ring_theory.polynomial.vieta ⟷ Mathlib.RingTheory.Polynomial.Vieta

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Hanting Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Hanting Zhang
 -/
-import Data.Polynomial.Splits
+import Algebra.Polynomial.Splits
 import RingTheory.MvPolynomial.Symmetric
 
 #align_import ring_theory.polynomial.vieta from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"

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

@@ -52,7 +52,7 @@ theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
   intro _ _
   rw [esymm, ← sum_hom', ← sum_map_mul_right, map_congr (Eq.refl _)]
   intro _ ht
-  rw [mem_powerset_len] at ht 
+  rw [mem_powerset_len] at ht
   simp [ht, map_const, prod_replicate, prod_hom', map_id', card_sub]
 #align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymm
 -/
@@ -70,7 +70,7 @@ theorem prod_X_add_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
   · intro j hj1 hj2
     suffices k ≠ card s - j by rw [if_neg this]
     · intro hn
-      rw [hn, Nat.sub_sub_self (nat.lt_succ_iff.mp (finset.mem_range.mp hj1))] at hj2 
+      rw [hn, Nat.sub_sub_self (nat.lt_succ_iff.mp (finset.mem_range.mp hj1))] at hj2
       exact Ne.irrefl hj2
   · rw [Finset.mem_range]
     exact Nat.sub_lt_succ s.card k

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

@@ -45,7 +45,15 @@ variable {R : Type _} [CommSemiring R]
 theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
     (s.map fun r => X + C r).Prod =
       ∑ j in Finset.range (s.card + 1), C (s.esymm j) * X ^ (s.card - j) :=
-  by classical
+  by
+  classical
+  rw [prod_map_add, antidiagonal_eq_map_powerset, map_map, ← bind_powerset_len, Function.comp,
+    map_bind, sum_bind, Finset.sum_eq_multiset_sum, Finset.range_val, map_congr (Eq.refl _)]
+  intro _ _
+  rw [esymm, ← sum_hom', ← sum_map_mul_right, map_congr (Eq.refl _)]
+  intro _ ht
+  rw [mem_powerset_len] at ht 
+  simp [ht, map_const, prod_replicate, prod_hom', map_id', card_sub]
 #align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymm
 -/
 

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

@@ -45,15 +45,7 @@ variable {R : Type _} [CommSemiring R]
 theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
     (s.map fun r => X + C r).Prod =
       ∑ j in Finset.range (s.card + 1), C (s.esymm j) * X ^ (s.card - j) :=
-  by
-  classical
-  rw [prod_map_add, antidiagonal_eq_map_powerset, map_map, ← bind_powerset_len, Function.comp,
-    map_bind, sum_bind, Finset.sum_eq_multiset_sum, Finset.range_val, map_congr (Eq.refl _)]
-  intro _ _
-  rw [esymm, ← sum_hom', ← sum_map_mul_right, map_congr (Eq.refl _)]
-  intro _ ht
-  rw [mem_powerset_len] at ht 
-  simp [ht, map_const, prod_replicate, prod_hom', map_id', card_sub]
+  by classical
 #align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymm
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -86,7 +86,7 @@ theorem prod_X_add_C_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h :
 
 #print Finset.prod_X_add_C_coeff /-
 theorem Finset.prod_X_add_C_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
-    (∏ i in s, (X + C (r i))).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i := by
+    (∏ i in s, (X + C (r i))).coeff k = ∑ t in s.powersetCard (s.card - k), ∏ i in t, r i := by
   rw [Finset.prod, prod_X_add_C_coeff' _ r h, Finset.esymm_map_val]; rfl
 #align finset.prod_X_add_C_coeff Finset.prod_X_add_C_coeff
 -/
@@ -100,7 +100,7 @@ variable {R : Type _} [CommRing R]
 #print Multiset.esymm_neg /-
 theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^ k * esymm s k :=
   by
-  rw [esymm, esymm, ← Multiset.sum_map_mul_left, Multiset.powersetLen_map, Multiset.map_map,
+  rw [esymm, esymm, ← Multiset.sum_map_mul_left, Multiset.powersetCard_map, Multiset.map_map,
     map_congr (Eq.refl _)]
   intro x hx
   rw [(mem_powerset_len.mp hx).right.symm, ← prod_replicate, ← Multiset.map_const]

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Hanting Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Hanting Zhang
 -/
-import Mathbin.Data.Polynomial.Splits
-import Mathbin.RingTheory.MvPolynomial.Symmetric
+import Data.Polynomial.Splits
+import RingTheory.MvPolynomial.Symmetric
 
 #align_import ring_theory.polynomial.vieta from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Hanting Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Hanting Zhang
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.vieta
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.Splits
 import Mathbin.RingTheory.MvPolynomial.Symmetric
 
+#align_import ring_theory.polynomial.vieta from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
+
 /-!
 # Vieta's Formula
 

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

@@ -41,6 +41,7 @@ section Semiring
 
 variable {R : Type _} [CommSemiring R]
 
+#print Multiset.prod_X_add_C_eq_sum_esymm /-
 /-- A sum version of Vieta's formula for `multiset`: the product of the linear terms `X + λ` where
 `λ` runs through a multiset `s` is equal to a linear combination of the symmetric functions
 `esymm s` of the `λ`'s .-/
@@ -57,7 +58,9 @@ theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
   rw [mem_powerset_len] at ht 
   simp [ht, map_const, prod_replicate, prod_hom', map_id', card_sub]
 #align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymm
+-/
 
+#print Multiset.prod_X_add_C_coeff /-
 /-- Vieta's formula for the coefficients of the product of linear terms `X + λ` where `λ` runs
 through a multiset `s` : the `k`th coefficient is the symmetric function `esymm (card s - k) s`. -/
 theorem prod_X_add_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
@@ -75,16 +78,21 @@ theorem prod_X_add_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
   · rw [Finset.mem_range]
     exact Nat.sub_lt_succ s.card k
 #align multiset.prod_X_add_C_coeff Multiset.prod_X_add_C_coeff
+-/
 
+#print Multiset.prod_X_add_C_coeff' /-
 theorem prod_X_add_C_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (s.map fun i => X + C (r i)).Prod.coeff k = (s.map r).esymm (s.card - k) := by
   rw [← map_map (fun r => X + C r) r, prod_X_add_C_coeff] <;> rwa [s.card_map r]
 #align multiset.prod_X_add_C_coeff' Multiset.prod_X_add_C_coeff'
+-/
 
+#print Finset.prod_X_add_C_coeff /-
 theorem Finset.prod_X_add_C_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (∏ i in s, (X + C (r i))).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i := by
   rw [Finset.prod, prod_X_add_C_coeff' _ r h, Finset.esymm_map_val]; rfl
 #align finset.prod_X_add_C_coeff Finset.prod_X_add_C_coeff
+-/
 
 end Semiring
 
@@ -92,6 +100,7 @@ section Ring
 
 variable {R : Type _} [CommRing R]
 
+#print Multiset.esymm_neg /-
 theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^ k * esymm s k :=
   by
   rw [esymm, esymm, ← Multiset.sum_map_mul_left, Multiset.powersetLen_map, Multiset.map_map,
@@ -102,7 +111,9 @@ theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^
   rw [← prod_map_mul, map_congr (Eq.refl _)]
   exact fun z _ => neg_one_mul z
 #align multiset.esymm_neg Multiset.esymm_neg
+-/
 
+#print Multiset.prod_X_sub_X_eq_sum_esymm /-
 theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
     (s.map fun t => X - C t).Prod =
       ∑ j in Finset.range (s.card + 1), (-1) ^ j * (C (s.esymm j) * X ^ (s.card - j)) :=
@@ -117,7 +128,9 @@ theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
   · rwa [map_map]
   · simp only [esymm_neg, card_map, mul_assoc, map_mul, map_pow, map_neg, map_one]
 #align multiset.prod_X_sub_C_eq_sum_esymm Multiset.prod_X_sub_X_eq_sum_esymm
+-/
 
+#print Multiset.prod_X_sub_C_coeff /-
 theorem prod_X_sub_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
     (s.map fun t => X - C t).Prod.coeff k = (-1) ^ (s.card - k) * s.esymm (s.card - k) :=
   by
@@ -133,7 +146,9 @@ theorem prod_X_sub_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
   · rwa [esymm_neg, card_map]
   · rwa [card_map]
 #align multiset.prod_X_sub_C_coeff Multiset.prod_X_sub_C_coeff
+-/
 
+#print Polynomial.coeff_eq_esymm_roots_of_card /-
 /-- Vieta's formula for the coefficients and the roots of a polynomial over an integral domain
   with as many roots as its degree. -/
 theorem Polynomial.coeff_eq_esymm_roots_of_card [IsDomain R] {p : R[X]}
@@ -144,13 +159,16 @@ theorem Polynomial.coeff_eq_esymm_roots_of_card [IsDomain R] {p : R[X]}
   rw [coeff_C_mul, mul_assoc]; congr
   convert p.roots.prod_X_sub_C_coeff _ using 3 <;> rw [hroots]; exact h
 #align polynomial.coeff_eq_esymm_roots_of_card Polynomial.coeff_eq_esymm_roots_of_card
+-/
 
+#print Polynomial.coeff_eq_esymm_roots_of_splits /-
 /-- Vieta's formula for split polynomials over a field. -/
 theorem Polynomial.coeff_eq_esymm_roots_of_splits {F} [Field F] {p : F[X]}
     (hsplit : p.Splits (RingHom.id F)) {k : ℕ} (h : k ≤ p.natDegree) :
     p.coeff k = p.leadingCoeff * (-1) ^ (p.natDegree - k) * p.roots.esymm (p.natDegree - k) :=
   Polynomial.coeff_eq_esymm_roots_of_card (splits_iff_card_roots.1 hsplit) h
 #align polynomial.coeff_eq_esymm_roots_of_splits Polynomial.coeff_eq_esymm_roots_of_splits
+-/
 
 end Ring
 
@@ -162,6 +180,7 @@ open Finset Polynomial Fintype
 
 variable (R σ : Type _) [CommSemiring R] [Fintype σ]
 
+#print MvPolynomial.prod_C_add_X_eq_sum_esymm /-
 /-- A sum version of Vieta's formula for `mv_polynomial`: viewing `X i` as variables,
 the product of linear terms `λ + X i` is equal to a linear combination of
 the symmetric polynomials `esymm σ R j`. -/
@@ -176,7 +195,9 @@ theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
     rwa [Multiset.map_map]
   · rw [Multiset.card_map]; rfl
 #align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymm
+-/
 
+#print MvPolynomial.prod_X_add_C_coeff /-
 theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
     (∏ i : σ, (X + C (MvPolynomial.X i))).coeff k = MvPolynomial.esymm σ R (card σ - k) :=
   by
@@ -187,6 +208,7 @@ theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
     rwa [Multiset.map_map]
   repeat' rw [Multiset.card_map]; rfl
 #align mv_polynomial.prod_X_add_C_coeff MvPolynomial.prod_X_add_C_coeff
+-/
 
 end MvPolynomial
 

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

@@ -82,7 +82,7 @@ theorem prod_X_add_C_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h :
 #align multiset.prod_X_add_C_coeff' Multiset.prod_X_add_C_coeff'
 
 theorem Finset.prod_X_add_C_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
-    (∏ i in s, X + C (r i)).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i := by
+    (∏ i in s, (X + C (r i))).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i := by
   rw [Finset.prod, prod_X_add_C_coeff' _ r h, Finset.esymm_map_val]; rfl
 #align finset.prod_X_add_C_coeff Finset.prod_X_add_C_coeff
 
@@ -166,7 +166,7 @@ variable (R σ : Type _) [CommSemiring R] [Fintype σ]
 the product of linear terms `λ + X i` is equal to a linear combination of
 the symmetric polynomials `esymm σ R j`. -/
 theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
-    (∏ i : σ, X + C (MvPolynomial.X i)) =
+    ∏ i : σ, (X + C (MvPolynomial.X i)) =
       ∑ j in range (card σ + 1), C (MvPolynomial.esymm σ R j) * X ^ (card σ - j) :=
   by
   let s := finset.univ.val.map fun i : σ => MvPolynomial.X i
@@ -178,7 +178,7 @@ theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
 #align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymm
 
 theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
-    (∏ i : σ, X + C (MvPolynomial.X i)).coeff k = MvPolynomial.esymm σ R (card σ - k) :=
+    (∏ i : σ, (X + C (MvPolynomial.X i))).coeff k = MvPolynomial.esymm σ R (card σ - k) :=
   by
   let s := finset.univ.val.map fun i => (MvPolynomial.X i : MvPolynomial σ R)
   rw [(_ : card σ = s.card)] at h ⊢

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

@@ -49,13 +49,13 @@ theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
       ∑ j in Finset.range (s.card + 1), C (s.esymm j) * X ^ (s.card - j) :=
   by
   classical
-    rw [prod_map_add, antidiagonal_eq_map_powerset, map_map, ← bind_powerset_len, Function.comp,
-      map_bind, sum_bind, Finset.sum_eq_multiset_sum, Finset.range_val, map_congr (Eq.refl _)]
-    intro _ _
-    rw [esymm, ← sum_hom', ← sum_map_mul_right, map_congr (Eq.refl _)]
-    intro _ ht
-    rw [mem_powerset_len] at ht 
-    simp [ht, map_const, prod_replicate, prod_hom', map_id', card_sub]
+  rw [prod_map_add, antidiagonal_eq_map_powerset, map_map, ← bind_powerset_len, Function.comp,
+    map_bind, sum_bind, Finset.sum_eq_multiset_sum, Finset.range_val, map_congr (Eq.refl _)]
+  intro _ _
+  rw [esymm, ← sum_hom', ← sum_map_mul_right, map_congr (Eq.refl _)]
+  intro _ ht
+  rw [mem_powerset_len] at ht 
+  simp [ht, map_const, prod_replicate, prod_hom', map_id', card_sub]
 #align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymm
 
 /-- Vieta's formula for the coefficients of the product of linear terms `X + λ` where `λ` runs

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

@@ -54,7 +54,7 @@ theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
     intro _ _
     rw [esymm, ← sum_hom', ← sum_map_mul_right, map_congr (Eq.refl _)]
     intro _ ht
-    rw [mem_powerset_len] at ht
+    rw [mem_powerset_len] at ht 
     simp [ht, map_const, prod_replicate, prod_hom', map_id', card_sub]
 #align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymm
 
@@ -70,7 +70,7 @@ theorem prod_X_add_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
   · intro j hj1 hj2
     suffices k ≠ card s - j by rw [if_neg this]
     · intro hn
-      rw [hn, Nat.sub_sub_self (nat.lt_succ_iff.mp (finset.mem_range.mp hj1))] at hj2
+      rw [hn, Nat.sub_sub_self (nat.lt_succ_iff.mp (finset.mem_range.mp hj1))] at hj2 
       exact Ne.irrefl hj2
   · rw [Finset.mem_range]
     exact Nat.sub_lt_succ s.card k
@@ -181,7 +181,7 @@ theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
     (∏ i : σ, X + C (MvPolynomial.X i)).coeff k = MvPolynomial.esymm σ R (card σ - k) :=
   by
   let s := finset.univ.val.map fun i => (MvPolynomial.X i : MvPolynomial σ R)
-  rw [(_ : card σ = s.card)] at h⊢
+  rw [(_ : card σ = s.card)] at h ⊢
   · rw [MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
     convert Multiset.prod_X_add_C_coeff s h
     rwa [Multiset.map_map]

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

@@ -31,7 +31,7 @@ the roots of `p` for a polynomial `p` that splits (i.e. having as many roots as
 -/
 
 
-open BigOperators Polynomial
+open scoped BigOperators Polynomial
 
 namespace Multiset
 

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

@@ -41,9 +41,6 @@ section Semiring
 
 variable {R : Type _} [CommSemiring R]
 
-/- warning: multiset.prod_X_add_C_eq_sum_esymm -> Multiset.prod_X_add_C_eq_sum_esymm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymmₓ'. -/
 /-- A sum version of Vieta's formula for `multiset`: the product of the linear terms `X + λ` where
 `λ` runs through a multiset `s` is equal to a linear combination of the symmetric functions
 `esymm s` of the `λ`'s .-/
@@ -61,9 +58,6 @@ theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
     simp [ht, map_const, prod_replicate, prod_hom', map_id', card_sub]
 #align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymm
 
-/- warning: multiset.prod_X_add_C_coeff -> Multiset.prod_X_add_C_coeff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align multiset.prod_X_add_C_coeff Multiset.prod_X_add_C_coeffₓ'. -/
 /-- Vieta's formula for the coefficients of the product of linear terms `X + λ` where `λ` runs
 through a multiset `s` : the `k`th coefficient is the symmetric function `esymm (card s - k) s`. -/
 theorem prod_X_add_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
@@ -82,17 +76,11 @@ theorem prod_X_add_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
     exact Nat.sub_lt_succ s.card k
 #align multiset.prod_X_add_C_coeff Multiset.prod_X_add_C_coeff
 
-/- warning: multiset.prod_X_add_C_coeff' -> Multiset.prod_X_add_C_coeff' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align multiset.prod_X_add_C_coeff' Multiset.prod_X_add_C_coeff'ₓ'. -/
 theorem prod_X_add_C_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (s.map fun i => X + C (r i)).Prod.coeff k = (s.map r).esymm (s.card - k) := by
   rw [← map_map (fun r => X + C r) r, prod_X_add_C_coeff] <;> rwa [s.card_map r]
 #align multiset.prod_X_add_C_coeff' Multiset.prod_X_add_C_coeff'
 
-/- warning: finset.prod_X_add_C_coeff -> Finset.prod_X_add_C_coeff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.prod_X_add_C_coeff Finset.prod_X_add_C_coeffₓ'. -/
 theorem Finset.prod_X_add_C_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (∏ i in s, X + C (r i)).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i := by
   rw [Finset.prod, prod_X_add_C_coeff' _ r h, Finset.esymm_map_val]; rfl
@@ -104,12 +92,6 @@ section Ring
 
 variable {R : Type _} [CommRing R]
 
-/- warning: multiset.esymm_neg -> Multiset.esymm_neg is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) (k : Nat), Eq.{succ u1} R (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Multiset.map.{u1, u1} R R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) s) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) k) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s k))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) (k : Nat), Eq.{succ u1} R (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Multiset.map.{u1, u1} R R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) s) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) k) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s k))
-Case conversion may be inaccurate. Consider using '#align multiset.esymm_neg Multiset.esymm_negₓ'. -/
 theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^ k * esymm s k :=
   by
   rw [esymm, esymm, ← Multiset.sum_map_mul_left, Multiset.powersetLen_map, Multiset.map_map,
@@ -121,9 +103,6 @@ theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^
   exact fun z _ => neg_one_mul z
 #align multiset.esymm_neg Multiset.esymm_neg
 
-/- warning: multiset.prod_X_sub_C_eq_sum_esymm -> Multiset.prod_X_sub_X_eq_sum_esymm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_eq_sum_esymm Multiset.prod_X_sub_X_eq_sum_esymmₓ'. -/
 theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
     (s.map fun t => X - C t).Prod =
       ∑ j in Finset.range (s.card + 1), (-1) ^ j * (C (s.esymm j) * X ^ (s.card - j)) :=
@@ -139,9 +118,6 @@ theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
   · simp only [esymm_neg, card_map, mul_assoc, map_mul, map_pow, map_neg, map_one]
 #align multiset.prod_X_sub_C_eq_sum_esymm Multiset.prod_X_sub_X_eq_sum_esymm
 
-/- warning: multiset.prod_X_sub_C_coeff -> Multiset.prod_X_sub_C_coeff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_coeff Multiset.prod_X_sub_C_coeffₓ'. -/
 theorem prod_X_sub_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
     (s.map fun t => X - C t).Prod.coeff k = (-1) ^ (s.card - k) * s.esymm (s.card - k) :=
   by
@@ -158,12 +134,6 @@ theorem prod_X_sub_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
   · rwa [card_map]
 #align multiset.prod_X_sub_C_coeff Multiset.prod_X_sub_C_coeff
 
-/- warning: polynomial.coeff_eq_esymm_roots_of_card -> Polynomial.coeff_eq_esymm_roots_of_card is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (forall {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) k))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) k)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (forall {k : Nat}, (LE.le.{0} Nat instLENat k (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) k))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) k)))))
-Case conversion may be inaccurate. Consider using '#align polynomial.coeff_eq_esymm_roots_of_card Polynomial.coeff_eq_esymm_roots_of_cardₓ'. -/
 /-- Vieta's formula for the coefficients and the roots of a polynomial over an integral domain
   with as many roots as its degree. -/
 theorem Polynomial.coeff_eq_esymm_roots_of_card [IsDomain R] {p : R[X]}
@@ -175,12 +145,6 @@ theorem Polynomial.coeff_eq_esymm_roots_of_card [IsDomain R] {p : R[X]}
   convert p.roots.prod_X_sub_C_coeff _ using 3 <;> rw [hroots]; exact h
 #align polynomial.coeff_eq_esymm_roots_of_card Polynomial.coeff_eq_esymm_roots_of_card
 
-/- warning: polynomial.coeff_eq_esymm_roots_of_splits -> Polynomial.coeff_eq_esymm_roots_of_splits is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_2 : Field.{u1} F] {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))}, (Polynomial.Splits.{u1, u1} F F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) _inst_2 (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) p) -> (forall {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p)) -> (Eq.{succ u1} F (Polynomial.coeff.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p k) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) (Polynomial.leadingCoeff.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p) (HPow.hPow.{u1, 0, u1} F Nat F (instHPow.{u1, 0} F Nat (Monoid.Pow.{u1} F (Ring.toMonoid.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) (Neg.neg.{u1} F (SubNegMonoid.toHasNeg.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))))) (OfNat.ofNat.{u1} F 1 (OfNat.mk.{u1} F 1 (One.one.{u1} F (AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p) k))) (Multiset.esymm.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)) (Polynomial.roots.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) (Field.isDomain.{u1} F _inst_2) p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p) k)))))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_2 : Field.{u1} F] {p : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)))}, (Polynomial.Splits.{u1, u1} F F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) _inst_2 (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))) p) -> (forall {k : Nat}, (LE.le.{0} Nat instLENat k (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p)) -> (Eq.{succ u1} F (Polynomial.coeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p k) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) (HPow.hPow.{u1, 0, u1} F Nat F (instHPow.{u1, 0} F Nat (Monoid.Pow.{u1} F (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))))) (Neg.neg.{u1} F (Ring.toNeg.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) (OfNat.ofNat.{u1} F 1 (One.toOfNat1.{u1} F (Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) k))) (Multiset.esymm.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)) (Polynomial.roots.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) (Field.isDomain.{u1} F _inst_2) p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) k)))))
-Case conversion may be inaccurate. Consider using '#align polynomial.coeff_eq_esymm_roots_of_splits Polynomial.coeff_eq_esymm_roots_of_splitsₓ'. -/
 /-- Vieta's formula for split polynomials over a field. -/
 theorem Polynomial.coeff_eq_esymm_roots_of_splits {F} [Field F] {p : F[X]}
     (hsplit : p.Splits (RingHom.id F)) {k : ℕ} (h : k ≤ p.natDegree) :
@@ -198,9 +162,6 @@ open Finset Polynomial Fintype
 
 variable (R σ : Type _) [CommSemiring R] [Fintype σ]
 
-/- warning: mv_polynomial.prod_C_add_X_eq_sum_esymm -> MvPolynomial.prod_C_add_X_eq_sum_esymm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymmₓ'. -/
 /-- A sum version of Vieta's formula for `mv_polynomial`: viewing `X i` as variables,
 the product of linear terms `λ + X i` is equal to a linear combination of
 the symmetric polynomials `esymm σ R j`. -/
@@ -216,9 +177,6 @@ theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
   · rw [Multiset.card_map]; rfl
 #align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymm
 
-/- warning: mv_polynomial.prod_X_add_C_coeff -> MvPolynomial.prod_X_add_C_coeff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.prod_X_add_C_coeff MvPolynomial.prod_X_add_C_coeffₓ'. -/
 theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
     (∏ i : σ, X + C (MvPolynomial.X i)).coeff k = MvPolynomial.esymm σ R (card σ - k) :=
   by

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

@@ -94,10 +94,8 @@ theorem prod_X_add_C_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h :
 <too large>
 Case conversion may be inaccurate. Consider using '#align finset.prod_X_add_C_coeff Finset.prod_X_add_C_coeffₓ'. -/
 theorem Finset.prod_X_add_C_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
-    (∏ i in s, X + C (r i)).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i :=
-  by
-  rw [Finset.prod, prod_X_add_C_coeff' _ r h, Finset.esymm_map_val]
-  rfl
+    (∏ i in s, X + C (r i)).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i := by
+  rw [Finset.prod, prod_X_add_C_coeff' _ r h, Finset.esymm_map_val]; rfl
 #align finset.prod_X_add_C_coeff Finset.prod_X_add_C_coeff
 
 end Semiring
@@ -215,8 +213,7 @@ theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
   · simp_rw [MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
     convert Multiset.prod_X_add_C_eq_sum_esymm s
     rwa [Multiset.map_map]
-  · rw [Multiset.card_map]
-    rfl
+  · rw [Multiset.card_map]; rfl
 #align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymm
 
 /- warning: mv_polynomial.prod_X_add_C_coeff -> MvPolynomial.prod_X_add_C_coeff is a dubious translation:

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

@@ -42,10 +42,7 @@ section Semiring
 variable {R : Type _} [CommSemiring R]
 
 /- warning: multiset.prod_X_add_C_eq_sum_esymm -> Multiset.prod_X_add_C_eq_sum_esymm is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) j))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finset.range (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) j))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymmₓ'. -/
 /-- A sum version of Vieta's formula for `multiset`: the product of the linear terms `X + λ` where
 `λ` runs through a multiset `s` is equal to a linear combination of the symmetric functions
@@ -65,10 +62,7 @@ theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
 #align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymm
 
 /- warning: multiset.prod_X_add_C_coeff -> Multiset.prod_X_add_C_coeff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) k) (Multiset.esymm.{u1} R _inst_1 s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) k)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) k) (Multiset.esymm.{u1} R _inst_1 s (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_add_C_coeff Multiset.prod_X_add_C_coeffₓ'. -/
 /-- Vieta's formula for the coefficients of the product of linear terms `X + λ` where `λ` runs
 through a multiset `s` : the `k`th coefficient is the symmetric function `esymm (card s - k) s`. -/
@@ -89,10 +83,7 @@ theorem prod_X_add_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
 #align multiset.prod_X_add_C_coeff Multiset.prod_X_add_C_coeff
 
 /- warning: multiset.prod_X_add_C_coeff' -> Multiset.prod_X_add_C_coeff' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Multiset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} σ) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} σ) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u2, u1} σ (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i))) s)) k) (Multiset.esymm.{u1} R _inst_1 (Multiset.map.{u2, u1} σ R r s) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} σ) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} σ) s) k)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Multiset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) (fun (_x : Multiset.{u2} σ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} σ) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} σ) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u2, u1} σ (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i))) s)) k) (Multiset.esymm.{u1} R _inst_1 (Multiset.map.{u2, u1} σ R r s) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) s) instSubNat) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) (fun (_x : Multiset.{u2} σ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} σ) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} σ) s) k)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_add_C_coeff' Multiset.prod_X_add_C_coeff'ₓ'. -/
 theorem prod_X_add_C_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (s.map fun i => X + C (r i)).Prod.coeff k = (s.map r).esymm (s.card - k) := by
@@ -100,10 +91,7 @@ theorem prod_X_add_C_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h :
 #align multiset.prod_X_add_C_coeff' Multiset.prod_X_add_C_coeff'
 
 /- warning: finset.prod_X_add_C_coeff -> Finset.prod_X_add_C_coeff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Finset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (Finset.card.{u2} σ s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) σ (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) s (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)))) k) (Finset.sum.{u1, u2} R (Finset.{u2} σ) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finset.powersetLen.{u2} σ (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} σ s) k) s) (fun (t : Finset.{u2} σ) => Finset.prod.{u1, u2} R σ (CommSemiring.toCommMonoid.{u1} R _inst_1) t (fun (i : σ) => r i))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Finset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat instLENat k (Finset.card.{u2} σ s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) σ (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) s (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)))) k) (Finset.sum.{u1, u2} R (Finset.{u2} σ) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finset.powersetLen.{u2} σ (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} σ s) k) s) (fun (t : Finset.{u2} σ) => Finset.prod.{u1, u2} R σ (CommSemiring.toCommMonoid.{u1} R _inst_1) t (fun (i : σ) => r i))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align finset.prod_X_add_C_coeff Finset.prod_X_add_C_coeffₓ'. -/
 theorem Finset.prod_X_add_C_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (∏ i in s, X + C (r i)).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i :=
@@ -136,10 +124,7 @@ theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^
 #align multiset.esymm_neg Multiset.esymm_neg
 
 /- warning: multiset.prod_X_sub_C_eq_sum_esymm -> Multiset.prod_X_sub_X_eq_sum_esymm is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.neg'.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) j) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) j)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)))))) (Finset.range (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.neg'.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) j) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) j)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_eq_sum_esymm Multiset.prod_X_sub_X_eq_sum_esymmₓ'. -/
 theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
     (s.map fun t => X - C t).Prod =
@@ -157,10 +142,7 @@ theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
 #align multiset.prod_X_sub_C_eq_sum_esymm Multiset.prod_X_sub_X_eq_sum_esymm
 
 /- warning: multiset.prod_X_sub_C_coeff -> Multiset.prod_X_sub_C_coeff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t)) s)) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) k)) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) k))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t)) s)) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) R (instHPow.{u1, 0} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k)) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_coeff Multiset.prod_X_sub_C_coeffₓ'. -/
 theorem prod_X_sub_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
     (s.map fun t => X - C t).Prod.coeff k = (-1) ^ (s.card - k) * s.esymm (s.card - k) :=
@@ -219,10 +201,7 @@ open Finset Polynomial Fintype
 variable (R σ : Type _) [CommSemiring R] [Fintype σ]
 
 /- warning: mv_polynomial.prod_C_add_X_eq_sum_esymm -> MvPolynomial.prod_C_add_X_eq_sum_esymm is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ], Eq.{succ (max u2 u1)} (Polynomial.{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.prod.{max u2 u1, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{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))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{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))) (Polynomial.{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))) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{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)))) (Polynomial.X.{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))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) -> (Polynomial.{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)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) (Finset.sum.{max u2 u1, 0} (Polynomial.{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))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Fintype.card.{u2} σ _inst_2) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (j : Nat) => HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{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))) (Polynomial.{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))) (Polynomial.{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))) (instHMul.{max u2 u1} (Polynomial.{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))) (Polynomial.mul'.{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)))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) -> (Polynomial.{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)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (Polynomial.C.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Polynomial.{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))) Nat (Polynomial.{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))) (instHPow.{max u2 u1, 0} (Polynomial.{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))) Nat (Monoid.Pow.{max u2 u1} (Polynomial.{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))) (MonoidWithZero.toMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toMonoidWithZero.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))))) (Polynomial.X.{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))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Fintype.card.{u2} σ _inst_2) j))))
-but is expected to have type
-  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ], Eq.{succ (max u2 u1)} (Polynomial.{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.prod.{max u2 u1, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{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))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.X.{u1, u2} R σ _inst_1 i)) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{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)))) (Polynomial.X.{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))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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))) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 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.toMul.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))) (RingHom.instRingHomClassRingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) (Finset.sum.{max u2 u1, 0} (Polynomial.{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))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fintype.card.{u2} σ _inst_2) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{max u1 u2, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (Polynomial.{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))) (Polynomial.{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))) (instHMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (Polynomial.mul'.{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)))) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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))) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{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))) (NonUnitalNonAssocSemiring.toMul.{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))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (Polynomial.{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))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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 u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{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))) (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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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 u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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)))))))) (Polynomial.C.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Polynomial.{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))) Nat (Polynomial.{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))) (instHPow.{max u1 u2, 0} (Polynomial.{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))) Nat (Monoid.Pow.{max u1 u2} (Polynomial.{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))) (MonoidWithZero.toMonoid.{max u1 u2} (Polynomial.{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.toMonoidWithZero.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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))))))) (Polynomial.X.{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))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u2} σ _inst_2) j))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymmₓ'. -/
 /-- A sum version of Vieta's formula for `mv_polynomial`: viewing `X i` as variables,
 the product of linear terms `λ + X i` is equal to a linear combination of
@@ -241,10 +220,7 @@ theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
 #align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymm
 
 /- warning: mv_polynomial.prod_X_add_C_coeff -> MvPolynomial.prod_X_add_C_coeff is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ] (k : Nat), (LE.le.{0} Nat Nat.hasLe k (Fintype.card.{u2} σ _inst_2)) -> (Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.coeff.{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.prod.{max u2 u1, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{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))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{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))) (Polynomial.{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))) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{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)))) (Polynomial.X.{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))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) -> (Polynomial.{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)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) k) (MvPolynomial.esymm.{u2, u1} σ R _inst_1 _inst_2 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Fintype.card.{u2} σ _inst_2) k)))
-but is expected to have type
-  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ] (k : Nat), (LE.le.{0} Nat instLENat k (Fintype.card.{u2} σ _inst_2)) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.coeff.{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)) (Finset.prod.{max u1 u2, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u1 u2} (Polynomial.{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))) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u1 u2} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.X.{u1, u2} R σ _inst_1 i)) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{max u1 u2} (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)))) (Polynomial.X.{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))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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))) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 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.toMul.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))) (RingHom.instRingHomClassRingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) k) (MvPolynomial.esymm.{u2, u1} σ R _inst_1 _inst_2 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u2} σ _inst_2) k)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.prod_X_add_C_coeff MvPolynomial.prod_X_add_C_coeffₓ'. -/
 theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
     (∏ i : σ, X + C (MvPolynomial.X i)).coeff k = MvPolynomial.esymm σ R (card σ - k) :=

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

@@ -45,7 +45,7 @@ variable {R : Type _} [CommSemiring R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) j))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finset.range (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) j))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finset.range (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) j))))
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymmₓ'. -/
 /-- A sum version of Vieta's formula for `multiset`: the product of the linear terms `X + λ` where
 `λ` runs through a multiset `s` is equal to a linear combination of the symmetric functions
@@ -68,7 +68,7 @@ theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) k) (Multiset.esymm.{u1} R _inst_1 s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) k)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) k) (Multiset.esymm.{u1} R _inst_1 s (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) k) (Multiset.esymm.{u1} R _inst_1 s (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k)))
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_add_C_coeff Multiset.prod_X_add_C_coeffₓ'. -/
 /-- Vieta's formula for the coefficients of the product of linear terms `X + λ` where `λ` runs
 through a multiset `s` : the `k`th coefficient is the symmetric function `esymm (card s - k) s`. -/
@@ -92,7 +92,7 @@ theorem prod_X_add_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Multiset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} σ) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} σ) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u2, u1} σ (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i))) s)) k) (Multiset.esymm.{u1} R _inst_1 (Multiset.map.{u2, u1} σ R r s) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} σ) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} σ) s) k)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Multiset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) (fun (_x : Multiset.{u2} σ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} σ) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} σ) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u2, u1} σ (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i))) s)) k) (Multiset.esymm.{u1} R _inst_1 (Multiset.map.{u2, u1} σ R r s) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) s) instSubNat) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) (fun (_x : Multiset.{u2} σ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} σ) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} σ) s) k)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Multiset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) (fun (_x : Multiset.{u2} σ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} σ) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} σ) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u2, u1} σ (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i))) s)) k) (Multiset.esymm.{u1} R _inst_1 (Multiset.map.{u2, u1} σ R r s) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) s) instSubNat) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) (fun (_x : Multiset.{u2} σ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} σ) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} σ) s) k)))
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_add_C_coeff' Multiset.prod_X_add_C_coeff'ₓ'. -/
 theorem prod_X_add_C_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (s.map fun i => X + C (r i)).Prod.coeff k = (s.map r).esymm (s.card - k) := by
@@ -103,7 +103,7 @@ theorem prod_X_add_C_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Finset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (Finset.card.{u2} σ s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) σ (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) s (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)))) k) (Finset.sum.{u1, u2} R (Finset.{u2} σ) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finset.powersetLen.{u2} σ (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} σ s) k) s) (fun (t : Finset.{u2} σ) => Finset.prod.{u1, u2} R σ (CommSemiring.toCommMonoid.{u1} R _inst_1) t (fun (i : σ) => r i))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Finset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat instLENat k (Finset.card.{u2} σ s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) σ (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) s (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)))) k) (Finset.sum.{u1, u2} R (Finset.{u2} σ) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finset.powersetLen.{u2} σ (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} σ s) k) s) (fun (t : Finset.{u2} σ) => Finset.prod.{u1, u2} R σ (CommSemiring.toCommMonoid.{u1} R _inst_1) t (fun (i : σ) => r i))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Finset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat instLENat k (Finset.card.{u2} σ s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) σ (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) s (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)))) k) (Finset.sum.{u1, u2} R (Finset.{u2} σ) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finset.powersetLen.{u2} σ (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} σ s) k) s) (fun (t : Finset.{u2} σ) => Finset.prod.{u1, u2} R σ (CommSemiring.toCommMonoid.{u1} R _inst_1) t (fun (i : σ) => r i))))
 Case conversion may be inaccurate. Consider using '#align finset.prod_X_add_C_coeff Finset.prod_X_add_C_coeffₓ'. -/
 theorem Finset.prod_X_add_C_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (∏ i in s, X + C (r i)).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i :=
@@ -139,7 +139,7 @@ theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.neg'.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) j) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) j)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)))))) (Finset.range (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.neg'.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) j) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) j)))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)))))) (Finset.range (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.neg'.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) j) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) j)))))
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_eq_sum_esymm Multiset.prod_X_sub_X_eq_sum_esymmₓ'. -/
 theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
     (s.map fun t => X - C t).Prod =
@@ -160,7 +160,7 @@ theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t)) s)) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) k)) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) k))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t)) s)) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) R (instHPow.{u1, 0} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k)) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t)) s)) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) R (instHPow.{u1, 0} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k)) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k))))
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_coeff Multiset.prod_X_sub_C_coeffₓ'. -/
 theorem prod_X_sub_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
     (s.map fun t => X - C t).Prod.coeff k = (-1) ^ (s.card - k) * s.esymm (s.card - k) :=
@@ -222,7 +222,7 @@ variable (R σ : Type _) [CommSemiring R] [Fintype σ]
 lean 3 declaration is
   forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ], Eq.{succ (max u2 u1)} (Polynomial.{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.prod.{max u2 u1, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{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))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{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))) (Polynomial.{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))) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{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)))) (Polynomial.X.{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))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) -> (Polynomial.{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)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) (Finset.sum.{max u2 u1, 0} (Polynomial.{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))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Fintype.card.{u2} σ _inst_2) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (j : Nat) => HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{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))) (Polynomial.{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))) (Polynomial.{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))) (instHMul.{max u2 u1} (Polynomial.{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))) (Polynomial.mul'.{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)))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) -> (Polynomial.{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)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (Polynomial.C.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Polynomial.{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))) Nat (Polynomial.{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))) (instHPow.{max u2 u1, 0} (Polynomial.{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))) Nat (Monoid.Pow.{max u2 u1} (Polynomial.{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))) (MonoidWithZero.toMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toMonoidWithZero.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))))) (Polynomial.X.{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))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Fintype.card.{u2} σ _inst_2) j))))
 but is expected to have type
-  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ], Eq.{succ (max u2 u1)} (Polynomial.{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.prod.{max u2 u1, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{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))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.X.{u1, u2} R σ _inst_1 i)) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{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)))) (Polynomial.X.{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))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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))) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 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.toMul.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))) (RingHom.instRingHomClassRingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) (Finset.sum.{max u2 u1, 0} (Polynomial.{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))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fintype.card.{u2} σ _inst_2) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{max u1 u2, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (Polynomial.{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))) (Polynomial.{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))) (instHMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (Polynomial.mul'.{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)))) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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))) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{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))) (NonUnitalNonAssocSemiring.toMul.{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))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (Polynomial.{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))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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 u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{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))) (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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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 u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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)))))))) (Polynomial.C.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Polynomial.{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))) Nat (Polynomial.{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))) (instHPow.{max u1 u2, 0} (Polynomial.{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))) Nat (Monoid.Pow.{max u1 u2} (Polynomial.{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))) (MonoidWithZero.toMonoid.{max u1 u2} (Polynomial.{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.toMonoidWithZero.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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))))))) (Polynomial.X.{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))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u2} σ _inst_2) j))))
+  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ], Eq.{succ (max u2 u1)} (Polynomial.{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.prod.{max u2 u1, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{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))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.X.{u1, u2} R σ _inst_1 i)) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{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)))) (Polynomial.X.{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))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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))) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 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.toMul.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))) (RingHom.instRingHomClassRingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) (Finset.sum.{max u2 u1, 0} (Polynomial.{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))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fintype.card.{u2} σ _inst_2) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{max u1 u2, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (Polynomial.{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))) (Polynomial.{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))) (instHMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (Polynomial.mul'.{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)))) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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))) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{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))) (NonUnitalNonAssocSemiring.toMul.{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))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (Polynomial.{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))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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 u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{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))) (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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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 u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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)))))))) (Polynomial.C.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Polynomial.{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))) Nat (Polynomial.{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))) (instHPow.{max u1 u2, 0} (Polynomial.{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))) Nat (Monoid.Pow.{max u1 u2} (Polynomial.{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))) (MonoidWithZero.toMonoid.{max u1 u2} (Polynomial.{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.toMonoidWithZero.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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))))))) (Polynomial.X.{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))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u2} σ _inst_2) j))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymmₓ'. -/
 /-- A sum version of Vieta's formula for `mv_polynomial`: viewing `X i` as variables,
 the product of linear terms `λ + X i` is equal to a linear combination of
@@ -244,7 +244,7 @@ theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
 lean 3 declaration is
   forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ] (k : Nat), (LE.le.{0} Nat Nat.hasLe k (Fintype.card.{u2} σ _inst_2)) -> (Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.coeff.{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.prod.{max u2 u1, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{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))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{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))) (Polynomial.{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))) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{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)))) (Polynomial.X.{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))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) -> (Polynomial.{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)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) k) (MvPolynomial.esymm.{u2, u1} σ R _inst_1 _inst_2 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Fintype.card.{u2} σ _inst_2) k)))
 but is expected to have type
-  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ] (k : Nat), (LE.le.{0} Nat instLENat k (Fintype.card.{u2} σ _inst_2)) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.coeff.{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)) (Finset.prod.{max u1 u2, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u1 u2} (Polynomial.{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))) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u1 u2} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.X.{u1, u2} R σ _inst_1 i)) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{max u1 u2} (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)))) (Polynomial.X.{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))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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))) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 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.toMul.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))) (RingHom.instRingHomClassRingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) k) (MvPolynomial.esymm.{u2, u1} σ R _inst_1 _inst_2 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u2} σ _inst_2) k)))
+  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ] (k : Nat), (LE.le.{0} Nat instLENat k (Fintype.card.{u2} σ _inst_2)) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.coeff.{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)) (Finset.prod.{max u1 u2, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u1 u2} (Polynomial.{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))) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u1 u2} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.X.{u1, u2} R σ _inst_1 i)) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{max u1 u2} (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)))) (Polynomial.X.{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))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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))) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 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.toMul.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))) (RingHom.instRingHomClassRingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) k) (MvPolynomial.esymm.{u2, u1} σ R _inst_1 _inst_2 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u2} σ _inst_2) k)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.prod_X_add_C_coeff MvPolynomial.prod_X_add_C_coeffₓ'. -/
 theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
     (∏ i : σ, X + C (MvPolynomial.X i)).coeff k = MvPolynomial.esymm σ R (card σ - k) :=

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

@@ -199,7 +199,7 @@ theorem Polynomial.coeff_eq_esymm_roots_of_card [IsDomain R] {p : R[X]}
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_2 : Field.{u1} F] {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))}, (Polynomial.Splits.{u1, u1} F F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) _inst_2 (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) p) -> (forall {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p)) -> (Eq.{succ u1} F (Polynomial.coeff.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p k) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) (Polynomial.leadingCoeff.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p) (HPow.hPow.{u1, 0, u1} F Nat F (instHPow.{u1, 0} F Nat (Monoid.Pow.{u1} F (Ring.toMonoid.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) (Neg.neg.{u1} F (SubNegMonoid.toHasNeg.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))))) (OfNat.ofNat.{u1} F 1 (OfNat.mk.{u1} F 1 (One.one.{u1} F (AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p) k))) (Multiset.esymm.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)) (Polynomial.roots.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) (Field.isDomain.{u1} F _inst_2) p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p) k)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_2 : Field.{u1} F] {p : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)))}, (Polynomial.Splits.{u1, u1} F F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) _inst_2 (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))) p) -> (forall {k : Nat}, (LE.le.{0} Nat instLENat k (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p)) -> (Eq.{succ u1} F (Polynomial.coeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p k) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) (HPow.hPow.{u1, 0, u1} F Nat F (instHPow.{u1, 0} F Nat (Monoid.Pow.{u1} F (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))))) (Neg.neg.{u1} F (Ring.toNeg.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) (OfNat.ofNat.{u1} F 1 (One.toOfNat1.{u1} F (Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) k))) (Multiset.esymm.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)) (Polynomial.roots.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) k)))))
+  forall {F : Type.{u1}} [_inst_2 : Field.{u1} F] {p : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)))}, (Polynomial.Splits.{u1, u1} F F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) _inst_2 (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))) p) -> (forall {k : Nat}, (LE.le.{0} Nat instLENat k (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p)) -> (Eq.{succ u1} F (Polynomial.coeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p k) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) (HPow.hPow.{u1, 0, u1} F Nat F (instHPow.{u1, 0} F Nat (Monoid.Pow.{u1} F (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))))) (Neg.neg.{u1} F (Ring.toNeg.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) (OfNat.ofNat.{u1} F 1 (One.toOfNat1.{u1} F (Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) k))) (Multiset.esymm.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)) (Polynomial.roots.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) (Field.isDomain.{u1} F _inst_2) p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) k)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_eq_esymm_roots_of_splits Polynomial.coeff_eq_esymm_roots_of_splitsₓ'. -/
 /-- Vieta's formula for split polynomials over a field. -/
 theorem Polynomial.coeff_eq_esymm_roots_of_splits {F} [Field F] {p : F[X]}

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

@@ -122,7 +122,7 @@ variable {R : Type _} [CommRing R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) (k : Nat), Eq.{succ u1} R (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Multiset.map.{u1, u1} R R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) s) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) k) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s k))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) (k : Nat), Eq.{succ u1} R (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Multiset.map.{u1, u1} R R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) s) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) k) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s k))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) (k : Nat), Eq.{succ u1} R (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Multiset.map.{u1, u1} R R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) s) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) k) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s k))
 Case conversion may be inaccurate. Consider using '#align multiset.esymm_neg Multiset.esymm_negₓ'. -/
 theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^ k * esymm s k :=
   by
@@ -139,7 +139,7 @@ theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.neg'.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) j) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) j)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Finset.range (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.neg'.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) j) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) j)))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)))))) (Finset.range (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.neg'.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) j) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) j)))))
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_eq_sum_esymm Multiset.prod_X_sub_X_eq_sum_esymmₓ'. -/
 theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
     (s.map fun t => X - C t).Prod =
@@ -160,7 +160,7 @@ theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t)) s)) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) k)) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) k))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t)) s)) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) R (instHPow.{u1, 0} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k)) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) t)) s)) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) R (instHPow.{u1, 0} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k)) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k))))
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_coeff Multiset.prod_X_sub_C_coeffₓ'. -/
 theorem prod_X_sub_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
     (s.map fun t => X - C t).Prod.coeff k = (-1) ^ (s.card - k) * s.esymm (s.card - k) :=
@@ -182,7 +182,7 @@ theorem prod_X_sub_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (forall {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) k))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) k)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (forall {k : Nat}, (LE.le.{0} Nat instLENat k (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) k))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) k)))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (forall {k : Nat}, (LE.le.{0} Nat instLENat k (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) k))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) k)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_eq_esymm_roots_of_card Polynomial.coeff_eq_esymm_roots_of_cardₓ'. -/
 /-- Vieta's formula for the coefficients and the roots of a polynomial over an integral domain
   with as many roots as its degree. -/
@@ -199,7 +199,7 @@ theorem Polynomial.coeff_eq_esymm_roots_of_card [IsDomain R] {p : R[X]}
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_2 : Field.{u1} F] {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))}, (Polynomial.Splits.{u1, u1} F F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) _inst_2 (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) p) -> (forall {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p)) -> (Eq.{succ u1} F (Polynomial.coeff.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p k) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) (Polynomial.leadingCoeff.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p) (HPow.hPow.{u1, 0, u1} F Nat F (instHPow.{u1, 0} F Nat (Monoid.Pow.{u1} F (Ring.toMonoid.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) (Neg.neg.{u1} F (SubNegMonoid.toHasNeg.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))))) (OfNat.ofNat.{u1} F 1 (OfNat.mk.{u1} F 1 (One.one.{u1} F (AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p) k))) (Multiset.esymm.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)) (Polynomial.roots.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) (Field.isDomain.{u1} F _inst_2) p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p) k)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_2 : Field.{u1} F] {p : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)))}, (Polynomial.Splits.{u1, u1} F F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) _inst_2 (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) p) -> (forall {k : Nat}, (LE.le.{0} Nat instLENat k (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p)) -> (Eq.{succ u1} F (Polynomial.coeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p k) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) (HPow.hPow.{u1, 0, u1} F Nat F (instHPow.{u1, 0} F Nat (Monoid.Pow.{u1} F (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))))) (Neg.neg.{u1} F (Ring.toNeg.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) (OfNat.ofNat.{u1} F 1 (One.toOfNat1.{u1} F (NonAssocRing.toOne.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) k))) (Multiset.esymm.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)) (Polynomial.roots.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) k)))))
+  forall {F : Type.{u1}} [_inst_2 : Field.{u1} F] {p : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)))}, (Polynomial.Splits.{u1, u1} F F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) _inst_2 (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))) p) -> (forall {k : Nat}, (LE.le.{0} Nat instLENat k (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p)) -> (Eq.{succ u1} F (Polynomial.coeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p k) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) (HPow.hPow.{u1, 0, u1} F Nat F (instHPow.{u1, 0} F Nat (Monoid.Pow.{u1} F (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))))) (Neg.neg.{u1} F (Ring.toNeg.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) (OfNat.ofNat.{u1} F 1 (One.toOfNat1.{u1} F (Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) k))) (Multiset.esymm.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)) (Polynomial.roots.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) k)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_eq_esymm_roots_of_splits Polynomial.coeff_eq_esymm_roots_of_splitsₓ'. -/
 /-- Vieta's formula for split polynomials over a field. -/
 theorem Polynomial.coeff_eq_esymm_roots_of_splits {F} [Field F] {p : F[X]}
@@ -222,7 +222,7 @@ variable (R σ : Type _) [CommSemiring R] [Fintype σ]
 lean 3 declaration is
   forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ], Eq.{succ (max u2 u1)} (Polynomial.{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.prod.{max u2 u1, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{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))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{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))) (Polynomial.{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))) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{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)))) (Polynomial.X.{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))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) -> (Polynomial.{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)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) (Finset.sum.{max u2 u1, 0} (Polynomial.{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))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Fintype.card.{u2} σ _inst_2) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (j : Nat) => HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{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))) (Polynomial.{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))) (Polynomial.{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))) (instHMul.{max u2 u1} (Polynomial.{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))) (Polynomial.mul'.{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)))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) -> (Polynomial.{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)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (Polynomial.C.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Polynomial.{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))) Nat (Polynomial.{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))) (instHPow.{max u2 u1, 0} (Polynomial.{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))) Nat (Monoid.Pow.{max u2 u1} (Polynomial.{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))) (MonoidWithZero.toMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toMonoidWithZero.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))))) (Polynomial.X.{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))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Fintype.card.{u2} σ _inst_2) j))))
 but is expected to have type
-  forall (R : Type.{u2}) (σ : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Fintype.{u1} σ], Eq.{succ (max u2 u1)} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Finset.prod.{max u2 u1, u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Finset.univ.{u1} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u1 u2, max u1 u2, max u2 u1} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (MvPolynomial.X.{u2, u1} R σ _inst_1 i)) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (instHAdd.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.add'.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (Polynomial.X.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (RingHom.instRingHomClassRingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))))) (Polynomial.C.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (MvPolynomial.X.{u2, u1} R σ _inst_1 i)))) (Finset.sum.{max u2 u1, 0} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (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 instAddNat) (Fintype.card.{u1} σ _inst_2) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} 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.esymm.{u1, u2} σ R _inst_1 _inst_2 j)) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} 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.esymm.{u1, u2} σ R _inst_1 _inst_2 j)) (Polynomial.mul'.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} 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.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} 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.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} 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.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} 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 u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} 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.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} 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.{max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))))) (Polynomial.C.{max u2 u1} (MvPolynomial.{u1, u2} 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.esymm.{u1, u2} σ R _inst_1 _inst_2 j)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) Nat (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (instHPow.{max u2 u1, 0} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) Nat (Monoid.Pow.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (MonoidWithZero.toMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toMonoidWithZero.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (Polynomial.X.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u1} σ _inst_2) j))))
+  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ], Eq.{succ (max u2 u1)} (Polynomial.{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.prod.{max u2 u1, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{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))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.X.{u1, u2} R σ _inst_1 i)) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{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)))) (Polynomial.X.{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))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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))) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 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.toMul.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))) (RingHom.instRingHomClassRingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) (Finset.sum.{max u2 u1, 0} (Polynomial.{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))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fintype.card.{u2} σ _inst_2) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{max u1 u2, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (Polynomial.{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))) (Polynomial.{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))) (instHMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (Polynomial.mul'.{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)))) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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))) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{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))) (NonUnitalNonAssocSemiring.toMul.{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))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (Polynomial.{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))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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 u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{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))) (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)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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 u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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)))))))) (Polynomial.C.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Polynomial.{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))) Nat (Polynomial.{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))) (instHPow.{max u1 u2, 0} (Polynomial.{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))) Nat (Monoid.Pow.{max u1 u2} (Polynomial.{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))) (MonoidWithZero.toMonoid.{max u1 u2} (Polynomial.{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.toMonoidWithZero.{max u1 u2} (Polynomial.{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))) (Polynomial.semiring.{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))))))) (Polynomial.X.{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))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u2} σ _inst_2) j))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymmₓ'. -/
 /-- A sum version of Vieta's formula for `mv_polynomial`: viewing `X i` as variables,
 the product of linear terms `λ + X i` is equal to a linear combination of
@@ -244,7 +244,7 @@ theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
 lean 3 declaration is
   forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ] (k : Nat), (LE.le.{0} Nat Nat.hasLe k (Fintype.card.{u2} σ _inst_2)) -> (Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.coeff.{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.prod.{max u2 u1, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{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))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{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))) (Polynomial.{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))) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{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)))) (Polynomial.X.{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))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) -> (Polynomial.{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)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) k) (MvPolynomial.esymm.{u2, u1} σ R _inst_1 _inst_2 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Fintype.card.{u2} σ _inst_2) k)))
 but is expected to have type
-  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ] (k : Nat), (LE.le.{0} Nat instLENat k (Fintype.card.{u2} σ _inst_2)) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.coeff.{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)) (Finset.prod.{max u1 u2, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u1 u2} (Polynomial.{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))) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u1 u2} (Polynomial.{max u2 u1} (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))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{max u2 u1} (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.X.{u1, u2} R σ _inst_1 i)) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.add'.{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)))) (Polynomial.X.{max u2 u1} (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))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{max u2 u1} (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))) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (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))) (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 u2 u1} (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))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Polynomial.{max u2 u1} (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))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (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))) (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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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)))))))) (Polynomial.C.{max u2 u1} (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.X.{u1, u2} R σ _inst_1 i)))) k) (MvPolynomial.esymm.{u2, u1} σ R _inst_1 _inst_2 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u2} σ _inst_2) k)))
+  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ] (k : Nat), (LE.le.{0} Nat instLENat k (Fintype.card.{u2} σ _inst_2)) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.coeff.{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)) (Finset.prod.{max u1 u2, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u1 u2} (Polynomial.{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))) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u1 u2} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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.X.{u1, u2} R σ _inst_1 i)) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{max u1 u2} (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)))) (Polynomial.X.{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))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{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))) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 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.toMul.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))) (RingHom.instRingHomClassRingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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)))))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) k) (MvPolynomial.esymm.{u2, u1} σ R _inst_1 _inst_2 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u2} σ _inst_2) k)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.prod_X_add_C_coeff MvPolynomial.prod_X_add_C_coeffₓ'. -/
 theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
     (∏ i : σ, X + C (MvPolynomial.X i)).coeff k = MvPolynomial.esymm σ R (card σ - k) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c

@@ -108,7 +108,7 @@ Case conversion may be inaccurate. Consider using '#align finset.prod_X_add_C_co
 theorem Finset.prod_X_add_C_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (∏ i in s, X + C (r i)).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i :=
   by
-  rw [Finset.prod, prod_X_add_C_coeff' _ r h, Multiset.Finset.esymm_map_val]
+  rw [Finset.prod, prod_X_add_C_coeff' _ r h, Finset.esymm_map_val]
   rfl
 #align finset.prod_X_add_C_coeff Finset.prod_X_add_C_coeff
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Hanting Zhang
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.vieta
-! leanprover-community/mathlib commit f694c7dead66f5d4c80f446c796a5aad14707f0e
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.MvPolynomial.Symmetric
 /-!
 # Vieta's Formula
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The main result is `multiset.prod_X_add_C_eq_sum_esymm`, which shows that the product of
 linear terms `X + λ` with `λ` in a `multiset s` is equal to a linear combination of the
 symmetric functions `esymm s`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/0148d455199ed64bf8eb2f493a1e7eb9211ce170

@@ -38,10 +38,16 @@ section Semiring
 
 variable {R : Type _} [CommSemiring R]
 
+/- warning: multiset.prod_X_add_C_eq_sum_esymm -> Multiset.prod_X_add_C_eq_sum_esymm is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) j))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finset.range (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Multiset.esymm.{u1} R _inst_1 s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) j))))
+Case conversion may be inaccurate. Consider using '#align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymmₓ'. -/
 /-- A sum version of Vieta's formula for `multiset`: the product of the linear terms `X + λ` where
 `λ` runs through a multiset `s` is equal to a linear combination of the symmetric functions
 `esymm s` of the `λ`'s .-/
-theorem prod_x_add_c_eq_sum_esymm (s : Multiset R) :
+theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
     (s.map fun r => X + C r).Prod =
       ∑ j in Finset.range (s.card + 1), C (s.esymm j) * X ^ (s.card - j) :=
   by
@@ -53,11 +59,17 @@ theorem prod_x_add_c_eq_sum_esymm (s : Multiset R) :
     intro _ ht
     rw [mem_powerset_len] at ht
     simp [ht, map_const, prod_replicate, prod_hom', map_id', card_sub]
-#align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_x_add_c_eq_sum_esymm
-
+#align multiset.prod_X_add_C_eq_sum_esymm Multiset.prod_X_add_C_eq_sum_esymm
+
+/- warning: multiset.prod_X_add_C_coeff -> Multiset.prod_X_add_C_coeff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) k) (Multiset.esymm.{u1} R _inst_1 s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) k)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (r : R) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) s)) k) (Multiset.esymm.{u1} R _inst_1 s (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k)))
+Case conversion may be inaccurate. Consider using '#align multiset.prod_X_add_C_coeff Multiset.prod_X_add_C_coeffₓ'. -/
 /-- Vieta's formula for the coefficients of the product of linear terms `X + λ` where `λ` runs
 through a multiset `s` : the `k`th coefficient is the symmetric function `esymm (card s - k) s`. -/
-theorem prod_x_add_c_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
+theorem prod_X_add_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
     (s.map fun r => X + C r).Prod.coeff k = s.esymm (s.card - k) :=
   by
   convert polynomial.ext_iff.mp (prod_X_add_C_eq_sum_esymm s) k
@@ -71,19 +83,31 @@ theorem prod_x_add_c_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
       exact Ne.irrefl hj2
   · rw [Finset.mem_range]
     exact Nat.sub_lt_succ s.card k
-#align multiset.prod_X_add_C_coeff Multiset.prod_x_add_c_coeff
-
-theorem prod_x_add_c_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
+#align multiset.prod_X_add_C_coeff Multiset.prod_X_add_C_coeff
+
+/- warning: multiset.prod_X_add_C_coeff' -> Multiset.prod_X_add_C_coeff' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Multiset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} σ) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} σ) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u2, u1} σ (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i))) s)) k) (Multiset.esymm.{u1} R _inst_1 (Multiset.map.{u2, u1} σ R r s) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} σ) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.orderedCancelAddCommMonoid.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} σ) s) k)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Multiset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) (fun (_x : Multiset.{u2} σ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} σ) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} σ) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) (Multiset.map.{u2, u1} σ (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i))) s)) k) (Multiset.esymm.{u1} R _inst_1 (Multiset.map.{u2, u1} σ R r s) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) s) instSubNat) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) (fun (_x : Multiset.{u2} σ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} σ) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} σ) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} σ) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} σ) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} σ) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} σ) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} σ) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} σ) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} σ)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} σ) s) k)))
+Case conversion may be inaccurate. Consider using '#align multiset.prod_X_add_C_coeff' Multiset.prod_X_add_C_coeff'ₓ'. -/
+theorem prod_X_add_C_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (s.map fun i => X + C (r i)).Prod.coeff k = (s.map r).esymm (s.card - k) := by
   rw [← map_map (fun r => X + C r) r, prod_X_add_C_coeff] <;> rwa [s.card_map r]
-#align multiset.prod_X_add_C_coeff' Multiset.prod_x_add_c_coeff'
-
-theorem Finset.prod_x_add_c_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
+#align multiset.prod_X_add_C_coeff' Multiset.prod_X_add_C_coeff'
+
+/- warning: finset.prod_X_add_C_coeff -> Finset.prod_X_add_C_coeff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Finset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (Finset.card.{u2} σ s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) σ (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) s (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)))) k) (Finset.sum.{u1, u2} R (Finset.{u2} σ) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finset.powersetLen.{u2} σ (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} σ s) k) s) (fun (t : Finset.{u2} σ) => Finset.prod.{u1, u2} R σ (CommSemiring.toCommMonoid.{u1} R _inst_1) t (fun (i : σ) => r i))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {σ : Type.{u2}} (s : Finset.{u2} σ) (r : σ -> R) {k : Nat}, (LE.le.{0} Nat instLENat k (Finset.card.{u2} σ s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) σ (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) s (fun (i : σ) => HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (r i)))) k) (Finset.sum.{u1, u2} R (Finset.{u2} σ) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finset.powersetLen.{u2} σ (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} σ s) k) s) (fun (t : Finset.{u2} σ) => Finset.prod.{u1, u2} R σ (CommSemiring.toCommMonoid.{u1} R _inst_1) t (fun (i : σ) => r i))))
+Case conversion may be inaccurate. Consider using '#align finset.prod_X_add_C_coeff Finset.prod_X_add_C_coeffₓ'. -/
+theorem Finset.prod_X_add_C_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (∏ i in s, X + C (r i)).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i :=
   by
   rw [Finset.prod, prod_X_add_C_coeff' _ r h, Multiset.Finset.esymm_map_val]
   rfl
-#align finset.prod_X_add_C_coeff Finset.prod_x_add_c_coeff
+#align finset.prod_X_add_C_coeff Finset.prod_X_add_C_coeff
 
 end Semiring
 
@@ -91,6 +115,12 @@ section Ring
 
 variable {R : Type _} [CommRing R]
 
+/- warning: multiset.esymm_neg -> Multiset.esymm_neg is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) (k : Nat), Eq.{succ u1} R (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Multiset.map.{u1, u1} R R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) s) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) k) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s k))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) (k : Nat), Eq.{succ u1} R (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Multiset.map.{u1, u1} R R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) s) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) k) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s k))
+Case conversion may be inaccurate. Consider using '#align multiset.esymm_neg Multiset.esymm_negₓ'. -/
 theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^ k * esymm s k :=
   by
   rw [esymm, esymm, ← Multiset.sum_map_mul_left, Multiset.powersetLen_map, Multiset.map_map,
@@ -102,7 +132,13 @@ theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^
   exact fun z _ => neg_one_mul z
 #align multiset.esymm_neg Multiset.esymm_neg
 
-theorem prod_x_sub_c_eq_sum_esymm (s : Multiset R) :
+/- warning: multiset.prod_X_sub_C_eq_sum_esymm -> Multiset.prod_X_sub_X_eq_sum_esymm is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Neg.neg.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.neg'.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) j) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) j)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t)) s)) (Finset.sum.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Finset.range (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.neg'.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) j) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s j)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) j)))))
+Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_eq_sum_esymm Multiset.prod_X_sub_X_eq_sum_esymmₓ'. -/
+theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
     (s.map fun t => X - C t).Prod =
       ∑ j in Finset.range (s.card + 1), (-1) ^ j * (C (s.esymm j) * X ^ (s.card - j)) :=
   by
@@ -115,9 +151,15 @@ theorem prod_x_sub_c_eq_sum_esymm (s : Multiset R) :
   convert prod_X_add_C_eq_sum_esymm (map (fun t => -t) s) using 1
   · rwa [map_map]
   · simp only [esymm_neg, card_map, mul_assoc, map_mul, map_pow, map_neg, map_one]
-#align multiset.prod_X_sub_C_eq_sum_esymm Multiset.prod_x_sub_c_eq_sum_esymm
-
-theorem prod_x_sub_c_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
+#align multiset.prod_X_sub_C_eq_sum_esymm Multiset.prod_X_sub_X_eq_sum_esymm
+
+/- warning: multiset.prod_X_sub_C_coeff -> Multiset.prod_X_sub_C_coeff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t)) s)) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) k)) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s) k))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (s : Multiset.{u1} R) {k : Nat}, (LE.le.{0} Nat instLENat k (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (t : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) t)) s)) k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) R (instHPow.{u1, 0} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k)) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) s (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) instSubNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s) k))))
+Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_coeff Multiset.prod_X_sub_C_coeffₓ'. -/
+theorem prod_X_sub_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
     (s.map fun t => X - C t).Prod.coeff k = (-1) ^ (s.card - k) * s.esymm (s.card - k) :=
   by
   conv_lhs =>
@@ -131,8 +173,14 @@ theorem prod_x_sub_c_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
   · rwa [map_map]
   · rwa [esymm_neg, card_map]
   · rwa [card_map]
-#align multiset.prod_X_sub_C_coeff Multiset.prod_x_sub_c_coeff
-
+#align multiset.prod_X_sub_C_coeff Multiset.prod_X_sub_C_coeff
+
+/- warning: polynomial.coeff_eq_esymm_roots_of_card -> Polynomial.coeff_eq_esymm_roots_of_card is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (forall {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) k))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) k)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (forall {k : Nat}, (LE.le.{0} Nat instLENat k (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p k) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) k))) (Multiset.esymm.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) k)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_eq_esymm_roots_of_card Polynomial.coeff_eq_esymm_roots_of_cardₓ'. -/
 /-- Vieta's formula for the coefficients and the roots of a polynomial over an integral domain
   with as many roots as its degree. -/
 theorem Polynomial.coeff_eq_esymm_roots_of_card [IsDomain R] {p : R[X]}
@@ -144,6 +192,12 @@ theorem Polynomial.coeff_eq_esymm_roots_of_card [IsDomain R] {p : R[X]}
   convert p.roots.prod_X_sub_C_coeff _ using 3 <;> rw [hroots]; exact h
 #align polynomial.coeff_eq_esymm_roots_of_card Polynomial.coeff_eq_esymm_roots_of_card
 
+/- warning: polynomial.coeff_eq_esymm_roots_of_splits -> Polynomial.coeff_eq_esymm_roots_of_splits is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_2 : Field.{u1} F] {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))}, (Polynomial.Splits.{u1, u1} F F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) _inst_2 (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) p) -> (forall {k : Nat}, (LE.le.{0} Nat Nat.hasLe k (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p)) -> (Eq.{succ u1} F (Polynomial.coeff.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p k) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) (Polynomial.leadingCoeff.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p) (HPow.hPow.{u1, 0, u1} F Nat F (instHPow.{u1, 0} F Nat (Monoid.Pow.{u1} F (Ring.toMonoid.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) (Neg.neg.{u1} F (SubNegMonoid.toHasNeg.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))))) (OfNat.ofNat.{u1} F 1 (OfNat.mk.{u1} F 1 (One.one.{u1} F (AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p) k))) (Multiset.esymm.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)) (Polynomial.roots.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) (Field.isDomain.{u1} F _inst_2) p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) p) k)))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_2 : Field.{u1} F] {p : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)))}, (Polynomial.Splits.{u1, u1} F F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) _inst_2 (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))) p) -> (forall {k : Nat}, (LE.le.{0} Nat instLENat k (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p)) -> (Eq.{succ u1} F (Polynomial.coeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p k) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2)))))) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) (HPow.hPow.{u1, 0, u1} F Nat F (instHPow.{u1, 0} F Nat (Monoid.Pow.{u1} F (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))))))) (Neg.neg.{u1} F (Ring.toNeg.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))) (OfNat.ofNat.{u1} F 1 (One.toOfNat1.{u1} F (NonAssocRing.toOne.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_2))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) k))) (Multiset.esymm.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2)) (Polynomial.roots.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_2)) p) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_2))) p) k)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_eq_esymm_roots_of_splits Polynomial.coeff_eq_esymm_roots_of_splitsₓ'. -/
 /-- Vieta's formula for split polynomials over a field. -/
 theorem Polynomial.coeff_eq_esymm_roots_of_splits {F} [Field F] {p : F[X]}
     (hsplit : p.Splits (RingHom.id F)) {k : ℕ} (h : k ≤ p.natDegree) :
@@ -161,32 +215,44 @@ open Finset Polynomial Fintype
 
 variable (R σ : Type _) [CommSemiring R] [Fintype σ]
 
+/- warning: mv_polynomial.prod_C_add_X_eq_sum_esymm -> MvPolynomial.prod_C_add_X_eq_sum_esymm is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ], Eq.{succ (max u2 u1)} (Polynomial.{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.prod.{max u2 u1, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{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))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{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))) (Polynomial.{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))) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{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)))) (Polynomial.X.{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))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) -> (Polynomial.{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)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) (Finset.sum.{max u2 u1, 0} (Polynomial.{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))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Fintype.card.{u2} σ _inst_2) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (j : Nat) => HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{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))) (Polynomial.{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))) (Polynomial.{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))) (instHMul.{max u2 u1} (Polynomial.{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))) (Polynomial.mul'.{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)))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) -> (Polynomial.{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)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (Polynomial.C.{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.esymm.{u2, u1} σ R _inst_1 _inst_2 j)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Polynomial.{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))) Nat (Polynomial.{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))) (instHPow.{max u2 u1, 0} (Polynomial.{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))) Nat (Monoid.Pow.{max u2 u1} (Polynomial.{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))) (MonoidWithZero.toMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toMonoidWithZero.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))))) (Polynomial.X.{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))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Fintype.card.{u2} σ _inst_2) j))))
+but is expected to have type
+  forall (R : Type.{u2}) (σ : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Fintype.{u1} σ], Eq.{succ (max u2 u1)} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Finset.prod.{max u2 u1, u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Finset.univ.{u1} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u1 u2, max u1 u2, max u2 u1} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (MvPolynomial.X.{u2, u1} R σ _inst_1 i)) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (instHAdd.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.add'.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (Polynomial.X.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (RingHom.instRingHomClassRingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))))) (Polynomial.C.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (MvPolynomial.X.{u2, u1} R σ _inst_1 i)))) (Finset.sum.{max u2 u1, 0} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (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 instAddNat) (Fintype.card.{u1} σ _inst_2) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (j : Nat) => HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} 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.esymm.{u1, u2} σ R _inst_1 _inst_2 j)) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} 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.esymm.{u1, u2} σ R _inst_1 _inst_2 j)) (Polynomial.mul'.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} 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.{u1, u2} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u2} σ R _inst_1) => Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} 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.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} 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.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} 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 u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} 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.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} 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.{max u2 u1, max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))))) (Polynomial.C.{max u2 u1} (MvPolynomial.{u1, u2} 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.esymm.{u1, u2} σ R _inst_1 _inst_2 j)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) Nat (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (instHPow.{max u2 u1, 0} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) Nat (Monoid.Pow.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (MonoidWithZero.toMonoid.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toMonoidWithZero.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (Polynomial.X.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u1} σ _inst_2) j))))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymmₓ'. -/
 /-- A sum version of Vieta's formula for `mv_polynomial`: viewing `X i` as variables,
 the product of linear terms `λ + X i` is equal to a linear combination of
 the symmetric polynomials `esymm σ R j`. -/
-theorem MvPolynomial.prod_c_add_x_eq_sum_esymm :
+theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
     (∏ i : σ, X + C (MvPolynomial.X i)) =
       ∑ j in range (card σ + 1), C (MvPolynomial.esymm σ R j) * X ^ (card σ - j) :=
   by
   let s := finset.univ.val.map fun i : σ => MvPolynomial.X i
   rw [(_ : card σ = s.card)]
   · simp_rw [MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
-    convert Multiset.prod_x_add_c_eq_sum_esymm s
+    convert Multiset.prod_X_add_C_eq_sum_esymm s
     rwa [Multiset.map_map]
   · rw [Multiset.card_map]
     rfl
-#align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_c_add_x_eq_sum_esymm
-
-theorem MvPolynomial.prod_x_add_c_coeff (k : ℕ) (h : k ≤ card σ) :
+#align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymm
+
+/- warning: mv_polynomial.prod_X_add_C_coeff -> MvPolynomial.prod_X_add_C_coeff is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ] (k : Nat), (LE.le.{0} Nat Nat.hasLe k (Fintype.card.{u2} σ _inst_2)) -> (Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.coeff.{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.prod.{max u2 u1, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u2 u1} (Polynomial.{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))) (Polynomial.commSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{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))) (Polynomial.{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))) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{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))) (Polynomial.add'.{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)))) (Polynomial.X.{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))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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.{u2, u1} σ R _inst_1) -> (Polynomial.{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)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{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))) (Polynomial.semiring.{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))))) (Polynomial.C.{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.X.{u1, u2} R σ _inst_1 i)))) k) (MvPolynomial.esymm.{u2, u1} σ R _inst_1 _inst_2 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Fintype.card.{u2} σ _inst_2) k)))
+but is expected to have type
+  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Fintype.{u2} σ] (k : Nat), (LE.le.{0} Nat instLENat k (Fintype.card.{u2} σ _inst_2)) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.coeff.{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)) (Finset.prod.{max u1 u2, u2} (Polynomial.{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))) σ (CommSemiring.toCommMonoid.{max u1 u2} (Polynomial.{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))) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Finset.univ.{u2} σ _inst_2) (fun (i : σ) => HAdd.hAdd.{max u2 u1, max u2 u1, max u1 u2} (Polynomial.{max u2 u1} (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))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{max u2 u1} (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.X.{u1, u2} R σ _inst_1 i)) (Polynomial.{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))) (instHAdd.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.add'.{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)))) (Polynomial.X.{max u2 u1} (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))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R _inst_1) => Polynomial.{max u2 u1} (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))) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (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))) (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 u2 u1} (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))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Polynomial.{max u2 u1} (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))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (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))) (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 u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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, max u2 u1, max u2 u1} (RingHom.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Polynomial.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (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))) (Polynomial.semiring.{max u2 u1} (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)))))))) (Polynomial.C.{max u2 u1} (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.X.{u1, u2} R σ _inst_1 i)))) k) (MvPolynomial.esymm.{u2, u1} σ R _inst_1 _inst_2 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u2} σ _inst_2) k)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.prod_X_add_C_coeff MvPolynomial.prod_X_add_C_coeffₓ'. -/
+theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
     (∏ i : σ, X + C (MvPolynomial.X i)).coeff k = MvPolynomial.esymm σ R (card σ - k) :=
   by
   let s := finset.univ.val.map fun i => (MvPolynomial.X i : MvPolynomial σ R)
   rw [(_ : card σ = s.card)] at h⊢
   · rw [MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
-    convert Multiset.prod_x_add_c_coeff s h
+    convert Multiset.prod_X_add_C_coeff s h
     rwa [Multiset.map_map]
   repeat' rw [Multiset.card_map]; rfl
-#align mv_polynomial.prod_X_add_C_coeff MvPolynomial.prod_x_add_c_coeff
+#align mv_polynomial.prod_X_add_C_coeff MvPolynomial.prod_X_add_C_coeff
 
 end MvPolynomial
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/1f4705ccdfe1e557fc54a0ce081a05e33d2e6240

@@ -81,7 +81,7 @@ theorem prod_x_add_c_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h :
 theorem Finset.prod_x_add_c_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (∏ i in s, X + C (r i)).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i :=
   by
-  rw [Finset.prod, prod_X_add_C_coeff' _ r h, Finset.esymm_map_val]
+  rw [Finset.prod, prod_X_add_C_coeff' _ r h, Multiset.Finset.esymm_map_val]
   rfl
 #align finset.prod_X_add_C_coeff Finset.prod_x_add_c_coeff
 

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

@@ -165,10 +165,10 @@ variable (R σ : Type _) [CommSemiring R] [Fintype σ]
 the product of linear terms `λ + X i` is equal to a linear combination of
 the symmetric polynomials `esymm σ R j`. -/
 theorem MvPolynomial.prod_c_add_x_eq_sum_esymm :
-    (∏ i : σ, X + C (MvPolynomial.x i)) =
+    (∏ i : σ, X + C (MvPolynomial.X i)) =
       ∑ j in range (card σ + 1), C (MvPolynomial.esymm σ R j) * X ^ (card σ - j) :=
   by
-  let s := finset.univ.val.map fun i : σ => MvPolynomial.x i
+  let s := finset.univ.val.map fun i : σ => MvPolynomial.X i
   rw [(_ : card σ = s.card)]
   · simp_rw [MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
     convert Multiset.prod_x_add_c_eq_sum_esymm s
@@ -178,9 +178,9 @@ theorem MvPolynomial.prod_c_add_x_eq_sum_esymm :
 #align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_c_add_x_eq_sum_esymm
 
 theorem MvPolynomial.prod_x_add_c_coeff (k : ℕ) (h : k ≤ card σ) :
-    (∏ i : σ, X + C (MvPolynomial.x i)).coeff k = MvPolynomial.esymm σ R (card σ - k) :=
+    (∏ i : σ, X + C (MvPolynomial.X i)).coeff k = MvPolynomial.esymm σ R (card σ - k) :=
   by
-  let s := finset.univ.val.map fun i => (MvPolynomial.x i : MvPolynomial σ R)
+  let s := finset.univ.val.map fun i => (MvPolynomial.X i : MvPolynomial σ R)
   rw [(_ : card σ = s.card)] at h⊢
   · rw [MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
     convert Multiset.prod_x_add_c_coeff s h

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

@@ -42,8 +42,8 @@ variable {R : Type _} [CommSemiring R]
 `λ` runs through a multiset `s` is equal to a linear combination of the symmetric functions
 `esymm s` of the `λ`'s .-/
 theorem prod_x_add_c_eq_sum_esymm (s : Multiset R) :
-    (s.map fun r => x + c r).Prod =
-      ∑ j in Finset.range (s.card + 1), c (s.esymm j) * x ^ (s.card - j) :=
+    (s.map fun r => X + C r).Prod =
+      ∑ j in Finset.range (s.card + 1), C (s.esymm j) * X ^ (s.card - j) :=
   by
   classical
     rw [prod_map_add, antidiagonal_eq_map_powerset, map_map, ← bind_powerset_len, Function.comp,
@@ -58,7 +58,7 @@ theorem prod_x_add_c_eq_sum_esymm (s : Multiset R) :
 /-- Vieta's formula for the coefficients of the product of linear terms `X + λ` where `λ` runs
 through a multiset `s` : the `k`th coefficient is the symmetric function `esymm (card s - k) s`. -/
 theorem prod_x_add_c_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
-    (s.map fun r => x + c r).Prod.coeff k = s.esymm (s.card - k) :=
+    (s.map fun r => X + C r).Prod.coeff k = s.esymm (s.card - k) :=
   by
   convert polynomial.ext_iff.mp (prod_X_add_C_eq_sum_esymm s) k
   simp_rw [finset_sum_coeff, coeff_C_mul_X_pow]
@@ -74,12 +74,12 @@ theorem prod_x_add_c_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
 #align multiset.prod_X_add_C_coeff Multiset.prod_x_add_c_coeff
 
 theorem prod_x_add_c_coeff' {σ} (s : Multiset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
-    (s.map fun i => x + c (r i)).Prod.coeff k = (s.map r).esymm (s.card - k) := by
+    (s.map fun i => X + C (r i)).Prod.coeff k = (s.map r).esymm (s.card - k) := by
   rw [← map_map (fun r => X + C r) r, prod_X_add_C_coeff] <;> rwa [s.card_map r]
 #align multiset.prod_X_add_C_coeff' Multiset.prod_x_add_c_coeff'
 
 theorem Finset.prod_x_add_c_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
-    (∏ i in s, x + c (r i)).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i :=
+    (∏ i in s, X + C (r i)).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i :=
   by
   rw [Finset.prod, prod_X_add_C_coeff' _ r h, Finset.esymm_map_val]
   rfl
@@ -103,8 +103,8 @@ theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^
 #align multiset.esymm_neg Multiset.esymm_neg
 
 theorem prod_x_sub_c_eq_sum_esymm (s : Multiset R) :
-    (s.map fun t => x - c t).Prod =
-      ∑ j in Finset.range (s.card + 1), (-1) ^ j * (c (s.esymm j) * x ^ (s.card - j)) :=
+    (s.map fun t => X - C t).Prod =
+      ∑ j in Finset.range (s.card + 1), (-1) ^ j * (C (s.esymm j) * X ^ (s.card - j)) :=
   by
   conv_lhs =>
     congr
@@ -118,7 +118,7 @@ theorem prod_x_sub_c_eq_sum_esymm (s : Multiset R) :
 #align multiset.prod_X_sub_C_eq_sum_esymm Multiset.prod_x_sub_c_eq_sum_esymm
 
 theorem prod_x_sub_c_coeff (s : Multiset R) {k : ℕ} (h : k ≤ s.card) :
-    (s.map fun t => x - c t).Prod.coeff k = (-1) ^ (s.card - k) * s.esymm (s.card - k) :=
+    (s.map fun t => X - C t).Prod.coeff k = (-1) ^ (s.card - k) * s.esymm (s.card - k) :=
   by
   conv_lhs =>
     congr
@@ -165,8 +165,8 @@ variable (R σ : Type _) [CommSemiring R] [Fintype σ]
 the product of linear terms `λ + X i` is equal to a linear combination of
 the symmetric polynomials `esymm σ R j`. -/
 theorem MvPolynomial.prod_c_add_x_eq_sum_esymm :
-    (∏ i : σ, x + c (MvPolynomial.x i)) =
-      ∑ j in range (card σ + 1), c (MvPolynomial.esymm σ R j) * x ^ (card σ - j) :=
+    (∏ i : σ, X + C (MvPolynomial.x i)) =
+      ∑ j in range (card σ + 1), C (MvPolynomial.esymm σ R j) * X ^ (card σ - j) :=
   by
   let s := finset.univ.val.map fun i : σ => MvPolynomial.x i
   rw [(_ : card σ = s.card)]
@@ -178,7 +178,7 @@ theorem MvPolynomial.prod_c_add_x_eq_sum_esymm :
 #align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_c_add_x_eq_sum_esymm
 
 theorem MvPolynomial.prod_x_add_c_coeff (k : ℕ) (h : k ≤ card σ) :
-    (∏ i : σ, x + c (MvPolynomial.x i)).coeff k = MvPolynomial.esymm σ R (card σ - k) :=
+    (∏ i : σ, X + C (MvPolynomial.x i)).coeff k = MvPolynomial.esymm σ R (card σ - k) :=
   by
   let s := finset.univ.val.map fun i => (MvPolynomial.x i : MvPolynomial σ R)
   rw [(_ : card σ = s.card)] at h⊢

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

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

@@ -97,7 +97,8 @@ theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^
   intro x hx
   rw [(mem_powersetCard.mp hx).right.symm, ← prod_replicate, ← Multiset.map_const]
   nth_rw 3 [← map_id' x]
-  rw [← prod_map_mul, map_congr (Eq.refl _)];rfl
+  rw [← prod_map_mul, map_congr (Eq.refl _)]
+  · rfl
   exact fun z _ => neg_one_mul z
 #align multiset.esymm_neg Multiset.esymm_neg
 

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

@@ -37,7 +37,7 @@ variable {R : Type*} [CommSemiring R]
 
 /-- A sum version of **Vieta's formula** for `Multiset`: the product of the linear terms `X + λ`
 where `λ` runs through a multiset `s` is equal to a linear combination of the symmetric functions
-`esymm s` of the `λ`'s .-/
+`esymm s` of the `λ`'s . -/
 theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
     (s.map fun r => X + C r).prod =
       ∑ j in Finset.range (Multiset.card s + 1), (C (s.esymm j) * X ^ (Multiset.card s - j)) := by

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Hanting Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Hanting Zhang
 -/
-import Mathlib.Data.Polynomial.Splits
+import Mathlib.Algebra.Polynomial.Splits
 import Mathlib.RingTheory.MvPolynomial.Symmetric
 
 #align_import ring_theory.polynomial.vieta from "leanprover-community/mathlib"@"f694c7dead66f5d4c80f446c796a5aad14707f0e"

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -174,7 +174,7 @@ theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
     rw [Multiset.card_map, ← Finset.card_univ, Finset.card_def]
   simp_rw [this, MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
   convert Multiset.prod_X_add_C_eq_sum_esymm s
-  simp_rw [Multiset.map_map, Function.comp_apply]
+  simp_rw [s, Multiset.map_map, Function.comp_apply]
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymm
 
@@ -188,7 +188,7 @@ theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
   rw [MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
   convert Multiset.prod_X_add_C_coeff s h
   dsimp
-  simp_rw [Multiset.map_map, Function.comp_apply]
+  simp_rw [s, Multiset.map_map, Function.comp_apply]
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.prod_X_add_C_coeff MvPolynomial.prod_X_add_C_coeff
 

@@ -35,8 +35,8 @@ section Semiring
 
 variable {R : Type*} [CommSemiring R]
 
-/-- A sum version of Vieta's formula for `Multiset`: the product of the linear terms `X + λ` where
-`λ` runs through a multiset `s` is equal to a linear combination of the symmetric functions
+/-- A sum version of **Vieta's formula** for `Multiset`: the product of the linear terms `X + λ`
+where `λ` runs through a multiset `s` is equal to a linear combination of the symmetric functions
 `esymm s` of the `λ`'s .-/
 theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
     (s.map fun r => X + C r).prod =

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

@@ -171,7 +171,7 @@ theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
         (MvPolynomial.esymm σ R j) * Polynomial.X ^ (card σ - j) := by
   let s := Finset.univ.val.map fun i : σ => (MvPolynomial.X i : MvPolynomial σ R)
   have : Fintype.card σ = Multiset.card s := by
-    rw [Multiset.card_map, ←Finset.card_univ, Finset.card_def]
+    rw [Multiset.card_map, ← Finset.card_univ, Finset.card_def]
   simp_rw [this, MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
   convert Multiset.prod_X_add_C_eq_sum_esymm s
   simp_rw [Multiset.map_map, Function.comp_apply]
@@ -183,7 +183,7 @@ theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
     MvPolynomial.esymm σ R (card σ - k) := by
   let s := Finset.univ.val.map fun i => (MvPolynomial.X i : MvPolynomial σ R)
   have : Fintype.card σ = Multiset.card s := by
-    rw [Multiset.card_map, ←Finset.card_univ, Finset.card_def]
+    rw [Multiset.card_map, ← Finset.card_univ, Finset.card_def]
   rw [this] at h ⊢
   rw [MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
   convert Multiset.prod_X_add_C_coeff s h

@@ -68,7 +68,7 @@ theorem prod_X_add_C_coeff (s : Multiset R) {k : ℕ} (h : k ≤ Multiset.card s
       rw [hn, Nat.sub_sub_self (Nat.lt_succ_iff.mp (Finset.mem_range.mp hj1))] at hj2
       exact Ne.irrefl hj2
   · rw [Finset.mem_range]
-    exact Nat.sub_lt_succ (Multiset.card s) k
+    exact Nat.lt_succ_of_le (Nat.sub_le (Multiset.card s) k)
 set_option linter.uppercaseLean3 false in
 #align multiset.prod_X_add_C_coeff Multiset.prod_X_add_C_coeff
 

I don't understand why this was ever named powersetLen, there isn't even the notion of the length of a Finset/Multiset.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -47,7 +47,7 @@ theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
     intro _ _
     rw [esymm, ← sum_hom', ← sum_map_mul_right, map_congr (Eq.refl _)]
     intro s ht
-    rw [mem_powersetLen] at ht
+    rw [mem_powersetCard] at ht
     dsimp
     rw [prod_hom' s (Polynomial.C : R →+* R[X])]
     simp [ht, map_const, prod_replicate, prod_hom', map_id', card_sub]
@@ -79,7 +79,7 @@ set_option linter.uppercaseLean3 false in
 #align multiset.prod_X_add_C_coeff' Multiset.prod_X_add_C_coeff'
 
 theorem _root_.Finset.prod_X_add_C_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
-    (∏ i in s, (X + C (r i))).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i := by
+    (∏ i in s, (X + C (r i))).coeff k = ∑ t in s.powersetCard (s.card - k), ∏ i in t, r i := by
   rw [Finset.prod, prod_X_add_C_coeff' _ r h, Finset.esymm_map_val]
   rfl
 set_option linter.uppercaseLean3 false in
@@ -92,10 +92,10 @@ section Ring
 variable {R : Type*} [CommRing R]
 
 theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^ k * esymm s k := by
-  rw [esymm, esymm, ← Multiset.sum_map_mul_left, Multiset.powersetLen_map, Multiset.map_map,
+  rw [esymm, esymm, ← Multiset.sum_map_mul_left, Multiset.powersetCard_map, Multiset.map_map,
     map_congr (Eq.refl _)]
   intro x hx
-  rw [(mem_powersetLen.mp hx).right.symm, ← prod_replicate, ← Multiset.map_const]
+  rw [(mem_powersetCard.mp hx).right.symm, ← prod_replicate, ← Multiset.map_const]
   nth_rw 3 [← map_id' x]
   rw [← prod_map_mul, map_congr (Eq.refl _)];rfl
   exact fun z _ => neg_one_mul z

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

This has nice performance benefits.

@@ -33,7 +33,7 @@ open Polynomial
 
 section Semiring
 
-variable {R : Type _} [CommSemiring R]
+variable {R : Type*} [CommSemiring R]
 
 /-- A sum version of Vieta's formula for `Multiset`: the product of the linear terms `X + λ` where
 `λ` runs through a multiset `s` is equal to a linear combination of the symmetric functions
@@ -89,7 +89,7 @@ end Semiring
 
 section Ring
 
-variable {R : Type _} [CommRing R]
+variable {R : Type*} [CommRing R]
 
 theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^ k * esymm s k := by
   rw [esymm, esymm, ← Multiset.sum_map_mul_left, Multiset.powersetLen_map, Multiset.map_map,
@@ -160,7 +160,7 @@ section MvPolynomial
 
 open Finset Polynomial Fintype
 
-variable (R σ : Type _) [CommSemiring R] [Fintype σ]
+variable (R σ : Type*) [CommSemiring R] [Fintype σ]
 
 /-- A sum version of Vieta's formula for `MvPolynomial`: viewing `X i` as variables,
 the product of linear terms `λ + X i` is equal to a linear combination of

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Hanting Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Hanting Zhang
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.vieta
-! leanprover-community/mathlib commit f694c7dead66f5d4c80f446c796a5aad14707f0e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.Splits
 import Mathlib.RingTheory.MvPolynomial.Symmetric
 
+#align_import ring_theory.polynomial.vieta from "leanprover-community/mathlib"@"f694c7dead66f5d4c80f446c796a5aad14707f0e"
+
 /-!
 # Vieta's Formula
 

Mathport doesn't understand this, and apparently nor do many of the humans fixing the errors it creates.

If your #align statement complains the def doesn't exist, don't change the #align; work out why it doesn't exist instead.

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

@@ -83,7 +83,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem _root_.Finset.prod_X_add_C_coeff {σ} (s : Finset σ) (r : σ → R) {k : ℕ} (h : k ≤ s.card) :
     (∏ i in s, (X + C (r i))).coeff k = ∑ t in s.powersetLen (s.card - k), ∏ i in t, r i := by
-  rw [Finset.prod, prod_X_add_C_coeff' _ r h, Multiset.Finset.esymm_map_val]
+  rw [Finset.prod, prod_X_add_C_coeff' _ r h, Finset.esymm_map_val]
   rfl
 set_option linter.uppercaseLean3 false in
 #align finset.prod_X_add_C_coeff Finset.prod_X_add_C_coeff

@@ -38,7 +38,7 @@ section Semiring
 
 variable {R : Type _} [CommSemiring R]
 
-/-- A sum version of Vieta's formula for `multiset`: the product of the linear terms `X + λ` where
+/-- A sum version of Vieta's formula for `Multiset`: the product of the linear terms `X + λ` where
 `λ` runs through a multiset `s` is equal to a linear combination of the symmetric functions
 `esymm s` of the `λ`'s .-/
 theorem prod_X_add_C_eq_sum_esymm (s : Multiset R) :
@@ -106,8 +106,8 @@ theorem esymm_neg (s : Multiset R) (k : ℕ) : (map Neg.neg s).esymm k = (-1) ^
 
 theorem prod_X_sub_X_eq_sum_esymm (s : Multiset R) :
     (s.map fun t => X - C t).prod =
-      ∑ j in Finset.range (Multiset.card s + 1), (-1) ^ j * (C (s.esymm j) *
-      X ^ (Multiset.card s - j)) := by
+      ∑ j in Finset.range (Multiset.card s + 1),
+        (-1) ^ j * (C (s.esymm j) * X ^ (Multiset.card s - j)) := by
   conv_lhs =>
     congr
     congr
@@ -173,12 +173,11 @@ theorem MvPolynomial.prod_C_add_X_eq_sum_esymm :
       ∑ j in range (card σ + 1), Polynomial.C
         (MvPolynomial.esymm σ R j) * Polynomial.X ^ (card σ - j) := by
   let s := Finset.univ.val.map fun i : σ => (MvPolynomial.X i : MvPolynomial σ R)
-  rw [(_ : card σ = Multiset.card s)]
-  · simp_rw [MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
-    convert Multiset.prod_X_add_C_eq_sum_esymm s
-    rw [Multiset.map_map]; rfl
-  · rw [Multiset.card_map]
-    rfl
+  have : Fintype.card σ = Multiset.card s := by
+    rw [Multiset.card_map, ←Finset.card_univ, Finset.card_def]
+  simp_rw [this, MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
+  convert Multiset.prod_X_add_C_eq_sum_esymm s
+  simp_rw [Multiset.map_map, Function.comp_apply]
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.prod_C_add_X_eq_sum_esymm MvPolynomial.prod_C_add_X_eq_sum_esymm
 
@@ -186,12 +185,13 @@ theorem MvPolynomial.prod_X_add_C_coeff (k : ℕ) (h : k ≤ card σ) :
     (∏ i : σ, (Polynomial.X + Polynomial.C (MvPolynomial.X i)) : Polynomial _).coeff k =
     MvPolynomial.esymm σ R (card σ - k) := by
   let s := Finset.univ.val.map fun i => (MvPolynomial.X i : MvPolynomial σ R)
-  rw [(_ : card σ = Multiset.card s)] at h⊢
-  · rw [MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
-    convert Multiset.prod_X_add_C_coeff s h
-    dsimp
-    rw [Multiset.map_map]; rfl
-  repeat' rw [Multiset.card_map]; rfl
+  have : Fintype.card σ = Multiset.card s := by
+    rw [Multiset.card_map, ←Finset.card_univ, Finset.card_def]
+  rw [this] at h ⊢
+  rw [MvPolynomial.esymm_eq_multiset_esymm σ R, Finset.prod_eq_multiset_prod]
+  convert Multiset.prod_X_add_C_coeff s h
+  dsimp
+  simp_rw [Multiset.map_map, Function.comp_apply]
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.prod_X_add_C_coeff MvPolynomial.prod_X_add_C_coeff
 

Co-authored-by: Matthew Ballard <matt@mrb.email>