℕ) :=
-  ∀ ⦃d⦄, coeff d φ ≠ 0 → (∑ i in d.support, d i) = n
+  ∀ ⦃d⦄, coeff d φ ≠ 0 → ∑ i in d.support, d i = n
 #align mv_polynomial.is_homogeneous MvPolynomial.IsHomogeneous
 
 variable (σ R)
@@ -79,7 +79,7 @@ variable (σ R)
 
 /-- While equal, the former has a convenient definitional reduction. -/
 theorem homogeneousSubmodule_eq_finsupp_supported [CommSemiring R] (n : ℕ) :
-    homogeneousSubmodule σ R n = Finsupp.supported _ R { d | (∑ i in d.support, d i) = n } := by
+    homogeneousSubmodule σ R n = Finsupp.supported _ R { d | ∑ i in d.support, d i = n } := by
   ext
   rw [Finsupp.mem_supported, Set.subset_def]
   simp only [Finsupp.mem_support_iff, Finset.mem_coe]
@@ -114,7 +114,7 @@ section
 
 variable [CommSemiring R]
 
-theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : (∑ i in d.support, d i) = n) :
+theorem isHomogeneous_monomial (d : σ →₀ ℕ) (r : R) (n : ℕ) (hn : ∑ i in d.support, d i = n) :
     IsHomogeneous (monomial d r) n := by
   intro c hc
   classical
@@ -166,7 +166,7 @@ namespace IsHomogeneous
 
 variable [CommSemiring R] {φ ψ : MvPolynomial σ R} {m n : ℕ}
 
-theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : (∑ i in d.support, d i) ≠ n) :
+theorem coeff_eq_zero (hφ : IsHomogeneous φ n) (d : σ →₀ ℕ) (hd : ∑ i in d.support, d i ≠ n) :
     coeff d φ = 0 := by
   have aux := mt (@hφ d) hd
   classical
@@ -244,7 +244,7 @@ open Finset
 See `sum_homogeneousComponent` for the statement that `φ` is equal to the sum
 of all its homogeneous components. -/
 def homogeneousComponent [CommSemiring R] (n : ℕ) : MvPolynomial σ R →ₗ[R] MvPolynomial σ R :=
-  (Submodule.subtype _).comp <| Finsupp.restrictDom _ _ { d | (∑ i in d.support, d i) = n }
+  (Submodule.subtype _).comp <| Finsupp.restrictDom _ _ { d | ∑ i in d.support, d i = n }
 #align mv_polynomial.homogeneous_component MvPolynomial.homogeneousComponent
 
 section HomogeneousComponent
@@ -255,13 +255,13 @@ variable [CommSemiring R] (n : ℕ) (φ ψ : MvPolynomial σ R)
 
 theorem coeff_homogeneousComponent (d : σ →₀ ℕ) :
     coeff d (homogeneousComponent n φ) = if (∑ i in d.support, d i) = n then coeff d φ else 0 :=
-  Finsupp.filter_apply (fun d : σ →₀ ℕ => (∑ i in d.support, d i) = n) φ d
+  Finsupp.filter_apply (fun d : σ →₀ ℕ => ∑ i in d.support, d i = n) φ d
 #align mv_polynomial.coeff_homogeneous_component MvPolynomial.coeff_homogeneousComponent
 
 theorem homogeneousComponent_apply :
     homogeneousComponent n φ =
-      ∑ d in φ.support.filter fun d => (∑ i in d.support, d i) = n, monomial d (coeff d φ) :=
-  Finsupp.filter_eq_sum (fun d : σ →₀ ℕ => (∑ i in d.support, d i) = n) φ
+      ∑ d in φ.support.filter fun d => ∑ i in d.support, d i = n, monomial d (coeff d φ) :=
+  Finsupp.filter_eq_sum (fun d : σ →₀ ℕ => ∑ i in d.support, d i = n) φ
 #align mv_polynomial.homogeneous_component_apply MvPolynomial.homogeneousComponent_apply
 
 theorem homogeneousComponent_isHomogeneous : (homogeneousComponent n φ).IsHomogeneous n := by
@@ -290,7 +290,7 @@ set_option linter.uppercaseLean3 false in
 #align mv_polynomial.homogeneous_component_C_mul MvPolynomial.homogeneousComponent_C_mul
 
 theorem homogeneousComponent_eq_zero'
-    (h : ∀ d : σ →₀ ℕ, d ∈ φ.support → (∑ i in d.support, d i) ≠ n) :
+    (h : ∀ d : σ →₀ ℕ, d ∈ φ.support → ∑ i in d.support, d i ≠ n) :
     homogeneousComponent n φ = 0 := by
   rw [homogeneousComponent_apply, sum_eq_zero]
   intro d hd; rw [mem_filter] at hd